TSTP Solution File: SWV589-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV589-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:26:57 EDT 2022
% Result : Timeout 300.06s 300.47s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV589-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : bliksem %s
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % DateTime : Wed Jun 15 13:44:04 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.09/1.46 *** allocated 10000 integers for termspace/termends
% 1.09/1.46 *** allocated 10000 integers for clauses
% 1.09/1.46 *** allocated 10000 integers for justifications
% 1.09/1.46 *** allocated 15000 integers for termspace/termends
% 1.09/1.46 *** allocated 22500 integers for termspace/termends
% 1.09/1.46 Bliksem 1.12
% 1.09/1.46
% 1.09/1.46
% 1.09/1.46 Automatic Strategy Selection
% 1.09/1.46
% 1.09/1.46 Clauses:
% 1.09/1.46 [
% 1.09/1.46 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.09/1.46 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.09/1.46 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 1.09/1.46 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.09/1.46 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.09/1.46 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.09/1.46 , Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.09/1.46 , Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.09/1.46 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.09/1.46 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.09/1.46 X ), Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.09/1.46 , T ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.46 , 'tc_nat' ), 'tc_nat' ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.09/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.09/1.46 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.46 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.09/1.46 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.09/1.46 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.46 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.09/1.46 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.46 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.09/1.46 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.46 'tc_Int_Oint' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.46 'tc_Int_Oint' ), Z ), Y ), 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 X, Z, 'tc_Int_Oint' ) ) ],
% 1.09/1.46 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( 'c_Suc', Y )
% 1.09/1.46 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastAtMost'( X, Y, 'tc_nat'
% 1.09/1.46 ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.09/1.46 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.09/1.46 , hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.09/1.46 'c_Suc', T ), Z, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.09/1.46 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.09/1.46 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.09/1.46 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.46 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.09/1.46 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.09/1.46 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.09/1.46 , U ) ), hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z
% 1.09/1.46 ), T ), U ) ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ),
% 1.09/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.09/1.46 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.46 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.09/1.46 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.09/1.46 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.09/1.46 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.09/1.46 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.09/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.09/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.09/1.46 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.46 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.46 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.46 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.09/1.46 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.09/1.46 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.46 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.09/1.46 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.09/1.46 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.09/1.46 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.09/1.46 Z, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.09/1.46 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.09/1.46 , T, X ), X ), T, X ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.09/1.46 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.09/1.46 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.09/1.46 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.09/1.46 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.09/1.46 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.09/1.46 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.09/1.46 , V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.46 T, X, U, W, Y, V0 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.46 T, X, U, Y, W, V0 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.09/1.46 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.09/1.46 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.09/1.46 , V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.46 X, T, U, Y, W, V0 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.09/1.46 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.09/1.46 , V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.09/1.46 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.09/1.46 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.09/1.46 , V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.09/1.46 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.09/1.46 W, V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.09/1.46 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.09/1.46 W, V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.09/1.46 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.09/1.46 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.09/1.46 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.09/1.46 W, V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.09/1.46 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.09/1.46 , V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.09/1.46 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.09/1.46 W, V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.09/1.46 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.09/1.46 , V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.09/1.46 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.09/1.46 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.09/1.46 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.09/1.46 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.09/1.46 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.09/1.46 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.46 T, X, U, W, Z, V0 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.46 T, X, U, W, Y, V0 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.46 T, X, U, Z, W, V0 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.46 T, X, U, Y, W, V0 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.09/1.46 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.09/1.46 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.09/1.46 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.46 X, T, U, Z, W, V0 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.46 X, T, U, Y, W, V0 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.09/1.46 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.09/1.46 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.09/1.46 , V0, U, V1 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.09/1.46 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.09/1.46 , V0, U, V1 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.09/1.46 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.09/1.46 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.09/1.46 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.09/1.46 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.09/1.46 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.46 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.09/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.09/1.46 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.09/1.46 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 1.09/1.46 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.09/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.09/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.09/1.46 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.09/1.46 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.46 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.09/1.46 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.46 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.09/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.09/1.46 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.09/1.46 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.09/1.46 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.46 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.09/1.46 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.46 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.46 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.09/1.46 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.09/1.46 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.09/1.46 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.09/1.46 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.09/1.46 V0, V1 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.09/1.46 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.09/1.46 V0, V1 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.09/1.46 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.09/1.46 , V0, V1 ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.09/1.46 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.09/1.46 , V0, V1 ) ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.09/1.46 ), =( Z, Y ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.46 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.09/1.46 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.09/1.46 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.46 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.09/1.46 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.09/1.46 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.09/1.46 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.09/1.46 , hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.09/1.46 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.09/1.46 ) ), hAPP( Y, hAPP( 'c_Suc', T ) ) ) ), 'c_HOL_Oord__class_Oless'( hAPP(
