TSTP Solution File: SWV690-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV690-1 : 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 16:27:48 EDT 2022
% Result : Unsatisfiable 32.52s 32.93s
% Output : Refutation 32.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWV690-1 : TPTP v8.1.0. Released v4.1.0.
% 0.09/0.12 % Command : bliksem %s
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Wed Jun 15 19:54:33 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.87/1.24 *** allocated 10000 integers for termspace/termends
% 0.87/1.24 *** allocated 10000 integers for clauses
% 0.87/1.24 *** allocated 10000 integers for justifications
% 0.87/1.24 *** allocated 15000 integers for termspace/termends
% 0.87/1.24 *** allocated 22500 integers for termspace/termends
% 0.87/1.24 Bliksem 1.12
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 Automatic Strategy Selection
% 0.87/1.24
% 0.87/1.24 Clauses:
% 0.87/1.24 [
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.24 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.24 ), X ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.87/1.24 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ],
% 0.87/1.24 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.87/1.24 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.87/1.24 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 0.87/1.24 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.87/1.24 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.87/1.24 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 0.87/1.24 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.87/1.24 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 0.87/1.24 , Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.87/1.24 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.87/1.24 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) )
% 0.87/1.24 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 0.87/1.24 , 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.87/1.24 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.87/1.24 X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.87/1.24 X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.87/1.24 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.87/1.24 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.87/1.24 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.24 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.87/1.24 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 0.87/1.24 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 0.87/1.24 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 0.87/1.24 'c_lessequals'( T, X, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 0.87/1.24 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat'
% 0.87/1.24 ), 'tc_nat' ) ],
% 0.87/1.24 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.24 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.24 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.24 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ =( 'c_Orderings_Oord__class_Omin'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.24 , T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Z, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.24 , T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Z, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.24 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.87/1.24 , X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.87/1.24 , T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.87/1.24 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.87/1.24 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.87/1.24 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.87/1.24 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.87/1.24 , X ), W, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 0.87/1.24 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.87/1.24 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.87/1.24 , X ), T, X ), W, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.87/1.24 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.87/1.24 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 0.87/1.24 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.87/1.24 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z,
% 0.87/1.24 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.87/1.24 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.24 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.24 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.24 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.87/1.24 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.87/1.24 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 0.87/1.24 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.87/1.24 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.87/1.24 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 0.87/1.24 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 0.87/1.24 , X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.87/1.24 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.87/1.24 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.87/1.24 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.87/1.24 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.87/1.24 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.24 , Y, X ), X ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.24 , Z, X ), X ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.24 , Z, X ), X ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.24 Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.87/1.24 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 0.87/1.24 Y, X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.24 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.24 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.87/1.24 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.87/1.24 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.87/1.24 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 0.87/1.24 ), X ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.87/1.24 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 0.87/1.24 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 0.87/1.24 ],
% 0.87/1.24 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.87/1.24 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.24 , Y, X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.24 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.24 , Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.24 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.87/1.24 , T, X ), X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.24 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.87/1.24 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.24 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.24 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.24 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.87/1.24 , X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.87/1.24 , X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.24 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.24 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 0.87/1.24 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 0.87/1.24 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.24 , Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.24 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.87/1.24 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.24 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.87/1.24 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.87/1.24 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.24 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.24 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.24 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.87/1.24 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 0.87/1.24 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.24 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.24 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 0.87/1.24 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 0.87/1.24 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 0.87/1.24 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.87/1.24 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.24 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.24 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.24 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 0.87/1.24 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.24 T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.87/1.24 X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.24 T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.24 X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.87/1.24 T, X ), X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.24 X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.87/1.24 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.87/1.24 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.87/1.24 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.87/1.24 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 0.87/1.24 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.87/1.24 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.87/1.24 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 0.87/1.24 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.24 Y, 'tc_nat' ), 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.87/1.24 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.24 Y, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.87/1.24 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ],
