TSTP Solution File: SWV577-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV577-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 16:26:51 EDT 2022
% Result : Timeout 300.07s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : SWV577-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Thu Jun 16 02:45:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.04/1.45 *** allocated 10000 integers for termspace/termends
% 1.04/1.45 *** allocated 10000 integers for clauses
% 1.04/1.45 *** allocated 10000 integers for justifications
% 1.04/1.45 *** allocated 15000 integers for termspace/termends
% 1.04/1.45 *** allocated 22500 integers for termspace/termends
% 1.04/1.45 *** allocated 33750 integers for termspace/termends
% 1.04/1.45 Bliksem 1.12
% 1.04/1.45
% 1.04/1.45
% 1.04/1.45 Automatic Strategy Selection
% 1.04/1.45
% 1.04/1.45 Clauses:
% 1.04/1.45 [
% 1.04/1.45 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.04/1.45 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.04/1.45 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.04/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.45 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.04/1.45 ), X ), Y ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.45 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.45 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.45 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.45 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.45 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.45 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.04/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.45 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.45 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.45 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.45 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.45 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.45 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.04/1.45 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.04/1.45 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.45 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.04/1.45 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.04/1.45 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.45 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.04/1.45 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.04/1.45 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.04/1.45 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.45 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.45 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.04/1.45 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.45 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.45 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.04/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.04/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.04/1.45 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.04/1.45 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.04/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.04/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.04/1.45 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.04/1.45 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ) ) ],
% 1.04/1.45 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.04/1.45 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP(
% 1.04/1.45 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Z ) ) ) ],
% 1.04/1.45 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.04/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.04/1.45 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.45 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.04/1.45 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.04/1.45 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.04/1.45 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.45 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.04/1.45 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.04/1.45 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.04/1.45 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 1.04/1.45 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.04/1.45 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.45 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.04/1.45 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.04/1.45 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 1.04/1.45 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 1.04/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.04/1.45 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.04/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.04/1.45 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.04/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.04/1.45 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.04/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.04/1.45 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.04/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.04/1.45 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.04/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.04/1.45 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.04/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.04/1.45 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.04/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.04/1.45 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.04/1.45 ), X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.04/1.45 ), X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.04/1.45 ), X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.04/1.45 ), X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.04/1.45 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.04/1.45 ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.04/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.04/1.45 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.45 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.45 X ), X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.45 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.45 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.45 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.04/1.45 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.04/1.45 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.45 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.04/1.45 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.04/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.04/1.45 ,
% 1.04/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.45 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.04/1.46 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.04/1.46 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.04/1.46 'c_Suc'( X ), 'tc_nat' ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.04/1.46 'c_Suc'( X ), 'tc_nat' ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.04/1.46 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.04/1.46 , Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), X,
% 1.04/1.46 'tc_nat' ) ],
% 1.04/1.46 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.04/1.46 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.04/1.46 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.04/1.46 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.04/1.46 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.04/1.46 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.04/1.46 ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.04/1.46 ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.04/1.46 ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.04/1.46 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), Y ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.04/1.46 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.04/1.46 , X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.04/1.46 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.04/1.46 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.04/1.46 'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.04/1.46 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.04/1.46 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.04/1.46 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.04/1.46 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.04/1.46 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.04/1.46 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.04/1.46 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.04/1.46 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.04/1.46 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.04/1.46 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, 'c_Suc'( X ),
% 1.04/1.46 'tc_nat' ), 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.04/1.46 'tc_nat', 'tc_bool' ) ), 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 1.04/1.46 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.04/1.46 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.04/1.46 ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.04/1.46 Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.04/1.46 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.04/1.46 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.04/1.46 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.04/1.46 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), T ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.04/1.46 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), Y ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.04/1.46 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.04/1.46 ) ), Y ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.04/1.46 , 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, Z, 'tc_Int_Oint' ),
% 1.04/1.46 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.04/1.46 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.04/1.46 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.04/1.46 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.04/1.46 'c_lessequals'( Z, Y, X ) ) ],
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.04/1.46 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.04/1.46 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.04/1.46 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.04/1.46 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.04/1.46 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.04/1.46 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.04/1.46 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.04/1.46 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.04/1.46 , Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.04/1.46 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.04/1.46 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.04/1.46 ), =( Z, Y ) ],
% 1.04/1.46 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.04/1.46 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.04/1.46 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.04/1.46 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 1.04/1.46 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.04/1.46 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.04/1.46 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.04/1.46 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 1.04/1.46 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.04/1.46 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.04/1.46 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.04/1.46 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 1.04/1.46 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.04/1.46 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.04/1.46 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.04/1.46 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.04/1.46 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.04/1.46 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 1.04/1.46 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.04/1.46 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.04/1.46 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.04/1.46 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.04/1.46 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.04/1.46 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.04/1.46 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.04/1.46 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, 'c_Suc'( Y ),
% 1.04/1.46 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool'
% 1.04/1.46 ) ) ), 'c_lessequals'( X, Y, 'tc_nat' ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 , X ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.04/1.46 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.04/1.46 'tc_nat' ) ],
% 1.04/1.46 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 1.04/1.46 , X, 'tc_nat' ) ) ],
% 1.04/1.46 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.04/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 1.04/1.46 'tc_nat' ) ],
% 1.04/1.46 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.04/1.46 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.04/1.46 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.04/1.46 T, X ) ), T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.04/1.46 ) ), Z ), T, X ) ) ],
% 1.04/1.46 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.04/1.46 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.04/1.46 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.04/1.46 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.04/1.46 , Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.04/1.46 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.04/1.46 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Obot__class_Obot'(
% 1.04/1.46 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.04/1.46 Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.04/1.46 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.04/1.46 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ) ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.04/1.46 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.04/1.46 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.04/1.46 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ), X ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.04/1.46 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.04/1.46 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.04/1.46 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.04/1.46 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.04/1.46 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.04/1.46 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.04/1.46 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.04/1.46 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.04/1.46 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint'
% 1.04/1.46 ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X
% 1.04/1.46 ), Z ), 'tc_Int_Oint' ), ~( 'c_lessequals'( Y, Z, 'tc_Int_Oint' ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.04/1.46 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 1.04/1.46 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.04/1.46 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.04/1.46 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0,
% 1.04/1.46 V1 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.04/1.46 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0,