% 1.09/1.46 'c_Suc', T ), Z, 'tc_nat' ) ],
% 1.09/1.46 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.09/1.46 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.09/1.46 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.46 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.09/1.46 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.46 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.09/1.46 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.46 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.09/1.46 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.09/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.46 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.09/1.46 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.09/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ), 'tc_nat' ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.09/1.46 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.09/1.46 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z,
% 1.09/1.46 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.09/1.46 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.09/1.46 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.09/1.46 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.09/1.46 , X ) ), hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.09/1.46 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.09/1.46 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.46 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.09/1.46 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), T,
% 1.09/1.46 'tc_nat' ), 'tc_nat', X ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T,
% 1.09/1.46 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.09/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.09/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.46 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.46 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.46 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.09/1.46 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.46 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.09/1.46 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.46 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.09/1.46 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.46 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.46 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.46 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.09/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.09/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.46 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.46 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.46 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.46 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.46 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.46 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.09/1.46 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.46 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.46 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.09/1.46 ), T ) ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.46 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.46 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.09/1.46 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.09/1.46 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.46 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.09/1.46 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.46 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.09/1.46 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.09/1.46 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.46 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 1.09/1.46 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ),
% 1.09/1.46 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X
% 1.09/1.46 ) ), U ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.09/1.46 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 1.09/1.46 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.09/1.46 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 1.09/1.46 ) ), Z ) ), T ), W ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.09/1.46 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.09/1.46 ) ), Z ) ), W ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.47 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.47 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.47 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.09/1.47 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.09/1.47 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.09/1.47 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.09/1.47 , X ) ), T ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.09/1.47 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( T, X ) ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.47 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.09/1.47 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.09/1.47 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ), T ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.09/1.47 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.47 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y,
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.47 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.09/1.47 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.09/1.47 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.09/1.47 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.09/1.47 'c_Int_OBit0'( X ) ), 'c_Int_OBit1'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.09/1.47 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.09/1.47 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.09/1.47 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X,
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.47 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.09/1.47 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.09/1.47 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.09/1.47 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.09/1.47 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.09/1.47 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.09/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.47 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Z ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.09/1.47 , T, X ) ) ), =( Z, T ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.47 , T, X ) ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.47 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.09/1.47 ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.09/1.47 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.47 , Y, X ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 1.09/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 1.09/1.47 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.47 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.09/1.47 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.09/1.47 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.09/1.47 , Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.09/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.09/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.09/1.47 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.47 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.47 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.47 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.47 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.09/1.47 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.47 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.09/1.47 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.09/1.47 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.47 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.47 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.09/1.47 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.09/1.47 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.09/1.47 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.47 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.47 ), Y ), T ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.09/1.47 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.09/1.47 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.09/1.47 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.09/1.47 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.47 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.09/1.47 