% 0.87/1.24 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.87/1.24 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.87/1.24 X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 0.87/1.24 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X
% 0.87/1.24 ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y
% 0.87/1.24 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.24 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.87/1.24 X ) ) ), =( Z, T ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.87/1.24 X ) ) ), =( Z, T ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.87/1.24 X ) ) ), =( Y, T ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.24 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.87/1.24 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.24 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.87/1.24 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.24 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.87/1.24 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 0.87/1.24 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.24 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X )
% 0.87/1.24 , 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.24 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.24 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.24 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ) ), =( Y, Z ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.87/1.24 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.24 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.24 , T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Z, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 0.87/1.24 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 0.87/1.24 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.87/1.24 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.87/1.24 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 0.87/1.24 Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.87/1.24 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.24 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.87/1.24 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 X ), X ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.87/1.24 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 0.87/1.24 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 0.87/1.24 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 0.87/1.24 , X, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 0.87/1.24 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.24 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.24 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.87/1.24 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.87/1.24 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat' ) ) )
% 0.87/1.24 ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 0.87/1.24 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.87/1.24 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 0.87/1.24 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 0.87/1.24 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.87/1.24 , X ), X ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.87/1.24 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.87/1.24 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.87/1.24 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.87/1.24 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 0.87/1.24 X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 0.87/1.24 X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.24 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.87/1.24 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' )
% 0.87/1.24 ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.87/1.24 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.87/1.24 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 0.87/1.24 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.87/1.24 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.87/1.24 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.87/1.24 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.87/1.24 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z,
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.87/1.24 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, U,
% 0.87/1.24 X ), X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.24 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Z
% 0.87/1.24 , Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 0.87/1.24 , Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 0.87/1.24 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.87/1.24 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.87/1.24 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.87/1.24 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.87/1.24 , X ), W, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 X ) ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 0.87/1.24 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 0.87/1.24 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.87/1.24 X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.87/1.24 X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.87/1.24 X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.24 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.87/1.24 , T, X ), X ), T, X ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.24 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.24 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.87/1.24 T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.87/1.24 T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.87/1.24 T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.87/1.24 T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.24 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.24 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.87/1.24 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.87/1.24 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 0.87/1.24 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 0.87/1.24 Z, X ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 0.87/1.24 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 0.87/1.24 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.87/1.24 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.87/1.24 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.87/1.24 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.87/1.24 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 0.87/1.24 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.87/1.24 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.87/1.24 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.87/1.24 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.87/1.24 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), Y,
% 0.87/1.24 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.87/1.24 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.87/1.24 , T ), =( X, Z ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.87/1.24 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.87/1.24 , T ), =( X, Z ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.24 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.24 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.24 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.24 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.87/1.24 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 0.87/1.24 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 0.87/1.24 X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.87/1.24 , X ), X ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.24 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.24 ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.87/1.24 ],
% 0.87/1.24 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.24 ), 'tc_nat' ), X ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.24 , X, 'tc_nat' ), X ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.87/1.24 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.24 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.24 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.87/1.24 X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Z, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Z, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.87/1.24 X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.24 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.24 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.24 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.87/1.24 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.24 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.24 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.87/1.24 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.24 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.24 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.24 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.24 Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.87/1.24 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.87/1.24 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.87/1.24 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.24 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.87/1.24 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( T
% 0.87/1.24 , Z, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z