% 1.04/1.46 V1 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.04/1.46 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.04/1.46 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.04/1.46 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.04/1.46 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.04/1.46 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.04/1.46 ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.04/1.46 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.04/1.46 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.04/1.46 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.04/1.46 ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.04/1.46 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.04/1.46 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.04/1.46 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.04/1.46 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.04/1.46 ), X ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.04/1.46 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.04/1.46 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.04/1.46 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 , X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.04/1.46 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.04/1.46 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.04/1.46 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.04/1.46 ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.04/1.46 ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.04/1.46 ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.04/1.46 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.04/1.46 ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.04/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.04/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.04/1.46 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.04/1.46 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.04/1.46 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.04/1.46 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.04/1.46 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.04/1.46 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 T, X ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.04/1.46 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.04/1.46 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.04/1.46 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.04/1.46 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.04/1.46 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.04/1.46 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.04/1.46 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.04/1.46 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.04/1.46 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.04/1.46 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.04/1.46 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.04/1.46 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.04/1.46 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.04/1.46 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.04/1.46 ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.04/1.46 , X ) ), Z ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.04/1.46 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.04/1.46 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.04/1.46 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.04/1.46 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.04/1.46 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.04/1.46 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.04/1.46 , 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.04/1.46 , 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.04/1.46 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.04/1.46 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.04/1.46 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.04/1.46 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.04/1.46 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.04/1.46 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.04/1.46 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.04/1.46 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.04/1.46 ), T ) ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.04/1.46 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.04/1.46 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.04/1.46 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.04/1.46 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.04/1.46 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 X ), Y ), Z ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.04/1.46 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.04/1.46 ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.04/1.46 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.04/1.46 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.04/1.46 ), X ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.04/1.46 ), Z ) ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.04/1.46 ), Z ) ), Y ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.04/1.46 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.04/1.46 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.04/1.46 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.04/1.46 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.04/1.46 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.04/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.04/1.46 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.04/1.46 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.04/1.46 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.04/1.46 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.04/1.46 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.04/1.46 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.04/1.46 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.04/1.46 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.04/1.46 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.04/1.46 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.04/1.46 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.04/1.46 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.04/1.46 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.04/1.46 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.04/1.46 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.04/1.46 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.04/1.46 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.04/1.46 Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.04/1.46 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.04/1.46 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.04/1.46 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.04/1.46 X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.04/1.46 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 , X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 'tc_nat' ) ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.04/1.46 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.04/1.46 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.04/1.46 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.04/1.46 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.04/1.46 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.04/1.46 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.04/1.46 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.04/1.46 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.04/1.46 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.04/1.46 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.04/1.46 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.04/1.46 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.04/1.46 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.04/1.46 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.04/1.46 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.04/1.46 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.04/1.46 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.04/1.46 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.04/1.46 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.04/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.04/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), Z ), T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.04/1.46 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.04/1.46 'c_lessequals'( Y, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.04/1.46 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.04/1.46 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.04/1.46 'c_lessequals'( Z, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.04/1.46 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.04/1.46 'c_lessequals'( Y, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.04/1.46 'c_lessequals'( Z, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.04/1.46 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.04/1.46 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.04/1.46 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Z
% 1.04/1.46 , T, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.04/1.46 X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.04/1.46 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Z ), Y ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Z ), Y ), X ) ) ],
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.04/1.46 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.04/1.46 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.04/1.46 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.04/1.46 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) ), =( Y, T ),
% 1.04/1.46 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.04/1.46 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.04/1.46 , X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.04/1.46 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.04/1.46 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), T ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.04/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), T ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.04/1.46 , X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.04/1.46 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), T ), Z, X ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.04/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.04/1.46 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.04/1.46 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.04/1.46 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.04/1.46 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.04/1.46 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.04/1.46 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.04/1.46 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.04/1.46 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.04/1.46 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.04/1.46 , V0, U, V1 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.04/1.46 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.04/1.46 , V0, U, V1 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.04/1.46 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.04/1.46 X, T, U, Y, W, V0 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.04/1.46 X, T, U, Z, W, V0 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.04/1.46 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.04/1.46 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.04/1.46 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.04/1.46 T, X, U, Y, W, V0 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.04/1.46 T, X, U, Z, W, V0 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.04/1.46 T, X, U, W, Y, V0 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.04/1.46 T, X, U, W, Z, V0 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.04/1.46 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.04/1.46 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.04/1.46 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.04/1.46 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.04/1.46 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.04/1.46 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.04/1.46 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.04/1.46 , V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.04/1.46 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.04/1.46 W, V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.04/1.46 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.04/1.46 , V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.04/1.46 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.04/1.46 W, V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.04/1.46 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.04/1.46 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.04/1.46 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.04/1.46 W, V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.04/1.46 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.04/1.46 W, V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.04/1.46 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.04/1.46 , V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.04/1.46 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.04/1.46 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.04/1.46 , V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.04/1.46 X, T, U, Y, W, V0 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.04/1.46 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.04/1.46 , V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.04/1.46 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.04/1.46 T, X, U, Y, W, V0 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.04/1.46 T, X, U, W, Y, V0 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.04/1.46 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.04/1.46 , V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.04/1.46 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.04/1.46 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.04/1.46 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.04/1.46 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.04/1.46 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.04/1.46 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.04/1.46 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.04/1.46 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.04/1.46 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.04/1.46 ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.04/1.46 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.04/1.46 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.04/1.46 Y ) ) ) ],
% 1.04/1.46 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.04/1.46 , X ) ), T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.04/1.46 ), Z ), T, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.04/1.46 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 Y, Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.04/1.46 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.04/1.46 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.04/1.46 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.04/1.46 Y ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.04/1.46 Y ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.04/1.46 Y ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.04/1.46 Y ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.04/1.46 Y ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.04/1.46 Y ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.04/1.46 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.04/1.46 ],
% 1.04/1.46 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.04/1.46 , Y ) ) ],
% 1.04/1.46 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.04/1.46 'tc_nat' ) ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.04/1.46 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.04/1.46 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.04/1.46 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.04/1.46 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.04/1.46 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.04/1.46 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.04/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.04/1.46 ), 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.04/1.46 ), 'tc_nat' ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.04/1.46 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.04/1.46 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.04/1.46 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.04/1.46 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.04/1.46 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.04/1.46 ],
% 1.04/1.46 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.04/1.46 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.04/1.46 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.04/1.46 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.04/1.46 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.04/1.46 'c_Int_OPls' ), X ), X ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ),
% 1.04/1.46 'c_Int_OPls' ), X ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.04/1.46 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.04/1.46 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.04/1.46 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.04/1.46 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.04/1.46 'c_Int_OBit0'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit0'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.04/1.46 [ =( 'c_Int_OBit0'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 'tc_Int_Oint' ), X ), X ) ) ],
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.04/1.46 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.04/1.46 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.04/1.46 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.04/1.46 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.04/1.46 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.04/1.46 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.04/1.46 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.04/1.46 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.04/1.46 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.04/1.46 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.04/1.46 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), 'c_lessequals'( X, Y
% 1.04/1.46 , 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'(
% 1.04/1.46 X, 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.04/1.46 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.04/1.46 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.04/1.46 'tc_nat' ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.04/1.46 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.04/1.46 'tc_nat' ) ), Y ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.04/1.46 'tc_nat' ) ), Y ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ), ~( 'c_lessequals'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OPls',
% 1.04/1.46 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.04/1.46 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.04/1.46 ), X ), ~( 'c_lessequals'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OPls', Y,
% 1.04/1.46 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.04/1.46 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.04/1.46 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.04/1.46 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.04/1.46 Z, 'c_Suc'( T ), 'tc_nat' ), 'tc_nat', X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.04/1.46 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.04/1.46 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.04/1.46 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_Suc'( Z ), T, 'tc_nat' )