T, X ) ), T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.47 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.09/1.47 ) ), Z ), T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.09/1.47 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ), W, X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.09/1.47 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.09/1.47 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.47 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.47 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.09/1.47 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.47 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.47 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.47 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.09/1.47 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.47 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.47 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.47 T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.09/1.47 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), T ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), Z ), T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.09/1.47 ), Z ), Y ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.09/1.47 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.09/1.47 , X ) ), T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.09/1.47 ), Z ), T, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), Z ), Z, X ), Y ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.09/1.47 ) ), 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.47 , X ), T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ), T, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.47 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.09/1.47 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.09/1.47 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.47 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.09/1.47 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.09/1.47 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.09/1.47 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.09/1.47 , 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.09/1.47 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.09/1.47 , 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.09/1.47 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.09/1.47 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.09/1.47 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.09/1.47 ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.47 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.09/1.47 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 , Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.47 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.09/1.47 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 , X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.47 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.47 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.47 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.47 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.09/1.47 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 , X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.09/1.47 ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.09/1.47 ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.09/1.47 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.09/1.47 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.09/1.47 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.09/1.47 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.09/1.47 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.09/1.47 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.09/1.47 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.09/1.47 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.09/1.47 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.09/1.47 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.47 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.09/1.47 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.09/1.47 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.09/1.47 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.09/1.47 [ 'c_Fun_Oinj__on'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.09/1.47 , 'tc_nat', 'tc_nat', 'tc_nat' ), Y, 'tc_nat', 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.47 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.09/1.47 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.09/1.47 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.09/1.47 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.09/1.47 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.09/1.47 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.47 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.09/1.47 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.09/1.47 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.47 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.47 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.47 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.09/1.47 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.47 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.47 ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.47 ), Z ) ), T ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.47 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.09/1.47 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.47 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.09/1.47 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ) ), Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.47 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.09/1.47 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.09/1.47 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.09/1.47 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.09/1.47 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.09/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.09/1.47 , X ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.09/1.47 X ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ), X ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.09/1.47 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.09/1.47 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.09/1.47 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.09/1.47 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.09/1.47 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.09/1.47 , X, Z, U, W, V0 ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), Z ) ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.09/1.47 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.09/1.47 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ), =( 'c_Finite__Set_Osetsum'( Y,
% 1.09/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 1.09/1.47 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.09/1.47 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.09/1.47 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.09/1.47 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.09/1.47 , Y ) ) ],
% 1.09/1.47 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.09/1.47 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.09/1.47 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.09/1.47 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.09/1.47 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.09/1.47 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.09/1.47 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls',
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.09/1.47 'c_Int_OPls' ), X ), X ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ),
% 1.09/1.47 'c_Int_OPls' ), X ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.09/1.47 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.09/1.47 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.09/1.47 'c_Int_OBit0'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit0'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.09/1.47 [ =( 'c_Int_OBit0'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_Int_Oint' ), X ), X ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.09/1.47 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.09/1.47 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.09/1.47 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.09/1.47 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.47 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.09/1.47 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.09/1.47 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.09/1.47 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' )
% 1.09/1.47 ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.09/1.47 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.47 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.09/1.47 ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.47 , Z ), Y ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.47 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.47 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.09/1.47 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.09/1.47 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.47 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 X, T, 'tc_nat' ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.09/1.47 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), X ), Y ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.09/1.47 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), X ), Y ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.09/1.47 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.09/1.47 'c_Suc', Y ) ) ) ],