% 0.87/1.24 , T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.24 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.87/1.24 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.87/1.24 , X ), W, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.87/1.24 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.87/1.24 W, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.87/1.24 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.87/1.24 , X ), T, X ), W, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.87/1.24 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.87/1.24 W, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.24 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.87/1.24 , Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.87/1.24 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.87/1.24 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.87/1.24 X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ),
% 0.87/1.24 T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.87/1.24 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.87/1.24 , T, X ), X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.24 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.24 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 0.87/1.24 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.24 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.87/1.24 ), Y ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 ) ), =( Y, Z ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 ) ), =( Y, Z ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.24 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.87/1.24 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.24 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.87/1.24 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.24 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.87/1.24 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.87/1.24 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.87/1.24 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.87/1.24 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.87/1.24 , U, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.87/1.24 ), Y ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.87/1.24 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.87/1.24 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.87/1.24 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.87/1.24 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 , X ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 0.87/1.24 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.24 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.87/1.24 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 0.87/1.24 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.87/1.24 , Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.24 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.24 Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.24 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 0.87/1.24 ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 0.87/1.24 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.87/1.24 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.24 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 0.87/1.24 ), X, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.87/1.24 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 0.87/1.24 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.87/1.24 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.24 , Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 0.87/1.24 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.87/1.24 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.87/1.24 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.87/1.24 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 0.87/1.24 , Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X
% 0.87/1.24 ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 0.87/1.24 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.24 ) ), X, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.24 ) ), X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 0.87/1.24 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.87/1.24 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.87/1.24 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.87/1.24 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 0.87/1.24 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.87/1.24 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 0.87/1.24 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.87/1.24 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 0.87/1.24 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 0.87/1.24 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.24 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.24 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.24 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.87/1.24 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.87/1.24 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.24 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.87/1.24 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Y, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.24 , T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.24 , T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Y, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.24 Y, X ), X ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 0.87/1.24 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.87/1.24 'c_lessequals'( Z, Y, X ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 X, T, 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.24 ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.24 ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.87/1.24 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.87/1.24 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.87/1.24 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.87/1.24 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.87/1.24 Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.87/1.24 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.87/1.24 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 0.87/1.24 , Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.87/1.24 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.87/1.24 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.87/1.24 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.87/1.24 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.87/1.24 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.87/1.24 , 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 0.87/1.24 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.87/1.24 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.87/1.24 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.87/1.24 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.87/1.24 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 0.87/1.24 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.87/1.24 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.24 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.87/1.24 , 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat'
% 0.87/1.24 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.87/1.24 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.87/1.24 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.87/1.24 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.87/1.24 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.24 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 0.87/1.24 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 0.87/1.24 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.87/1.24 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.87/1.24 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 0.87/1.24 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.87/1.24 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.87/1.24 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 0.87/1.24 , 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.87/1.24 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.24 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.24 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.24 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.24 , Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.24 , Y, X ) ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.87/1.24 ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.24 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.24 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.24 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.24 ), =( Z, Y ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( 'v_i', X,
% 0.87/1.24 'tc_nat' ), 'v_n', 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'v_i', 'v_n', 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.24 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.87/1.24 , T, X ) ) ), =( Z, T ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.24 , T, X ) ) ), =( Y, Z ) ],
% 0.87/1.24 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.24 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'v_k', 'v_n', 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( 'v_k',
% 0.87/1.24 'v_i', 'tc_nat' ), 'v_n', 'tc_nat' ) ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.87/1.24 ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.87/1.24 ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.87/1.24 ],
% 0.87/1.24 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.87/1.25 [ 'class_Orderings_Oorder'( 'tc_nat' ) ]
% 1.76/2.21 ] .