% 1.04/1.46 , 'tc_nat', X ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.04/1.46 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.04/1.46 Z, 'c_Suc'( T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.04/1.46 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.04/1.46 , X ) ), hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.04/1.46 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.04/1.46 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.04/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.04/1.46 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.04/1.46 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.04/1.46 ), T ) ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.04/1.46 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.04/1.46 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.04/1.46 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 1.04/1.46 'tc_nat' ) ) ],
% 1.04/1.46 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.04/1.46 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.04/1.46 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.04/1.46 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.04/1.46 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.04/1.46 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.04/1.46 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.04/1.46 , X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.04/1.46 ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.04/1.46 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.04/1.46 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.04/1.46 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.04/1.46 'c_Suc'( X ), 'tc_nat' ) ],
% 1.04/1.46 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.04/1.46 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 1.04/1.46 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.04/1.46 Z, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.04/1.46 , X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.04/1.46 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y, 'tc_nat' ), hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.04/1.46 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.04/1.46 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Obot'( X ) ), =( hAPP(
% 1.04/1.46 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 1.04/1.46 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.04/1.46 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.04/1.46 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.04/1.46 X ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.04/1.46 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.04/1.46 Y ) ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.04/1.46 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.04/1.46 ) ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.04/1.46 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.04/1.46 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.04/1.46 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.04/1.46 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.04/1.46 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.04/1.46 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.04/1.46 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.04/1.46 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.04/1.46 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.04/1.46 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.04/1.46 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y
% 1.04/1.46 , 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 1.04/1.46 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.04/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.04/1.46 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 1.04/1.46 X, T ), Y ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.04/1.46 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 X, T, 'tc_nat' ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ),
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U ) )
% 1.04/1.46 , hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T )
% 1.04/1.46 , U ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.04/1.46 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.04/1.46 'c_lessequals'( Z, Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.04/1.46 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.04/1.46 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_lessequals'( Z, Y, X ) ) ],
% 1.04/1.46 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.04/1.46 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.04/1.46 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.04/1.46 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.04/1.46 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.04/1.46 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.04/1.46 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.04/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.04/1.46 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.04/1.46 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.04/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.04/1.46 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.04/1.46 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.04/1.46 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.04/1.46 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 ), Y ), Y, X ) ) ],
% 1.04/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.04/1.46 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.04/1.46 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.04/1.46 , X ) ), Z ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.04/1.46 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.04/1.46 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.04/1.46 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.04/1.46 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.04/1.46 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.04/1.46 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.04/1.46 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.04/1.46 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.04/1.46 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.04/1.46 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.04/1.46 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.04/1.46 X ) ) ],
% 1.04/1.46 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 'tc_nat' ) ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.04/1.46 , Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.04/1.46 , X ) ) ],
% 1.04/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.04/1.46 , Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.04/1.46 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.04/1.46 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.04/1.46 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.04/1.46 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.04/1.46 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.04/1.46 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.04/1.46 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.04/1.46 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.04/1.46 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.04/1.46 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.04/1.46 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.04/1.46 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.04/1.46 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.04/1.46 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.04/1.46 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.04/1.46 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.04/1.46 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.04/1.46 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.04/1.46 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.04/1.46 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.04/1.46 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.04/1.46 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.04/1.46 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.04/1.46 ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.04/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.04/1.46 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.04/1.46 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.04/1.46 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.04/1.46 ,
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.04/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.04/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.04/1.46 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.04/1.46 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.04/1.46 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.04/1.46 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.04/1.46 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.04/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.04/1.46 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.04/1.46 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.04/1.46 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.04/1.46 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.04/1.46 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.04/1.46 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.04/1.46 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.04/1.46 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.04/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.04/1.46 ) ) ],
% 1.04/1.46 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.04/1.46 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.04/1.46 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.04/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.04/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.04/1.46 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.04/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.46 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.10/1.46 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.10/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ) ],
% 1.10/1.46 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.46 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.10/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ), hAPP( hAPP(
% 1.10/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( hAPP(
% 1.10/1.46 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ), T ) )
% 1.10/1.46 ],
% 1.10/1.46 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.10/1.46 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.10/1.46 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.10/1.46 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.46 , X ) ), T ) ) ) ],
% 1.10/1.46 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.10/1.46 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.10/1.46 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ), hAPP( hAPP(
% 1.10/1.46 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.46 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.10/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.46 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.10/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.46 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.10/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.46 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.46 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.10/1.46 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.46 ) ), Z ) ) ],
% 1.10/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.46 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.10/1.46 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.46 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.10/1.46 Y ) ) ],
% 1.10/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.46 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.46 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.10/1.46 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.46 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.46 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.46 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.46 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.10/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.46 ) ) ],
% 1.10/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.46 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.46 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.46 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.10/1.46 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.46 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.10/1.46 'c_Finite__Set_Osetsum'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.10/1.46 'tc_bool' ) ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.46 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.46 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.46 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.10/1.46 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.10/1.46 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.10/1.46 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.46 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.10/1.46 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.10/1.46 ), X ), X ) ) ],
% 1.10/1.46 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.46 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.10/1.46 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.46 , X ), X ) ) ],
% 1.10/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.46 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.10/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.46 , X ), ~( 'c_lessequals'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint'
% 1.10/1.46 ) ) ],
% 1.10/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.46 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OBit1'(
% 1.10/1.46 'c_Int_OPls' ), 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.46 , X ) ) ],
% 1.10/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.46 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.10/1.46 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.46 , X ), ~( 'c_lessequals'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint'
% 1.10/1.47 ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.47 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.47 , X ) ) ],
% 1.10/1.47 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), ~(
% 1.10/1.47 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.47 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.10/1.47 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.10/1.47 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.10/1.47 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.47 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.10/1.47 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.47 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.10/1.47 'c_Int_OBit0'( X ) ), 'c_Int_OBit1'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.10/1.47 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.10/1.47 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.47 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), ~(
% 1.10/1.47 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.47 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.10/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.10/1.47 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.10/1.47 ) ],
% 1.10/1.47 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.10/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.10/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.47 X ), Y ), Y ) ) ],
% 1.10/1.47 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.10/1.47 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.47 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.47 'tc_nat' ) ) ],
% 1.10/1.47 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.47 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X,
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.10/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool' ) ) ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.47 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.47 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.10/1.47 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.47 ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.10/1.47 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.47 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.10/1.47 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.10/1.47 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.10/1.47 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.10/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.47 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.47 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.10/1.47 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.47 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.47 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.47 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.10/1.47 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.47 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.47 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.47 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.10/1.47 ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.47 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.47 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.47 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.47 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.47 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.10/1.47 'tc_nat' ) ), Y ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.47 ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.47 ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.47 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.47 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.47 , X ), Y ), 'tc_nat' ) ],
% 1.10/1.47 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.47 , X ), Y ), 'tc_nat' ) ],
% 1.10/1.47 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.47 , Y ), X ), 'tc_nat' ) ],