% 1.09/1.47 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.09/1.47 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.09/1.47 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.09/1.47 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.09/1.47 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.09/1.47 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.09/1.47 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.09/1.47 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.47 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.47 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.47 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.47 ), X ), Z ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.09/1.47 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.09/1.47 , hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'(
% 1.09/1.47 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.09/1.47 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.09/1.47 ) ) ), 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', T ), Z, 'tc_nat' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.09/1.47 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ) ), Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ) ), Y ) ],
% 1.09/1.47 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.09/1.47 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'(
% 1.09/1.47 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.09/1.47 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.09/1.47 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.47 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.09/1.47 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.47 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.09/1.47 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.09/1.47 , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.09/1.47 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.09/1.47 'tc_Int_Oint' ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.09/1.47 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'(
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ), 'tc_nat', X
% 1.09/1.47 ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.09/1.47 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.09/1.47 , U, 'tc_nat' ), 'tc_nat', X ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_Int_OPls'
% 1.09/1.47 ) ), Y ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.09/1.47 ) ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ),
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.09/1.47 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), Y ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.47 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.09/1.47 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.09/1.47 ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.09/1.47 [ 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X, 'tc_nat', 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.09/1.47 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.09/1.47 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.09/1.47 ), Y ), Y ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.09/1.47 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.09/1.47 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.09/1.47 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.09/1.47 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.09/1.47 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.09/1.47 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.09/1.47 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.09/1.47 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.09/1.47 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( 'c_Finite__Set_Osetsum'( Y,
% 1.09/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), Z )
% 1.09/1.47 , 'tc_nat' ), 'tc_nat', X ), 'c_Finite__Set_Osetsum'( Y,
% 1.09/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.09/1.47 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.47 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.09/1.47 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.09/1.47 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.09/1.47 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.47 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.09/1.47 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.09/1.47 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.47 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.09/1.47 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.09/1.47 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.09/1.47 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.09/1.47 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.09/1.47 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.09/1.47 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.09/1.47 Y ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.09/1.47 , Z ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.09/1.47 , Z ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.47 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.09/1.47 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.47 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.09/1.47 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.09/1.47 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.09/1.47 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.47 ) ), Z ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.09/1.47 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.09/1.47 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ), 'tc_nat', X
% 1.09/1.47 ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.09/1.47 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.09/1.47 Z, U, 'tc_nat' ), 'tc_nat', X ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.47 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OPls', X ) ), Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.09/1.47 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.09/1.47 X ), Z, T, X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.09/1.47 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.09/1.47 X ), Z, T, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.47 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), Y ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.09/1.47 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), 'tc_nat', X
% 1.09/1.47 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'(
% 1.09/1.47 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T,
% 1.09/1.47 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', X, 'tc_nat' ),
% 1.09/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.09/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.47 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.09/1.47 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.09/1.47 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.09/1.47 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.09/1.47 , Y ) ],
% 1.09/1.47 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.47 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.47 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.09/1.47 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), Y ), Z ) ), T ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), Y ), Z ) ), T ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.09/1.47 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.09/1.47 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.09/1.47 , X ) ), T ) ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.09/1.47 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.09/1.47 ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.09/1.47 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.09/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat', X )
% 1.09/1.47 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( Y,
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( Y,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( Y,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'tc_nat' ), X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.09/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.09/1.47 , Y ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.09/1.47 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.09/1.47 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.47 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.09/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.09/1.47 Y ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ],
% 1.09/1.47 [ ~( =( 'c_Finite__Set_Osetsum'( 'v_f',
% 1.09/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_n' ), 'tc_nat' ), 'tc_nat', 't_a' ),
% 1.09/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ), 'c_Finite__Set_Osetsum'(
% 1.09/1.47 'c_COMBB'( 'v_f', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 't_a', 'tc_nat' ),
% 1.09/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat', 't_a' ) ),
% 1.09/1.47 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'v_f', 'c_COMBC'( 'c_COMBB'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.09/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.09/1.47 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.09/1.47 'tc_nat' ), 'tc_nat', 't_a', 'tc_nat' ),
% 1.09/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat', 't_a' ) ) ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.09/1.47 'class_OrderedGroup_Oab__semigroup__add'( X ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.09/1.47 'class_OrderedGroup_Omonoid__add'( X ) ],
% 1.09/1.47 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.09/1.47 'class_Orderings_Opreorder'( Y ) ) ],
% 1.09/1.47 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.09/1.47 'class_Orderings_Oorder'( Y ) ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.09/1.47 ],