% 1.76/2.21
% 1.76/2.21
% 1.76/2.21 percentage equality = 0.214819, percentage horn = 0.889051
% 1.76/2.21 This is a problem with some equality
% 1.76/2.21
% 1.76/2.21
% 1.76/2.21
% 1.76/2.21 Options Used:
% 1.76/2.21
% 1.76/2.21 useres = 1
% 1.76/2.21 useparamod = 1
% 1.76/2.21 useeqrefl = 1
% 1.76/2.21 useeqfact = 1
% 1.76/2.21 usefactor = 1
% 1.76/2.21 usesimpsplitting = 0
% 1.76/2.21 usesimpdemod = 5
% 1.76/2.21 usesimpres = 3
% 1.76/2.21
% 1.76/2.21 resimpinuse = 1000
% 1.76/2.21 resimpclauses = 20000
% 1.76/2.21 substype = eqrewr
% 1.76/2.21 backwardsubs = 1
% 1.76/2.21 selectoldest = 5
% 1.76/2.21
% 1.76/2.21 litorderings [0] = split
% 1.76/2.21 litorderings [1] = extend the termordering, first sorting on arguments
% 1.76/2.21
% 1.76/2.21 termordering = kbo
% 1.76/2.21
% 1.76/2.21 litapriori = 0
% 1.76/2.21 termapriori = 1
% 1.76/2.21 litaposteriori = 0
% 1.76/2.21 termaposteriori = 0
% 1.76/2.21 demodaposteriori = 0
% 1.76/2.21 ordereqreflfact = 0
% 1.76/2.21
% 1.76/2.21 litselect = negord
% 1.76/2.21
% 1.76/2.21 maxweight = 15
% 1.76/2.21 maxdepth = 30000
% 1.76/2.21 maxlength = 115
% 1.76/2.21 maxnrvars = 195
% 1.76/2.21 excuselevel = 1
% 1.76/2.21 increasemaxweight = 1
% 1.76/2.21
% 1.76/2.21 maxselected = 10000000
% 1.76/2.21 maxnrclauses = 10000000
% 1.76/2.21
% 1.76/2.21 showgenerated = 0
% 1.76/2.21 showkept = 0
% 1.76/2.21 showselected = 0
% 1.76/2.21 showdeleted = 0
% 1.76/2.21 showresimp = 1
% 1.76/2.21 showstatus = 2000
% 1.76/2.21
% 1.76/2.21 prologoutput = 1
% 1.76/2.21 nrgoals = 5000000
% 1.76/2.21 totalproof = 1
% 1.76/2.21
% 1.76/2.21 Symbols occurring in the translation:
% 1.76/2.21
% 1.76/2.21 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.76/2.21 . [1, 2] (w:1, o:106, a:1, s:1, b:0),
% 1.76/2.21 ! [4, 1] (w:0, o:47, a:1, s:1, b:0),
% 1.76/2.21 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.76/2.21 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.76/2.21 'class_Ring__and__Field_Oordered__semiring__strict' [40, 1] (w:1, o:
% 1.76/2.21 57, a:1, s:1, b:0),
% 1.76/2.21 'c_HOL_Ozero__class_Ozero' [41, 1] (w:1, o:58, a:1, s:1, b:0),
% 1.76/2.21 'c_HOL_Otimes__class_Otimes' [44, 3] (w:1, o:134, a:1, s:1, b:0),
% 1.76/2.21 'c_HOL_Oord__class_Oless' [45, 3] (w:1, o:135, a:1, s:1, b:0),
% 1.76/2.21 'c_Suc' [47, 1] (w:1, o:59, a:1, s:1, b:0),
% 1.76/2.21 'tc_nat' [49, 0] (w:1, o:18, a:1, s:1, b:0),
% 1.76/2.21 'c_HOL_Oplus__class_Oplus' [50, 3] (w:1, o:136, a:1, s:1, b:0),
% 1.76/2.21 'class_Ring__and__Field_Oordered__ring__strict' [51, 1] (w:1, o:56
% 1.76/2.21 , a:1, s:1, b:0),
% 1.76/2.21 'c_Ring__and__Field_Odvd__class_Odvd' [54, 3] (w:1, o:137, a:1, s:1
% 1.76/2.21 , b:0),
% 1.76/2.21 'class_OrderedGroup_Opordered__comm__monoid__add' [55, 1] (w:1, o:61