% 1.10/1.47 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.47 , X ), Y ), 'tc_nat' ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.47 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.10/1.47 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.10/1.47 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.10/1.47 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.47 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.10/1.47 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.47 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.47 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.10/1.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.10/1.47 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.47 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.10/1.47 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Suc'( T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Suc'( T ) ), X ) ) ],
% 1.10/1.47 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.10/1.47 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.47 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.10/1.47 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.47 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.10/1.47 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.10/1.47 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.47 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.10/1.47 , T ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.10/1.47 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.47 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.10/1.47 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.10/1.47 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 1.10/1.47 'tc_nat' ) ) ],
% 1.10/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 1.10/1.47 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.10/1.47 Z, X ) ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.47 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.10/1.47 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 1.10/1.47 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.47 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.10/1.47 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.10/1.47 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.47 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.10/1.47 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.47 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.47 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.10/1.47 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.47 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.47 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.10/1.47 ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.47 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.47 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.10/1.47 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.47 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.47 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.10/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.47 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.47 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.10/1.47 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.10/1.47 X ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.10/1.47 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.47 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.10/1.47 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.47 , X ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.47 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.47 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.47 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.47 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.47 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.47 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.47 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.10/1.47 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.10/1.47 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.47 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.10/1.47 ],
% 1.10/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.47 , Z ), Y ), 'tc_nat' ) ) ],
% 1.10/1.47 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.47 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.10/1.47 ],
% 1.10/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.10/1.47 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.10/1.47 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( Z, Y,
% 1.10/1.47 'tc_Int_Oint' ) ), ~( 'c_lessequals'( X, Z, 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.10/1.47 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.47 [ 'c_lessequals'( X, X, 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.10/1.47 , X ) ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.47 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.10/1.47 , X ) ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.47 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.10/1.47 ) ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.47 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.10/1.47 ) ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.47 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.47 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.47 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.47 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.47 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.47 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.47 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.47 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.47 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.47 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.47 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.47 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.10/1.47 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.47 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.47 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.47 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.10/1.47 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.47 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.10/1.47 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.10/1.47 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.47 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.10/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.10/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.47 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.10/1.47 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.47 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.10/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.47 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.10/1.47 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.47 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.10/1.47 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.47 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.47 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.10/1.47 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.47 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.10/1.47 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, 'c_Suc'( Y ),
% 1.10/1.47 'tc_nat' ), 'c_Set_Oinsert'( Y,
% 1.10/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( X, Y, 'tc_nat' ), 'tc_nat'
% 1.10/1.47 ) ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.47 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.10/1.47 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 1.10/1.47 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.47 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.47 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.47 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.47 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.10/1.47 'c_lessequals'( Z, Y, X ) ],
% 1.10/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), 'c_lessequals'( Y, X,
% 1.10/1.47 'tc_Int_Oint' ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.47 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.47 X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.47 X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.47 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.10/1.47 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.47 ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.10/1.47 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.10/1.47 ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.10/1.47 ), Y ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.47 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.10/1.47 ), Y ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.10/1.47 ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.10/1.47 , Y ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.10/1.47 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X,
% 1.10/1.47 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.10/1.47 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.10/1.47 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ), 'c_lessequals'( X
% 1.10/1.47 , 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.10/1.47 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.10/1.47 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.10/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.10/1.47 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.47 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.47 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.10/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.10/1.47 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.10/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.10/1.47 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.10/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, 'tc_nat' ), 'tc_nat'
% 1.10/1.47 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.10/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.10/1.47 , X ) ), ~( 'c_lessequals'( T, U, 'tc_nat' ) ), ~( 'c_lessequals'( Z, T,
% 1.10/1.47 'tc_nat' ) ) ],
% 1.10/1.47 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.10/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.10/1.47 'c_Set_Oinsert'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Set_Oinsert'(
% 1.10/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Set_Oinsert'(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Set_Oinsert'(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.10/1.47 'tc_nat', 'tc_bool' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) )
% 1.10/1.47 ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.47 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.47 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.10/1.47 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.10/1.47 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.10/1.47 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.47 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.10/1.47 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.10/1.47 , X, Z, U, W, V0 ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.47 ) ), =( 'c_Finite__Set_Osetsum'( Y,
% 1.10/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_Suc'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 1.10/1.47 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.47 ) ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ),
% 1.10/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_Int_OPls'
% 1.10/1.47 ) ), Y ), X ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.10/1.47 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.10/1.47 , Y ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.10/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.47 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.10/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.47 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.10/1.47 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.10/1.47 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.10/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.10/1.47 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.10/1.47 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.10/1.47 ), Y ), Y ) ) ],
% 1.10/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.10/1.47 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.10/1.47 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.10/1.47 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.10/1.47 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.10/1.47 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.10/1.47 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.10/1.47 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.10/1.47 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.47 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.10/1.47 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.10/1.47 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.10/1.47 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.10/1.47 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.10/1.47 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.10/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.10/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.10/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.47 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.10/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.10/1.47 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.10/1.47 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.10/1.47 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.10/1.47 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.10/1.47 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.10/1.47 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.10/1.47 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.47 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.10/1.47 ) ],
% 1.10/1.47 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.10/1.47 'tc_nat' ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.47 'c_Int_OPls', X ) ), Y ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.10/1.47 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.10/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.47 ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.47 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.10/1.47 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.47 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.10/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.10/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 X ), Y ), Z ) ), T ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.10/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 X ), Y ), Z ) ), T ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.10/1.47 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.10/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.10/1.47 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.47 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.10/1.47 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.47 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.10/1.47 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 Y ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.10/1.47 Y ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 Y ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.47 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.10/1.47 Y ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.10/1.47 Y ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.47 Y ) ],
% 1.10/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.10/1.47 Y ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ],
% 1.10/1.47 [ ~( =( 'c_Finite__Set_Osetsum'( 'v_x',
% 1.10/1.47 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.47 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.10/1.47 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' )
% 1.10/1.47 , 'tc_nat', 't_a' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ),
% 1.10/1.47 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( hAPP(
% 1.10/1.47 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( 'v_x',
% 1.10/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'v_x',
% 1.10/1.47 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( 'v_x',
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( 'v_x',
% 1.10/1.47 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.47 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.10/1.47 'class_OrderedGroup_Oab__semigroup__add'( X ) ],
% 1.10/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.10/1.47 'class_OrderedGroup_Omonoid__add'( X ) ],
% 1.10/1.47 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.10/1.47 'class_Orderings_Opreorder'( Y ) ) ],
% 1.10/1.47 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.10/1.47 'class_Orderings_Oorder'( Y ) ) ],
% 1.10/1.47 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.10/1.47 Y ) ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.10/1.47 ],
% 1.10/1.47 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.10/1.47 ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.10/1.47 ],
% 1.10/1.47 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.10/1.47 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.10/1.47 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.10/1.47 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.10/1.47 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.10/1.47 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.10/1.47 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.10/1.47 ],
% 1.10/1.47 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.10/1.47 ],
% 1.10/1.47 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.10/1.47 ,
% 1.10/1.47 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.10/1.47 [ 'c_fequal'( X, X, Y ) ],
% 1.10/1.47 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.10/1.47 ] .