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.09/1.47 ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.09/1.47 ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.09/1.47 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.09/1.47 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.09/1.47 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.09/1.47 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.09/1.47 ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.41/1.79 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.41/1.79 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.41/1.79 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.41/1.79 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.41/1.79 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.41/1.79 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.41/1.79 ,
% 1.41/1.79 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.41/1.79 ,
% 1.41/1.79 [ 'c_fequal'( X, X, Y ) ],
% 1.41/1.79 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.41/1.79 ] .
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 percentage equality = 0.363813, percentage horn = 0.889819
% 1.41/1.79 This is a problem with some equality
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 Options Used:
% 1.41/1.79
% 1.41/1.79 useres = 1
% 1.41/1.79 useparamod = 1
% 1.41/1.79 useeqrefl = 1
% 1.41/1.79 useeqfact = 1
% 1.41/1.79 usefactor = 1
% 1.41/1.79 usesimpsplitting = 0
% 1.41/1.79 usesimpdemod = 5
% 1.41/1.79 usesimpres = 3
% 1.41/1.79
% 1.41/1.79 resimpinuse = 1000
% 1.41/1.79 resimpclauses = 20000
% 1.41/1.79 substype = eqrewr
% 1.41/1.79 backwardsubs = 1
% 1.41/1.79 selectoldest = 5
% 1.41/1.79
% 1.41/1.79 litorderings [0] = split
% 1.41/1.79 litorderings [1] = extend the termordering, first sorting on arguments
% 1.41/1.79
% 1.41/1.79 termordering = kbo
% 1.41/1.79
% 1.41/1.79 litapriori = 0
% 1.41/1.79 termapriori = 1
% 1.41/1.79 litaposteriori = 0
% 1.41/1.79 termaposteriori = 0
% 1.41/1.79 demodaposteriori = 0
% 1.41/1.79 ordereqreflfact = 0
% 1.41/1.79
% 1.41/1.79 litselect = negord
% 1.41/1.79
% 1.41/1.79 maxweight = 15
% 1.41/1.79 maxdepth = 30000
% 1.41/1.79 maxlength = 115
% 1.41/1.79 maxnrvars = 195
% 1.41/1.79 excuselevel = 1
% 1.41/1.79 increasemaxweight = 1
% 1.41/1.79
% 1.41/1.79 maxselected = 10000000
% 1.41/1.79 maxnrclauses = 10000000
% 1.41/1.79
% 1.41/1.79 showgenerated = 0
% 1.41/1.79 showkept = 0
% 1.41/1.79 showselected = 0
% 1.41/1.79 showdeleted = 0
% 1.41/1.79 showresimp = 1
% 1.41/1.79 showstatus = 2000
% 1.41/1.79
% 1.41/1.79 prologoutput = 1
% 1.41/1.79 nrgoals = 5000000
% 1.41/1.79 totalproof = 1
% 1.41/1.79
% 1.41/1.79 Symbols occurring in the translation:
% 1.41/1.79
% 1.41/1.79 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.41/1.79 . [1, 2] (w:1, o:135, a:1, s:1, b:0),
% 1.41/1.79 ! [4, 1] (w:0, o:78, a:1, s:1, b:0),
% 1.41/1.79 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.41/1.79 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.41/1.79 'c_Suc' [41, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.41/1.79 hAPP [42, 2] (w:1, o:160, a:1, s:1, b:0),
% 1.41/1.79 'tc_nat' [43, 0] (w:1, o:18, a:1, s:1, b:0),
% 1.41/1.79 'c_HOL_Oord__class_Oless' [44, 3] (w:1, o:164, a:1, s:1, b:0),
% 1.41/1.79 'c_HOL_Ozero__class_Ozero' [45, 1] (w:1, o:83, a:1, s:1, b:0),
% 1.41/1.79 'c_Divides_Odiv__class_Omod' [46, 3] (w:1, o:165, a:1, s:1, b:0),
% 1.41/1.79 'class_Orderings_Olinorder' [48, 1] (w:1, o:84, a:1, s:1, b:0),
% 1.41/1.79 'class_Orderings_Oorder' [50, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.41/1.79 'tc_Int_Oint' [51, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.41/1.79 'class_Orderings_Opreorder' [52, 1] (w:1, o:86, a:1, s:1, b:0),
% 1.41/1.79 'class_Divides_Oring__div' [53, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.41/1.79 'c_HOL_Ominus__class_Ominus' [59, 3] (w:1, o:166, a:1, s:1, b:0),
% 1.41/1.79 'class_Ring__and__Field_Oordered__semidom' [60, 1] (w:1, o:91, a:1
% 1.41/1.79 , s:1, b:0),
% 1.41/1.79 'c_HOL_Oone__class_Oone' [61, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.41/1.79 'c_Power_Opower__class_Opower' [62, 1] (w:1, o:93, a:1, s:1, b:0),
% 1.41/1.79 'class_OrderedGroup_Opordered__ab__group__add' [63, 1] (w:1, o:94, a:
% 1.41/1.79 1, s:1, b:0),
% 1.41/1.79 'class_Ring__and__Field_Oordered__idom' [64, 1] (w:1, o:95, a:1, s:1
% 1.41/1.79 , b:0),
% 1.41/1.79 'c_Int_Onumber__class_Onumber__of' [66, 2] (w:1, o:161, a:1, s:1, b:0
% 1.41/1.79 ),
% 1.41/1.79 'c_Parity_Oeven__odd__class_Oeven' [67, 2] (w:1, o:162, a:1, s:1, b:0
% 1.41/1.79 ),
% 1.41/1.79 'class_Ring__and__Field_Ocomm__semiring__1' [68, 1] (w:1, o:96, a:1
% 1.41/1.79 , s:1, b:0),
% 1.41/1.79 'c_HOL_Otimes__class_Otimes' [69, 1] (w:1, o:97, a:1, s:1, b:0),
% 1.41/1.79 'c_Divides_Odiv__class_Odiv' [71, 3] (w:1, o:167, a:1, s:1, b:0),
% 1.41/1.79 'c_HOL_Oplus__class_Oplus' [74, 1] (w:1, o:98, a:1, s:1, b:0),
% 1.41/1.79 'c_SetInterval_Oord__class_OatLeastLessThan' [80, 3] (w:1, o:168, a:1
% 1.41/1.79 , s:1, b:0),
% 1.41/1.79 'c_SetInterval_Oord__class_OatLeastAtMost' [81, 3] (w:1, o:169, a:1
% 1.41/1.79 , s:1, b:0),
% 1.41/1.79 'class_OrderedGroup_Ocomm__monoid__add' [82, 1] (w:1, o:99, a:1, s:1
% 1.41/1.79 , b:0),
% 1.41/1.79 'c_Finite__Set_Osetsum' [84, 4] (w:1, o:172, a:1, s:1, b:0),
% 1.41/1.79 'class_Divides_Osemiring__div' [87, 1] (w:1, o:100, a:1, s:1, b:0),
% 1.41/1.79 'c_Power_Opower_Opower' [90, 3] (w:1, o:170, a:1, s:1, b:0),
% 1.41/1.79 'c_Groebner__Basis_Ogb__semiring' [97, 6] (w:1, o:176, a:1, s:1, b:0)
% 1.41/1.79 ,
% 1.41/1.79 'class_Int_Onumber__ring' [105, 1] (w:1, o:101, a:1, s:1, b:0),
% 8.68/9.07 hBOOL [109, 1] (w:1, o:102, a:1, s:1, b:0),
% 8.68/9.07 'c_Fun_Oinj__on' [110, 4] (w:1, o:173, a:1, s:1, b:0),
% 8.68/9.07 'c_Int_OPls' [111, 0] (w:1, o:58, a:1, s:1, b:0),
% 8.68/9.07 'class_Ring__and__Field_Oordered__ring__strict' [113, 1] (w:1, o:90
% 8.68/9.07 , a:1, s:1, b:0),
% 8.68/9.07 'class_Ring__and__Field_Oordered__semiring__strict' [114, 1] (w:1, o:
% 8.68/9.07 103, a:1, s:1, b:0),
% 8.68/9.07 'class_Ring__and__Field_Oordered__comm__semiring__strict' [115, 1]
% 8.68/9.07 (w:1, o:104, a:1, s:1, b:0),
% 8.68/9.07 'class_OrderedGroup_Opordered__comm__monoid__add' [116, 1] (w:1, o:
% 8.68/9.07 105, a:1, s:1, b:0),
% 8.68/9.07 'class_OrderedGroup_Olordered__ab__group__add' [117, 1] (w:1, o:106
% 8.68/9.07 , a:1, s:1, b:0),
% 8.68/9.07 'class_RealVector_Oreal__normed__algebra' [118, 1] (w:1, o:107, a:1
% 8.68/9.07 , s:1, b:0),
% 8.68/9.07 'class_Ring__and__Field_Oring' [119, 1] (w:1, o:108, a:1, s:1, b:0),
% 8.68/9.07
% 8.68/9.07 'class_Ring__and__Field_Ozero__neq__one' [121, 1] (w:1, o:109, a:1
% 8.68/9.07 , s:1, b:0),
% 8.68/9.07 'class_Ring__and__Field_Ono__zero__divisors' [122, 1] (w:1, o:89, a:1
% 8.68/9.07 , s:1, b:0),
% 8.68/9.07 'class_Ring__and__Field_Omult__zero' [123, 1] (w:1, o:88, a:1, s:1
% 8.68/9.07 , b:0),
% 8.68/9.07 'class_Power_Opower' [124, 1] (w:1, o:122, a:1, s:1, b:0),
% 8.68/9.07 'class_Ring__and__Field_Osemiring__0' [125, 1] (w:1, o:125, a:1, s:1
% 8.68/9.07 , b:0),
% 8.68/9.07 'class_Int_Onumber' [126, 1] (w:1, o:126, a:1, s:1, b:0),
% 8.68/9.07 'c_Int_OBit1' [127, 1] (w:1, o:128, a:1, s:1, b:0),
% 8.68/9.07 'class_OrderedGroup_Omonoid__mult' [128, 1] (w:1, o:110, a:1, s:1, b:
% 8.68/9.07 0),
% 8.68/9.07 'c_Int_OBit0' [130, 1] (w:1, o:127, a:1, s:1, b:0),
% 8.68/9.07 'class_OrderedGroup_Oab__group__add' [136, 1] (w:1, o:111, a:1, s:1
% 8.68/9.07 , b:0),
% 8.68/9.07 'class_Ring__and__Field_Oring__1__no__zero__divisors' [138, 1] (w:1
% 8.68/9.07 , o:123, a:1, s:1, b:0),
% 8.68/9.07 'class_OrderedGroup_Ogroup__add' [139, 1] (w:1, o:112, a:1, s:1, b:0)
% 8.68/9.07 ,
% 8.68/9.07 'class_Ring__and__Field_Oidom' [140, 1] (w:1, o:129, a:1, s:1, b:0),
% 8.68/9.07
% 8.68/9.07 'class_OrderedGroup_Ocomm__monoid__mult' [141, 1] (w:1, o:113, a:1
% 8.68/9.07 , s:1, b:0),
% 8.68/9.07 'class_Ring__and__Field_Opordered__ring' [143, 1] (w:1, o:130, a:1
% 8.68/9.07 , s:1, b:0),
% 8.68/9.07 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [144, 1]
% 8.68/9.07 (w:1, o:114, a:1, s:1, b:0),
% 8.68/9.07 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [145, 1]
% 8.68/9.07 (w:1, o:115, a:1, s:1, b:0),
% 8.68/9.07 'c_COMBC' [147, 5] (w:1, o:175, a:1, s:1, b:0),
% 8.68/9.07 'c_COMBB' [148, 5] (w:1, o:174, a:1, s:1, b:0),
% 8.68/9.07 'class_Ring__and__Field_Osemiring__1' [149, 1] (w:1, o:131, a:1, s:1
% 8.68/9.07 , b:0),
% 8.68/9.07 'class_Ring__and__Field_Ocomm__semiring' [151, 1] (w:1, o:132, a:1
% 8.68/9.07 , s:1, b:0),
% 8.68/9.07 'class_OrderedGroup_Ocancel__ab__semigroup__add' [152, 1] (w:1, o:116
% 8.68/9.07 , a:1, s:1, b:0),
% 8.68/9.07 'class_OrderedGroup_Ocancel__semigroup__add' [153, 1] (w:1, o:117, a:
% 8.68/9.07 1, s:1, b:0),
% 8.68/9.07 'class_Ring__and__Field_Oring__no__zero__divisors' [156, 1] (w:1, o:
% 8.68/9.07 124, a:1, s:1, b:0),
% 8.68/9.07 'class_Ring__and__Field_Osemiring' [157, 1] (w:1, o:133, a:1, s:1, b:
% 8.68/9.07 0),
% 8.68/9.07 'class_OrderedGroup_Oab__semigroup__mult' [158, 1] (w:1, o:118, a:1
% 8.68/9.07 , s:1, b:0),
% 8.68/9.07 'tc_fun' [159, 2] (w:1, o:163, a:1, s:1, b:0),
% 8.68/9.07 'class_OrderedGroup_Oab__semigroup__idem__mult' [160, 1] (w:1, o:119
% 8.68/9.07 , a:1, s:1, b:0),
% 8.68/9.07 'class_OrderedGroup_Oab__semigroup__add' [161, 1] (w:1, o:120, a:1
% 8.68/9.07 , s:1, b:0),
% 8.68/9.07 'class_Int_Oring__char__0' [165, 1] (w:1, o:134, a:1, s:1, b:0),
% 8.68/9.07 'class_OrderedGroup_Omonoid__add' [166, 1] (w:1, o:121, a:1, s:1, b:0
% 8.68/9.07 ),
% 8.68/9.07 't_a' [167, 0] (w:1, o:69, a:1, s:1, b:0),
% 8.68/9.07 'v_f' [168, 0] (w:1, o:70, a:1, s:1, b:0),
% 8.68/9.07 'v_n' [169, 0] (w:1, o:71, a:1, s:1, b:0),
% 8.68/9.07 'tc_bool' [173, 0] (w:1, o:75, a:1, s:1, b:0),
% 8.68/9.07 'c_fequal' [174, 3] (w:1, o:171, a:1, s:1, b:0).