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 percentage equality = 0.202592, percentage horn = 0.812563
% 1.10/1.47 This is a problem with some equality
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 Options Used:
% 1.10/1.47
% 1.10/1.47 useres = 1
% 1.10/1.47 useparamod = 1
% 1.10/1.47 useeqrefl = 1
% 1.10/1.47 useeqfact = 1
% 1.10/1.47 usefactor = 1
% 1.10/1.47 usesimpsplitting = 0
% 1.10/1.47 usesimpdemod = 5
% 1.10/1.47 usesimpres = 3
% 1.10/1.47
% 1.10/1.47 resimpinuse = 1000
% 1.10/1.47 resimpclauses = 20000
% 1.10/1.47 substype = eqrewr
% 1.10/1.47 backwardsubs = 1
% 1.10/1.47 selectoldest = 5
% 1.10/1.47
% 1.10/1.47 litorderings [0] = split
% 1.10/1.47 litorderings [1] = extend the termordering, first sorting on arguments
% 1.10/1.47
% 1.10/1.47 termordering = kbo
% 1.10/1.47
% 1.10/1.47 litapriori = 0
% 1.10/1.47 termapriori = 1
% 1.10/1.47 litaposteriori = 0
% 1.10/1.47 termaposteriori = 0
% 1.10/1.47 demodaposteriori = 0
% 1.10/1.47 ordereqreflfact = 0
% 1.10/1.47
% 1.10/1.47 litselect = negord
% 1.10/1.47
% 1.10/1.47 maxweight = 15
% 1.10/1.47 maxdepth = 30000
% 1.10/1.47 maxlength = 115
% 1.10/1.47 maxnrvars = 195
% 1.10/1.47 excuselevel = 1
% 1.10/1.47 increasemaxweight = 1
% 1.10/1.47
% 1.10/1.47 maxselected = 10000000
% 1.10/1.47 maxnrclauses = 10000000
% 1.10/1.47
% 1.10/1.47 showgenerated = 0
% 1.10/1.47 showkept = 0
% 1.10/1.47 showselected = 0
% 1.10/1.47 showdeleted = 0
% 1.10/1.47 showresimp = 1
% 1.10/1.47 showstatus = 2000
% 1.10/1.47
% 1.10/1.47 prologoutput = 1
% 1.10/1.47 nrgoals = 5000000
% 1.10/1.47 totalproof = 1
% 1.10/1.47
% 1.10/1.47 Symbols occurring in the translation:
% 1.10/1.47
% 1.10/1.47 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.10/1.47 . [1, 2] (w:1, o:137, a:1, s:1, b:0),
% 1.10/1.47 ! [4, 1] (w:0, o:69, a:1, s:1, b:0),
% 2.17/2.56 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.17/2.56 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.17/2.56 'c_Suc' [40, 1] (w:1, o:74, a:1, s:1, b:0),
% 2.17/2.56 'tc_nat' [42, 0] (w:1, o:17, a:1, s:1, b:0),
% 2.17/2.56 'c_Divides_Odiv__class_Omod' [43, 3] (w:1, o:167, a:1, s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Odivision__ring' [45, 1] (w:1, o:77, a:1, s:1
% 2.17/2.56 , b:0),
% 2.17/2.56 'class_Ring__and__Field_Odivision__by__zero' [46, 1] (w:1, o:78, a:1
% 2.17/2.56 , s:1, b:0),
% 2.17/2.56 'c_HOL_Oinverse__class_Oinverse' [48, 2] (w:1, o:162, a:1, s:1, b:0)
% 2.17/2.56 ,
% 2.17/2.56 'class_Ring__and__Field_Oordered__field' [49, 1] (w:1, o:82, a:1, s:1
% 2.17/2.56 , b:0),
% 2.17/2.56 'class_Int_Onumber' [50, 1] (w:1, o:83, a:1, s:1, b:0),
% 2.17/2.56 'c_Int_Onumber__class_Onumber__of' [53, 2] (w:1, o:163, a:1, s:1, b:0
% 2.17/2.56 ),
% 2.17/2.56 'c_HOL_Oinverse__class_Odivide' [54, 3] (w:1, o:168, a:1, s:1, b:0),
% 2.17/2.56
% 2.17/2.56 'c_HOL_Oord__class_Oless' [55, 3] (w:1, o:169, a:1, s:1, b:0),
% 2.17/2.56 'c_HOL_Ozero__class_Ozero' [56, 1] (w:1, o:84, a:1, s:1, b:0),
% 2.17/2.56 'c_HOL_Otimes__class_Otimes' [57, 1] (w:1, o:85, a:1, s:1, b:0),
% 2.17/2.56 hAPP [58, 2] (w:1, o:164, a:1, s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Ocomm__semiring__1' [59, 1] (w:1, o:75, a:1
% 2.17/2.56 , s:1, b:0),
% 2.17/2.56 'c_Power_Opower__class_Opower' [60, 1] (w:1, o:87, a:1, s:1, b:0),
% 2.17/2.56 'class_OrderedGroup_Omonoid__mult' [62, 1] (w:1, o:89, a:1, s:1, b:0)
% 2.17/2.56 ,
% 2.17/2.56 'class_Power_Opower' [63, 1] (w:1, o:108, a:1, s:1, b:0),
% 2.17/2.56 'c_lessequals' [67, 3] (w:1, o:170, a:1, s:1, b:0),
% 2.17/2.56 'class_Orderings_Oorder' [68, 1] (w:1, o:90, a:1, s:1, b:0),
% 2.17/2.56 'class_Orderings_Opreorder' [70, 1] (w:1, o:91, a:1, s:1, b:0),
% 2.17/2.56 'tc_Int_Oint' [71, 0] (w:1, o:40, a:1, s:1, b:0),
% 2.17/2.56 'c_HOL_Oplus__class_Oplus' [72, 1] (w:1, o:110, a:1, s:1, b:0),
% 2.17/2.56 'c_Set_Oinsert' [80, 3] (w:1, o:171, a:1, s:1, b:0),
% 2.17/2.56 'class_Orderings_Olinorder' [81, 1] (w:1, o:92, a:1, s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Oordered__semidom' [82, 1] (w:1, o:112, a:1
% 2.17/2.56 , s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Oordered__idom' [83, 1] (w:1, o:113, a:1, s:1
% 2.17/2.56 , b:0),
% 2.17/2.56 'class_Ring__and__Field_Oordered__semiring__strict' [84, 1] (w:1, o:
% 2.17/2.56 114, a:1, s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Oordered__ring__strict' [85, 1] (w:1, o:111
% 2.17/2.56 , a:1, s:1, b:0),
% 2.17/2.56 'c_HOL_Oone__class_Oone' [86, 1] (w:1, o:109, a:1, s:1, b:0),
% 2.17/2.56 'c_Divides_Odiv__class_Odiv' [87, 3] (w:1, o:172, a:1, s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Ofield' [88, 1] (w:1, o:115, a:1, s:1, b:0),
% 2.17/2.56
% 2.17/2.56 'class_Divides_Osemiring__div' [89, 1] (w:1, o:116, a:1, s:1, b:0),
% 2.17/2.56 'class_Int_Onumber__ring' [90, 1] (w:1, o:117, a:1, s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Osemiring__0' [92, 1] (w:1, o:120, a:1, s:1
% 2.17/2.56 , b:0),
% 2.17/2.56 'class_Orderings_Obot' [93, 1] (w:1, o:93, a:1, s:1, b:0),
% 2.17/2.56 'c_Orderings_Obot__class_Obot' [94, 1] (w:1, o:86, a:1, s:1, b:0),
% 2.17/2.56 'tc_bool' [95, 0] (w:1, o:49, a:1, s:1, b:0),
% 2.17/2.56 'tc_fun' [96, 2] (w:1, o:165, a:1, s:1, b:0),
% 2.17/2.56 'c_SetInterval_Oord__class_OatLeastLessThan' [97, 3] (w:1, o:173, a:1
% 2.17/2.56 , s:1, b:0),
% 2.17/2.56 'c_Power_Opower_Opower' [98, 3] (w:1, o:174, a:1, s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Oordered__semiring' [99, 1] (w:1, o:121, a:1
% 2.17/2.56 , s:1, b:0),
% 2.17/2.56 hBOOL [105, 1] (w:1, o:122, a:1, s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Oordered__comm__semiring__strict' [109, 1]
% 2.17/2.56 (w:1, o:123, a:1, s:1, b:0),
% 2.17/2.56 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [110, 1]
% 2.17/2.56 (w:1, o:94, a:1, s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Osemiring__1' [111, 1] (w:1, o:124, a:1, s:1
% 2.17/2.56 , b:0),
% 2.17/2.56 'c_Int_Oiszero' [112, 2] (w:1, o:166, a:1, s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Oring__no__zero__divisors' [113, 1] (w:1, o:
% 2.17/2.56 118, a:1, s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Omult__zero' [114, 1] (w:1, o:125, a:1, s:1
% 2.17/2.56 , b:0),
% 2.17/2.56 'class_RealVector_Oreal__normed__algebra' [115, 1] (w:1, o:126, a:1
% 2.17/2.56 , s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Oring__1__no__zero__divisors' [116, 1] (w:1
% 2.17/2.56 , o:119, a:1, s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Ozero__neq__one' [117, 1] (w:1, o:127, a:1