% 8.68/9.07
% 8.68/9.07
% 8.68/9.07 Starting Search:
% 8.68/9.07
% 8.68/9.07 Resimplifying inuse:
% 8.68/9.07 Done
% 8.68/9.07
% 8.68/9.07
% 8.68/9.07 Intermediate Status:
% 8.68/9.07 Generated: 5496
% 8.68/9.07 Kept: 2002
% 8.68/9.07 Inuse: 175
% 8.68/9.07 Deleted: 7
% 8.68/9.07 Deletedinuse: 0
% 8.68/9.07
% 8.68/9.07 Resimplifying inuse:
% 8.68/9.07 Done
% 8.68/9.07
% 8.68/9.07 Resimplifying inuse:
% 8.68/9.07 Done
% 8.68/9.07
% 8.68/9.07
% 8.68/9.07 Intermediate Status:
% 8.68/9.07 Generated: 10546
% 8.68/9.07 Kept: 4046
% 8.68/9.07 Inuse: 248
% 8.68/9.07 Deleted: 9
% 8.68/9.07 Deletedinuse: 1
% 8.68/9.07
% 8.68/9.07 Resimplifying inuse:
% 8.68/9.07 Done
% 8.68/9.07
% 8.68/9.07 Resimplifying inuse:
% 8.68/9.07 Done
% 8.68/9.07
% 8.68/9.07
% 8.68/9.07 Intermediate Status:
% 31.80/32.18 Generated: 17640
% 31.80/32.18 Kept: 6410
% 31.80/32.18 Inuse: 308
% 31.80/32.18 Deleted: 9
% 31.80/32.18 Deletedinuse: 1
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 23241
% 31.80/32.18 Kept: 8412
% 31.80/32.18 Inuse: 413
% 31.80/32.18 Deleted: 15
% 31.80/32.18 Deletedinuse: 1
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 33713
% 31.80/32.18 Kept: 10793
% 31.80/32.18 Inuse: 430
% 31.80/32.18 Deleted: 18
% 31.80/32.18 Deletedinuse: 2
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 39867
% 31.80/32.18 Kept: 12793
% 31.80/32.18 Inuse: 476
% 31.80/32.18 Deleted: 22
% 31.80/32.18 Deletedinuse: 2
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 47085
% 31.80/32.18 Kept: 14976
% 31.80/32.18 Inuse: 506
% 31.80/32.18 Deleted: 25
% 31.80/32.18 Deletedinuse: 5
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 53329
% 31.80/32.18 Kept: 17002
% 31.80/32.18 Inuse: 541
% 31.80/32.18 Deleted: 25
% 31.80/32.18 Deletedinuse: 5
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 60520
% 31.80/32.18 Kept: 19092
% 31.80/32.18 Inuse: 576
% 31.80/32.18 Deleted: 25
% 31.80/32.18 Deletedinuse: 5
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying clauses:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 68449
% 31.80/32.18 Kept: 21099
% 31.80/32.18 Inuse: 604
% 31.80/32.18 Deleted: 1019
% 31.80/32.18 Deletedinuse: 5
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 76259
% 31.80/32.18 Kept: 23161
% 31.80/32.18 Inuse: 636
% 31.80/32.18 Deleted: 1019
% 31.80/32.18 Deletedinuse: 5
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 84097
% 31.80/32.18 Kept: 25228
% 31.80/32.18 Inuse: 676
% 31.80/32.18 Deleted: 1020
% 31.80/32.18 Deletedinuse: 6
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 93563
% 31.80/32.18 Kept: 27669
% 31.80/32.18 Inuse: 716
% 31.80/32.18 Deleted: 1020
% 31.80/32.18 Deletedinuse: 6
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 103809
% 31.80/32.18 Kept: 30285
% 31.80/32.18 Inuse: 756
% 31.80/32.18 Deleted: 1020
% 31.80/32.18 Deletedinuse: 6
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 112368
% 31.80/32.18 Kept: 32391
% 31.80/32.18 Inuse: 771
% 31.80/32.18 Deleted: 1020
% 31.80/32.18 Deletedinuse: 6
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 119139
% 31.80/32.18 Kept: 34547
% 31.80/32.18 Inuse: 806
% 31.80/32.18 Deleted: 1020
% 31.80/32.18 Deletedinuse: 6
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 125137
% 31.80/32.18 Kept: 36549
% 31.80/32.18 Inuse: 838
% 31.80/32.18 Deleted: 1020
% 31.80/32.18 Deletedinuse: 6
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 132035
% 31.80/32.18 Kept: 38569
% 31.80/32.18 Inuse: 879
% 31.80/32.18 Deleted: 1020
% 31.80/32.18 Deletedinuse: 6
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying clauses:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 139211
% 31.80/32.18 Kept: 40571
% 31.80/32.18 Inuse: 914
% 31.80/32.18 Deleted: 1392
% 31.80/32.18 Deletedinuse: 6
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 152410
% 31.80/32.18 Kept: 43405
% 31.80/32.18 Inuse: 951
% 31.80/32.18 Deleted: 1392
% 31.80/32.18 Deletedinuse: 6
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 163035
% 31.80/32.18 Kept: 45764
% 31.80/32.18 Inuse: 1001
% 31.80/32.18 Deleted: 1392
% 31.80/32.18 Deletedinuse: 6
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 179465
% 31.80/32.18 Kept: 50909
% 31.80/32.18 Inuse: 1046
% 31.80/32.18 Deleted: 1393
% 31.80/32.18 Deletedinuse: 7
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 187634
% 31.80/32.18 Kept: 54350
% 31.80/32.18 Inuse: 1051
% 31.80/32.18 Deleted: 1393
% 31.80/32.18 Deletedinuse: 7
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 196484
% 31.80/32.18 Kept: 56464
% 31.80/32.18 Inuse: 1060
% 31.80/32.18 Deleted: 1394
% 31.80/32.18 Deletedinuse: 7
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 205154
% 31.80/32.18 Kept: 58729
% 31.80/32.18 Inuse: 1095
% 31.80/32.18 Deleted: 1394
% 31.80/32.18 Deletedinuse: 7
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 212812
% 31.80/32.18 Kept: 60827
% 31.80/32.18 Inuse: 1113
% 31.80/32.18 Deleted: 1394
% 31.80/32.18 Deletedinuse: 7
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying clauses:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18 Resimplifying inuse:
% 31.80/32.18 Done
% 31.80/32.18
% 31.80/32.18
% 31.80/32.18 Intermediate Status:
% 31.80/32.18 Generated: 219966
% 31.80/32.18 Kept: 62840
% 31.80/32.18 Inuse: 1124
% 112.19/112.57 Deleted: 1733