% 2.17/2.56 , s:1, b:0),
% 2.17/2.56 'class_Ring__and__Field_Ono__zero__divisors' [118, 1] (w:1, o:81, a:1
% 12.16/12.56 , s:1, b:0),
% 12.16/12.56 'c_Groebner__Basis_Ogb__semiring' [124, 6] (w:1, o:177, a:1, s:1, b:0
% 12.16/12.56 ),
% 12.16/12.56 'class_OrderedGroup_Oab__semigroup__idem__mult' [125, 1] (w:1, o:95
% 12.16/12.56 , a:1, s:1, b:0),
% 12.16/12.56 'class_Ring__and__Field_Omult__mono1' [126, 1] (w:1, o:79, a:1, s:1
% 12.16/12.56 , b:0),
% 12.16/12.56 'class_Ring__and__Field_Omult__mono' [127, 1] (w:1, o:80, a:1, s:1
% 12.16/12.56 , b:0),
% 12.16/12.56 'class_Ring__and__Field_Opordered__ring' [128, 1] (w:1, o:128, a:1
% 12.16/12.56 , s:1, b:0),
% 12.16/12.56 'class_OrderedGroup_Ocomm__monoid__mult' [129, 1] (w:1, o:96, a:1, s:
% 12.16/12.56 1, b:0),
% 12.16/12.56 'class_Ring__and__Field_Opordered__cancel__semiring' [130, 1] (w:1
% 12.16/12.56 , o:129, a:1, s:1, b:0),
% 12.16/12.56 'class_OrderedGroup_Oab__semigroup__mult' [131, 1] (w:1, o:97, a:1
% 12.16/12.56 , s:1, b:0),
% 12.16/12.56 'class_RealVector_Oreal__normed__field' [132, 1] (w:1, o:130, a:1, s:
% 12.16/12.56 1, b:0),
% 12.16/12.56 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [133, 1]
% 12.16/12.56 (w:1, o:98, a:1, s:1, b:0),
% 12.16/12.56 'class_OrderedGroup_Ocomm__monoid__add' [134, 1] (w:1, o:99, a:1, s:1
% 12.16/12.56 , b:0),
% 12.16/12.56 'class_OrderedGroup_Opordered__comm__monoid__add' [135, 1] (w:1, o:
% 12.16/12.56 100, a:1, s:1, b:0),
% 12.16/12.56 'class_OrderedGroup_Opordered__ab__group__add' [136, 1] (w:1, o:101
% 12.16/12.56 , a:1, s:1, b:0),
% 12.16/12.56 'class_Ring__and__Field_Oidom' [137, 1] (w:1, o:131, a:1, s:1, b:0),
% 12.16/12.56
% 12.16/12.56 'class_OrderedGroup_Opordered__ab__semigroup__add' [140, 1] (w:1, o:
% 12.16/12.56 102, a:1, s:1, b:0),
% 12.16/12.56 'class_Ring__and__Field_Ocomm__semiring' [141, 1] (w:1, o:76, a:1, s:
% 12.16/12.56 1, b:0),
% 12.16/12.56 'class_Ring__and__Field_Opordered__semiring' [144, 1] (w:1, o:132, a:
% 12.16/12.56 1, s:1, b:0),
% 12.16/12.56 'class_Ring__and__Field_Osemiring' [145, 1] (w:1, o:133, a:1, s:1, b:
% 12.16/12.56 0),
% 12.16/12.56 'c_Int_OBit1' [151, 1] (w:1, o:135, a:1, s:1, b:0),
% 12.16/12.56 'c_Int_OPls' [154, 0] (w:1, o:57, a:1, s:1, b:0),
% 12.16/12.56 'c_Int_OBit0' [155, 1] (w:1, o:134, a:1, s:1, b:0),
% 12.16/12.56 'c_Finite__Set_Osetsum' [157, 4] (w:1, o:176, a:1, s:1, b:0),
% 12.16/12.56 'class_OrderedGroup_Olordered__ab__group__add' [158, 1] (w:1, o:88
% 12.16/12.56 , a:1, s:1, b:0),
% 12.16/12.56 't_a' [161, 0] (w:1, o:61, a:1, s:1, b:0),
% 12.16/12.56 'v_x' [162, 0] (w:1, o:62, a:1, s:1, b:0),
% 12.16/12.56 'class_Int_Oring__char__0' [165, 1] (w:1, o:136, a:1, s:1, b:0),
% 12.16/12.56 'class_OrderedGroup_Oab__group__add' [166, 1] (w:1, o:103, a:1, s:1
% 12.16/12.56 , b:0),
% 12.16/12.56 'class_OrderedGroup_Ocancel__semigroup__add' [168, 1] (w:1, o:104, a:
% 12.16/12.56 1, s:1, b:0),
% 12.16/12.56 'class_OrderedGroup_Ocancel__ab__semigroup__add' [169, 1] (w:1, o:105
% 12.16/12.56 , a:1, s:1, b:0),
% 12.16/12.56 'class_OrderedGroup_Oab__semigroup__add' [170, 1] (w:1, o:106, a:1
% 12.16/12.56 , s:1, b:0),
% 12.16/12.56 'class_OrderedGroup_Omonoid__add' [171, 1] (w:1, o:107, a:1, s:1, b:0
% 12.16/12.56 ),
% 12.16/12.56 'c_fequal' [175, 3] (w:1, o:175, a:1, s:1, b:0).
% 12.16/12.56
% 12.16/12.56
% 12.16/12.56 Starting Search:
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56
% 12.16/12.56 Intermediate Status:
% 12.16/12.56 Generated: 4649
% 12.16/12.56 Kept: 2000
% 12.16/12.56 Inuse: 231
% 12.16/12.56 Deleted: 9
% 12.16/12.56 Deletedinuse: 0
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56
% 12.16/12.56 Intermediate Status:
% 12.16/12.56 Generated: 9699
% 12.16/12.56 Kept: 4000
% 12.16/12.56 Inuse: 365
% 12.16/12.56 Deleted: 21
% 12.16/12.56 Deletedinuse: 0
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56
% 12.16/12.56 Intermediate Status:
% 12.16/12.56 Generated: 15899
% 12.16/12.56 Kept: 6466
% 12.16/12.56 Inuse: 481
% 12.16/12.56 Deleted: 28
% 12.16/12.56 Deletedinuse: 3
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56
% 12.16/12.56 Intermediate Status:
% 12.16/12.56 Generated: 23336
% 12.16/12.56 Kept: 8466
% 12.16/12.56 Inuse: 552
% 12.16/12.56 Deleted: 33
% 12.16/12.56 Deletedinuse: 3
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56
% 12.16/12.56 Intermediate Status:
% 12.16/12.56 Generated: 32090
% 12.16/12.56 Kept: 10950
% 12.16/12.56 Inuse: 565
% 12.16/12.56 Deleted: 33
% 12.16/12.56 Deletedinuse: 3
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56
% 12.16/12.56 Intermediate Status:
% 12.16/12.56 Generated: 43610
% 12.16/12.56 Kept: 13536
% 12.16/12.56 Inuse: 576
% 12.16/12.56 Deleted: 33
% 12.16/12.56 Deletedinuse: 3
% 12.16/12.56
% 12.16/12.56
% 12.16/12.56 Intermediate Status:
% 12.16/12.56 Generated: 55662
% 12.16/12.56 Kept: 15565
% 12.16/12.56 Inuse: 581
% 12.16/12.56 Deleted: 33
% 12.16/12.56 Deletedinuse: 3
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56
% 12.16/12.56 Intermediate Status:
% 12.16/12.56 Generated: 69638
% 12.16/12.56 Kept: 17654
% 12.16/12.56 Inuse: 586
% 12.16/12.56 Deleted: 33
% 12.16/12.56 Deletedinuse: 3
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56 Resimplifying inuse:
% 12.16/12.56 Done
% 12.16/12.56
% 12.16/12.56
% 12.16/12.56 Intermediate Status:
% 12.16/12.56 Generated: 79445
% 12.16/12.56 Kept: 19658
% 12.16/12.56 Inuse: 619
% 12.16/12.56 Deleted: 33
% 12.16/12.56 Deletedinuse: 3
% 12.16/12.56
% 58.75/59.16 Resimplifying clauses:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16 Resimplifying inuse:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16 Resimplifying inuse:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16
% 58.75/59.16 Intermediate Status:
% 58.75/59.16 Generated: 86717
% 58.75/59.16 Kept: 21676
% 58.75/59.16 Inuse: 654
% 58.75/59.16 Deleted: 392
% 58.75/59.16 Deletedinuse: 4
% 58.75/59.16
% 58.75/59.16 Resimplifying inuse:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16 Resimplifying inuse:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16
% 58.75/59.16 Intermediate Status:
% 58.75/59.16 Generated: 100995
% 58.75/59.16 Kept: 24146
% 58.75/59.16 Inuse: 700
% 58.75/59.16 Deleted: 399
% 58.75/59.16 Deletedinuse: 10
% 58.75/59.16
% 58.75/59.16 Resimplifying inuse:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16 Resimplifying inuse:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16
% 58.75/59.16 Intermediate Status:
% 58.75/59.16 Generated: 110422
% 58.75/59.16 Kept: 26221
% 58.75/59.16 Inuse: 740
% 58.75/59.16 Deleted: 400
% 58.75/59.16 Deletedinuse: 11
% 58.75/59.16
% 58.75/59.16 Resimplifying inuse:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16 Resimplifying inuse:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16
% 58.75/59.16 Intermediate Status:
% 58.75/59.16 Generated: 120088
% 58.75/59.16 Kept: 28313
% 58.75/59.16 Inuse: 780
% 58.75/59.16 Deleted: 400
% 58.75/59.16 Deletedinuse: 11
% 58.75/59.16
% 58.75/59.16 Resimplifying inuse:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16 Resimplifying inuse:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16
% 58.75/59.16 Intermediate Status:
% 58.75/59.16 Generated: 128738
% 58.75/59.16 Kept: 30329
% 58.75/59.16 Inuse: 816
% 58.75/59.16 Deleted: 400
% 58.75/59.16 Deletedinuse: 11
% 58.75/59.16
% 58.75/59.16 Resimplifying inuse:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16 Resimplifying inuse:
% 58.75/59.16 Done
% 58.75/59.16
% 58.75/59.16
% 58.75/59.16 Intermediate Status:
% 58.75/59.16 Generated: 138219
% 58.75/59.16 Kept: 34134
% 58.75/59.16 Inuse: 840
% 58.75/59.16 Deleted: 400
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 144552
% 58.75/59.17 Kept: 36140
% 58.75/59.17 Inuse: 861
% 58.75/59.17 Deleted: 400
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 154947
% 58.75/59.17 Kept: 38156
% 58.75/59.17 Inuse: 900
% 58.75/59.17 Deleted: 400
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 188080
% 58.75/59.17 Kept: 40698
% 58.75/59.17 Inuse: 910
% 58.75/59.17 Deleted: 400
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying clauses:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 205371
% 58.75/59.17 Kept: 43445
% 58.75/59.17 Inuse: 920
% 58.75/59.17 Deleted: 770
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 220028
% 58.75/59.17 Kept: 45466
% 58.75/59.17 Inuse: 933
% 58.75/59.17 Deleted: 770
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 229275
% 58.75/59.17 Kept: 48155
% 58.75/59.17 Inuse: 959
% 58.75/59.17 Deleted: 770
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 239755
% 58.75/59.17 Kept: 50279
% 58.75/59.17 Inuse: 990
% 58.75/59.17 Deleted: 770
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 252511
% 58.75/59.17 Kept: 52773
% 58.75/59.17 Inuse: 1015
% 58.75/59.17 Deleted: 770
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 263431
% 58.75/59.17 Kept: 54951
% 58.75/59.17 Inuse: 1045
% 58.75/59.17 Deleted: 770
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 273640
% 58.75/59.17 Kept: 56953
% 58.75/59.17 Inuse: 1064
% 58.75/59.17 Deleted: 770
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 281707
% 58.75/59.17 Kept: 58958
% 58.75/59.17 Inuse: 1089
% 58.75/59.17 Deleted: 770
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 291251
% 58.75/59.17 Kept: 60993
% 58.75/59.17 Inuse: 1115
% 58.75/59.17 Deleted: 770
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying clauses:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 305720
% 58.75/59.17 Kept: 63022
% 58.75/59.17 Inuse: 1136
% 58.75/59.17 Deleted: 1004
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 321554
% 58.75/59.17 Kept: 66586
% 58.75/59.17 Inuse: 1155
% 58.75/59.17 Deleted: 1004
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 332434
% 58.75/59.17 Kept: 71415
% 58.75/59.17 Inuse: 1160
% 58.75/59.17 Deleted: 1004
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 342710
% 58.75/59.17 Kept: 73691
% 58.75/59.17 Inuse: 1165
% 58.75/59.17 Deleted: 1004
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 352320
% 58.75/59.17 Kept: 75960
% 58.75/59.17 Inuse: 1190
% 58.75/59.17 Deleted: 1004
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17
% 58.75/59.17 Intermediate Status:
% 58.75/59.17 Generated: 361024
% 58.75/59.17 Kept: 77963
% 58.75/59.17 Inuse: 1213
% 58.75/59.17 Deleted: 1004
% 58.75/59.17 Deletedinuse: 11
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 58.75/59.17
% 58.75/59.17 Resimplifying inuse:
% 58.75/59.17 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 371689
% 121.00/121.44 Kept: 80073
% 121.00/121.44 Inuse: 1235
% 121.00/121.44 Deleted: 1004
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying clauses:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 401089
% 121.00/121.44 Kept: 83741
% 121.00/121.44 Inuse: 1250
% 121.00/121.44 Deleted: 1178
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 419071
% 121.00/121.44 Kept: 86846
% 121.00/121.44 Inuse: 1260
% 121.00/121.44 Deleted: 1178
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 435909
% 121.00/121.44 Kept: 90112
% 121.00/121.44 Inuse: 1285
% 121.00/121.44 Deleted: 1178
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 471193
% 121.00/121.44 Kept: 93129
% 121.00/121.44 Inuse: 1295
% 121.00/121.44 Deleted: 1178
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 478736
% 121.00/121.44 Kept: 95393
% 121.00/121.44 Inuse: 1315
% 121.00/121.44 Deleted: 1178
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 491691
% 121.00/121.44 Kept: 98112
% 121.00/121.44 Inuse: 1330
% 121.00/121.44 Deleted: 1178
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 510500
% 121.00/121.44 Kept: 101720
% 121.00/121.44 Inuse: 1340
% 121.00/121.44 Deleted: 1178
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying clauses:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 541153
% 121.00/121.44 Kept: 106409
% 121.00/121.44 Inuse: 1350
% 121.00/121.44 Deleted: 1320
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 548643
% 121.00/121.44 Kept: 108413
% 121.00/121.44 Inuse: 1375
% 121.00/121.44 Deleted: 1320
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 563219
% 121.00/121.44 Kept: 111251
% 121.00/121.44 Inuse: 1390
% 121.00/121.44 Deleted: 1320
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 581286
% 121.00/121.44 Kept: 114603
% 121.00/121.44 Inuse: 1400
% 121.00/121.44 Deleted: 1320
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 590819
% 121.00/121.44 Kept: 116668
% 121.00/121.44 Inuse: 1430
% 121.00/121.44 Deleted: 1320
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 600161
% 121.00/121.44 Kept: 118876
% 121.00/121.44 Inuse: 1455
% 121.00/121.44 Deleted: 1320
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 609674
% 121.00/121.44 Kept: 121186
% 121.00/121.44 Inuse: 1480
% 121.00/121.44 Deleted: 1320
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying clauses:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 663430