% 112.19/112.57 Deletedinuse: 7
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 225914
% 112.19/112.57 Kept: 65101
% 112.19/112.57 Inuse: 1135
% 112.19/112.57 Deleted: 1733
% 112.19/112.57 Deletedinuse: 7
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 237476
% 112.19/112.57 Kept: 68434
% 112.19/112.57 Inuse: 1136
% 112.19/112.57 Deleted: 1733
% 112.19/112.57 Deletedinuse: 7
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 242979
% 112.19/112.57 Kept: 70507
% 112.19/112.57 Inuse: 1155
% 112.19/112.57 Deleted: 1733
% 112.19/112.57 Deletedinuse: 7
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 249978
% 112.19/112.57 Kept: 72769
% 112.19/112.57 Inuse: 1180
% 112.19/112.57 Deleted: 1733
% 112.19/112.57 Deletedinuse: 7
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 258313
% 112.19/112.57 Kept: 74826
% 112.19/112.57 Inuse: 1205
% 112.19/112.57 Deleted: 1733
% 112.19/112.57 Deletedinuse: 7
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 266150
% 112.19/112.57 Kept: 77077
% 112.19/112.57 Inuse: 1240
% 112.19/112.57 Deleted: 1733
% 112.19/112.57 Deletedinuse: 7
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 276267
% 112.19/112.57 Kept: 79336
% 112.19/112.57 Inuse: 1275
% 112.19/112.57 Deleted: 1734
% 112.19/112.57 Deletedinuse: 8
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying clauses:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 292423
% 112.19/112.57 Kept: 81359
% 112.19/112.57 Inuse: 1299
% 112.19/112.57 Deleted: 2144
% 112.19/112.57 Deletedinuse: 10
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 300444
% 112.19/112.57 Kept: 83362
% 112.19/112.57 Inuse: 1330
% 112.19/112.57 Deleted: 2144
% 112.19/112.57 Deletedinuse: 10
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 308622
% 112.19/112.57 Kept: 85414
% 112.19/112.57 Inuse: 1343
% 112.19/112.57 Deleted: 2144
% 112.19/112.57 Deletedinuse: 10
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 316470
% 112.19/112.57 Kept: 87548
% 112.19/112.57 Inuse: 1353
% 112.19/112.57 Deleted: 2144
% 112.19/112.57 Deletedinuse: 10
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 329614
% 112.19/112.57 Kept: 90753
% 112.19/112.57 Inuse: 1363
% 112.19/112.57 Deleted: 2144
% 112.19/112.57 Deletedinuse: 10
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 345175
% 112.19/112.57 Kept: 94265
% 112.19/112.57 Inuse: 1373
% 112.19/112.57 Deleted: 2144
% 112.19/112.57 Deletedinuse: 10
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 353036
% 112.19/112.57 Kept: 96276
% 112.19/112.57 Inuse: 1404
% 112.19/112.57 Deleted: 2145
% 112.19/112.57 Deletedinuse: 10
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 369405
% 112.19/112.57 Kept: 101935
% 112.19/112.57 Inuse: 1451
% 112.19/112.57 Deleted: 2148
% 112.19/112.57 Deletedinuse: 12
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying clauses:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 384528
% 112.19/112.57 Kept: 105471
% 112.19/112.57 Inuse: 1452
% 112.19/112.57 Deleted: 2856
% 112.19/112.57 Deletedinuse: 12
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 392073
% 112.19/112.57 Kept: 107503
% 112.19/112.57 Inuse: 1459
% 112.19/112.57 Deleted: 2856
% 112.19/112.57 Deletedinuse: 12
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 399691
% 112.19/112.57 Kept: 109651
% 112.19/112.57 Inuse: 1486
% 112.19/112.57 Deleted: 2879
% 112.19/112.57 Deletedinuse: 35
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 412588
% 112.19/112.57 Kept: 111867
% 112.19/112.57 Inuse: 1526
% 112.19/112.57 Deleted: 2879
% 112.19/112.57 Deletedinuse: 35
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 420821
% 112.19/112.57 Kept: 113904
% 112.19/112.57 Inuse: 1550
% 112.19/112.57 Deleted: 2879
% 112.19/112.57 Deletedinuse: 35
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 427510
% 112.19/112.57 Kept: 115912
% 112.19/112.57 Inuse: 1569
% 112.19/112.57 Deleted: 2881
% 112.19/112.57 Deletedinuse: 36
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 436663
% 112.19/112.57 Kept: 117930
% 112.19/112.57 Inuse: 1592
% 112.19/112.57 Deleted: 2885
% 112.19/112.57 Deletedinuse: 36
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 444995
% 112.19/112.57 Kept: 120352
% 112.19/112.57 Inuse: 1614
% 112.19/112.57 Deleted: 2895
% 112.19/112.57 Deletedinuse: 44
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57 Resimplifying clauses:
% 112.19/112.57 Done
% 112.19/112.57
% 112.19/112.57
% 112.19/112.57 Intermediate Status:
% 112.19/112.57 Generated: 453258
% 112.19/112.57 Kept: 122362
% 112.19/112.57 Inuse: 1638
% 112.19/112.57 Deleted: 5553
% 112.19/112.57 Deletedinuse: 44
% 112.19/112.57
% 112.19/112.57 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.35 Generated: 471517
% 276.94/277.35 Kept: 125577
% 276.94/277.35 Inuse: 1649
% 276.94/277.35 Deleted: 5553
% 276.94/277.35 Deletedinuse: 44
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.35 Generated: 478542
% 276.94/277.35 Kept: 127692
% 276.94/277.35 Inuse: 1669
% 276.94/277.35 Deleted: 5553
% 276.94/277.35 Deletedinuse: 44
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.35 Generated: 485650
% 276.94/277.35 Kept: 129697
% 276.94/277.35 Inuse: 1695
% 276.94/277.35 Deleted: 5553
% 276.94/277.35 Deletedinuse: 44