% 121.00/121.44 Kept: 126338
% 121.00/121.44 Inuse: 1495
% 121.00/121.44 Deleted: 1461
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 676613
% 121.00/121.44 Kept: 128603
% 121.00/121.44 Inuse: 1515
% 121.00/121.44 Deleted: 1461
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 687211
% 121.00/121.44 Kept: 130604
% 121.00/121.44 Inuse: 1536
% 121.00/121.44 Deleted: 1461
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 698628
% 121.00/121.44 Kept: 132967
% 121.00/121.44 Inuse: 1565
% 121.00/121.44 Deleted: 1461
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 710700
% 121.00/121.44 Kept: 135345
% 121.00/121.44 Inuse: 1590
% 121.00/121.44 Deleted: 1461
% 121.00/121.44 Deletedinuse: 11
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 727945
% 121.00/121.44 Kept: 137870
% 121.00/121.44 Inuse: 1619
% 121.00/121.44 Deleted: 1465
% 121.00/121.44 Deletedinuse: 14
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 747412
% 121.00/121.44 Kept: 140764
% 121.00/121.44 Inuse: 1629
% 121.00/121.44 Deleted: 1465
% 121.00/121.44 Deletedinuse: 14
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44 Resimplifying clauses:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 760665
% 121.00/121.44 Kept: 142781
% 121.00/121.44 Inuse: 1635
% 121.00/121.44 Deleted: 2240
% 121.00/121.44 Deletedinuse: 14
% 121.00/121.44
% 121.00/121.44 Resimplifying inuse:
% 121.00/121.44 Done
% 121.00/121.44
% 121.00/121.44
% 121.00/121.44 Intermediate Status:
% 121.00/121.44 Generated: 785174
% 121.00/121.44 Kept: 145559
% 121.00/121.44 Inuse: 1644
% 121.00/121.44 Deleted: 2241
% 121.00/121.44 Deletedinuse: 15
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 796522
% 208.69/209.12 Kept: 147653
% 208.69/209.12 Inuse: 1664
% 208.69/209.12 Deleted: 2241
% 208.69/209.12 Deletedinuse: 15
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 807791
% 208.69/209.12 Kept: 149752
% 208.69/209.12 Inuse: 1684
% 208.69/209.12 Deleted: 2241
% 208.69/209.12 Deletedinuse: 15
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 819244
% 208.69/209.12 Kept: 152135
% 208.69/209.12 Inuse: 1699
% 208.69/209.12 Deleted: 2241
% 208.69/209.12 Deletedinuse: 15
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 827758
% 208.69/209.12 Kept: 154243
% 208.69/209.12 Inuse: 1714
% 208.69/209.12 Deleted: 2241
% 208.69/209.12 Deletedinuse: 15
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 835569
% 208.69/209.12 Kept: 156368
% 208.69/209.12 Inuse: 1717
% 208.69/209.12 Deleted: 2241
% 208.69/209.12 Deletedinuse: 15
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 842805
% 208.69/209.12 Kept: 158467
% 208.69/209.12 Inuse: 1718
% 208.69/209.12 Deleted: 2241
% 208.69/209.12 Deletedinuse: 15
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 852892
% 208.69/209.12 Kept: 160847
% 208.69/209.12 Inuse: 1734
% 208.69/209.12 Deleted: 2241
% 208.69/209.12 Deletedinuse: 15
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 863518
% 208.69/209.12 Kept: 162976
% 208.69/209.12 Inuse: 1754
% 208.69/209.12 Deleted: 2241
% 208.69/209.12 Deletedinuse: 15
% 208.69/209.12
% 208.69/209.12 Resimplifying clauses:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 872953
% 208.69/209.12 Kept: 165513
% 208.69/209.12 Inuse: 1764
% 208.69/209.12 Deleted: 2528
% 208.69/209.12 Deletedinuse: 15
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 882437
% 208.69/209.12 Kept: 168118
% 208.69/209.12 Inuse: 1774
% 208.69/209.12 Deleted: 2528
% 208.69/209.12 Deletedinuse: 15
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 893016
% 208.69/209.12 Kept: 170412
% 208.69/209.12 Inuse: 1794
% 208.69/209.12 Deleted: 2529
% 208.69/209.12 Deletedinuse: 16
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 918973
% 208.69/209.12 Kept: 176537
% 208.69/209.12 Inuse: 1808
% 208.69/209.12 Deleted: 2529
% 208.69/209.12 Deletedinuse: 16
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 929452
% 208.69/209.12 Kept: 178775
% 208.69/209.12 Inuse: 1819
% 208.69/209.12 Deleted: 2529
% 208.69/209.12 Deletedinuse: 16
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 941910
% 208.69/209.12 Kept: 181344
% 208.69/209.12 Inuse: 1834
% 208.69/209.12 Deleted: 2529
% 208.69/209.12 Deletedinuse: 16
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying clauses:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 953671
% 208.69/209.12 Kept: 183682
% 208.69/209.12 Inuse: 1849
% 208.69/209.12 Deleted: 2871
% 208.69/209.12 Deletedinuse: 16
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 965178
% 208.69/209.12 Kept: 186441
% 208.69/209.12 Inuse: 1864
% 208.69/209.12 Deleted: 2871
% 208.69/209.12 Deletedinuse: 16
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 988336
% 208.69/209.12 Kept: 189493
% 208.69/209.12 Inuse: 1879
% 208.69/209.12 Deleted: 2871
% 208.69/209.12 Deletedinuse: 16
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 1006996
% 208.69/209.12 Kept: 191532
% 208.69/209.12 Inuse: 1884
% 208.69/209.12 Deleted: 2871
% 208.69/209.12 Deletedinuse: 16
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 1018402
% 208.69/209.12 Kept: 193926
% 208.69/209.12 Inuse: 1904
% 208.69/209.12 Deleted: 2871
% 208.69/209.12 Deletedinuse: 16
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 1059507
% 208.69/209.12 Kept: 198654
% 208.69/209.12 Inuse: 1914
% 208.69/209.12 Deleted: 2871
% 208.69/209.12 Deletedinuse: 16
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 1069660
% 208.69/209.12 Kept: 201249
% 208.69/209.12 Inuse: 1929
% 208.69/209.12 Deleted: 2871
% 208.69/209.12 Deletedinuse: 16
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying clauses:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 1079646
% 208.69/209.12 Kept: 203587
% 208.69/209.12 Inuse: 1944
% 208.69/209.12 Deleted: 3334
% 208.69/209.12 Deletedinuse: 16
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 1087521
% 208.69/209.12 Kept: 205789
% 208.69/209.12 Inuse: 1959
% 208.69/209.12 Deleted: 3335
% 208.69/209.12 Deletedinuse: 17
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 1101041
% 208.69/209.12 Kept: 208034
% 208.69/209.12 Inuse: 1994
% 208.69/209.12 Deleted: 3336
% 208.69/209.12 Deletedinuse: 18
% 208.69/209.12
% 208.69/209.12 Resimplifying inuse:
% 208.69/209.12 Done
% 208.69/209.12
% 208.69/209.12
% 208.69/209.12 Intermediate Status:
% 208.69/209.12 Generated: 1115Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------