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.35 Generated: 493652
% 276.94/277.35 Kept: 131976
% 276.94/277.35 Inuse: 1724
% 276.94/277.35 Deleted: 5553
% 276.94/277.35 Deletedinuse: 44
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.35 Generated: 499829
% 276.94/277.35 Kept: 134106
% 276.94/277.35 Inuse: 1739
% 276.94/277.35 Deleted: 5553
% 276.94/277.35 Deletedinuse: 44
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.35 Generated: 510399
% 276.94/277.35 Kept: 136172
% 276.94/277.35 Inuse: 1774
% 276.94/277.35 Deleted: 5553
% 276.94/277.35 Deletedinuse: 44
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.35 Generated: 517488
% 276.94/277.35 Kept: 138532
% 276.94/277.35 Inuse: 1794
% 276.94/277.35 Deleted: 5553
% 276.94/277.35 Deletedinuse: 44
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.35 Generated: 525965
% 276.94/277.35 Kept: 140557
% 276.94/277.35 Inuse: 1820
% 276.94/277.35 Deleted: 5554
% 276.94/277.35 Deletedinuse: 44
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35 Resimplifying clauses:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.35 Generated: 558872
% 276.94/277.35 Kept: 144316
% 276.94/277.35 Inuse: 1828
% 276.94/277.35 Deleted: 6208
% 276.94/277.35 Deletedinuse: 44
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.35 Generated: 576720
% 276.94/277.35 Kept: 146324
% 276.94/277.35 Inuse: 1836
% 276.94/277.35 Deleted: 6208
% 276.94/277.35 Deletedinuse: 44
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.35 Generated: 609609
% 276.94/277.35 Kept: 150016
% 276.94/277.35 Inuse: 1843
% 276.94/277.35 Deleted: 6208
% 276.94/277.35 Deletedinuse: 44
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35 Resimplifying inuse:
% 276.94/277.35 Done
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.35 Generated: 627314
% 276.94/277.35 Kept: 152043
% 276.94/277.35 Inuse: 1851
% 276.94/277.35 Deleted: 6208
% 276.94/277.35 Deletedinuse: 44
% 276.94/277.35
% 276.94/277.35
% 276.94/277.35 Intermediate Status:
% 276.94/277.36 Generated: 640158
% 276.94/277.36 Kept: 154866
% 276.94/277.36 Inuse: 1863
% 276.94/277.36 Deleted: 6208
% 276.94/277.36 Deletedinuse: 44
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36
% 276.94/277.36 Intermediate Status:
% 276.94/277.36 Generated: 688024
% 276.94/277.36 Kept: 159603
% 276.94/277.36 Inuse: 1883
% 276.94/277.36 Deleted: 6209
% 276.94/277.36 Deletedinuse: 45
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36
% 276.94/277.36 Intermediate Status:
% 276.94/277.36 Generated: 728111
% 276.94/277.36 Kept: 163150
% 276.94/277.36 Inuse: 1888
% 276.94/277.36 Deleted: 6209
% 276.94/277.36 Deletedinuse: 45
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36 Resimplifying clauses:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36
% 276.94/277.36 Intermediate Status:
% 276.94/277.36 Generated: 797655
% 276.94/277.36 Kept: 169586
% 276.94/277.36 Inuse: 1898
% 276.94/277.36 Deleted: 6333
% 276.94/277.36 Deletedinuse: 45
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36
% 276.94/277.36 Intermediate Status:
% 276.94/277.36 Generated: 865349
% 276.94/277.36 Kept: 175124
% 276.94/277.36 Inuse: 1903
% 276.94/277.36 Deleted: 6333
% 276.94/277.36 Deletedinuse: 45
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36
% 276.94/277.36 Intermediate Status:
% 276.94/277.36 Generated: 893847
% 276.94/277.36 Kept: 178794
% 276.94/277.36 Inuse: 1908
% 276.94/277.36 Deleted: 6333
% 276.94/277.36 Deletedinuse: 45
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36
% 276.94/277.36 Intermediate Status:
% 276.94/277.36 Generated: 909765
% 276.94/277.36 Kept: 181055
% 276.94/277.36 Inuse: 1938
% 276.94/277.36 Deleted: 6333
% 276.94/277.36 Deletedinuse: 45
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36
% 276.94/277.36 Intermediate Status:
% 276.94/277.36 Generated: 925331
% 276.94/277.36 Kept: 183586
% 276.94/277.36 Inuse: 1963
% 276.94/277.36 Deleted: 6333
% 276.94/277.36 Deletedinuse: 45
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36 Resimplifying clauses:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36
% 276.94/277.36 Intermediate Status:
% 276.94/277.36 Generated: 936137
% 276.94/277.36 Kept: 185596
% 276.94/277.36 Inuse: 1978
% 276.94/277.36 Deleted: 6476
% 276.94/277.36 Deletedinuse: 45
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36
% 276.94/277.36 Intermediate Status:
% 276.94/277.36 Generated: 955678
% 276.94/277.36 Kept: 189364
% 276.94/277.36 Inuse: 1993
% 276.94/277.36 Deleted: 6476
% 276.94/277.36 Deletedinuse: 45
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36
% 276.94/277.36 Intermediate Status:
% 276.94/277.36 Generated: 966473
% 276.94/277.36 Kept: 191640
% 276.94/277.36 Inuse: 1998
% 276.94/277.36 Deleted: 6476
% 276.94/277.36 Deletedinuse: 45
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36
% 276.94/277.36 Intermediate Status:
% 276.94/277.36 Generated: 984556
% 276.94/277.36 Kept: 194042
% 276.94/277.36 Inuse: 2023
% 276.94/277.36 Deleted: 6476
% 276.94/277.36 Deletedinuse: 45
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36 Resimplifying inuse:
% 276.94/277.36 Done
% 276.94/277.36
% 276.94/277.36
% 276.94/277.36 Intermediate Status:
% 276.94/277.36 Generated: 1012061
% 276.94/277.36 Kept: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------