% 1.76/2.21 , a:1, s:1, b:0),
% 1.76/2.21 'c_lessequals' [56, 3] (w:1, o:138, a:1, s:1, b:0),
% 1.76/2.21 'c_HOL_Ominus__class_Ominus' [60, 3] (w:1, o:139, a:1, s:1, b:0),
% 1.76/2.21 'class_Ring__and__Field_Ocomm__semiring__1' [61, 1] (w:1, o:64, a:1
% 1.76/2.21 , s:1, b:0),
% 1.76/2.21 'class_OrderedGroup_Opordered__ab__group__add__abs' [66, 1] (w:1, o:
% 1.76/2.21 65, a:1, s:1, b:0),
% 1.76/2.21 'c_HOL_Oabs__class_Oabs' [67, 2] (w:1, o:131, a:1, s:1, b:0),
% 1.76/2.21 'class_Orderings_Olinorder' [68, 1] (w:1, o:66, a:1, s:1, b:0),
% 1.76/2.21 'c_Orderings_Oord__class_Omin' [69, 3] (w:1, o:140, a:1, s:1, b:0),
% 1.76/2.21 'class_OrderedGroup_Olordered__ab__group__add__abs' [70, 1] (w:1, o:
% 1.76/2.21 67, a:1, s:1, b:0),
% 1.76/2.21 'class_Orderings_Oorder' [72, 1] (w:1, o:68, a:1, s:1, b:0),
% 1.76/2.21 'class_Ring__and__Field_Oidom' [74, 1] (w:1, o:69, a:1, s:1, b:0),
% 1.76/2.21 'class_OrderedGroup_Opordered__ab__semigroup__add' [75, 1] (w:1, o:70
% 1.76/2.21 , a:1, s:1, b:0),
% 1.76/2.21 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [76, 1]
% 1.76/2.21 (w:1, o:71, a:1, s:1, b:0),
% 1.76/2.21 'class_Ring__and__Field_Oordered__idom' [77, 1] (w:1, o:72, a:1, s:1
% 1.76/2.21 , b:0),
% 1.76/2.21 'class_Ring__and__Field_Opordered__ring__abs' [78, 1] (w:1, o:76, a:1
% 1.76/2.21 , s:1, b:0),
% 1.76/2.21 'class_OrderedGroup_Oab__semigroup__idem__mult' [79, 1] (w:1, o:77
% 1.76/2.21 , a:1, s:1, b:0),
% 1.76/2.21 'c_Divides_Odiv__class_Omod' [80, 3] (w:1, o:141, a:1, s:1, b:0),
% 1.76/2.21 'c_Parity_Oeven__odd__class_Oeven' [81, 2] (w:1, o:132, a:1, s:1, b:0
% 1.76/2.21 ),
% 1.76/2.21 'class_Divides_Osemiring__div' [82, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.76/2.21 'class_OrderedGroup_Olordered__ab__group__add' [83, 1] (w:1, o:80, a:
% 1.76/2.21 1, s:1, b:0),
% 1.76/2.21 'class_Ring__and__Field_Oring__no__zero__divisors' [84, 1] (w:1, o:81
% 1.76/2.21 , a:1, s:1, b:0),
% 1.76/2.21 'class_Ring__and__Field_Ono__zero__divisors' [85, 1] (w:1, o:55, a:1
% 1.76/2.21 , s:1, b:0),
% 1.76/2.21 'class_Ring__and__Field_Oordered__semiring' [88, 1] (w:1, o:73, a:1
% 1.76/2.21 , s:1, b:0),
% 1.76/2.21 'class_Int_Onumber__ring' [89, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.76/2.21 'class_Nat_Osemiring__char__0' [90, 1] (w:1, o:60, a:1, s:1, b:0),
% 20.95/21.37 'c_Nat_Osemiring__1__class_Oof__nat' [91, 2] (w:1, o:133, a:1, s:1
% 20.95/21.37 , b:0),
% 20.95/21.37 'class_Ring__and__Field_Opordered__ring' [92, 1] (w:1, o:83, a:1, s:1
% 20.95/21.37 , b:0),
% 20.95/21.37 'class_OrderedGroup_Ocomm__monoid__add' [95, 1] (w:1, o:84, a:1, s:1
% 20.95/21.37 , b:0),
% 20.95/21.37 'class_Ring__and__Field_Oring' [96, 1] (w:1, o:85, a:1, s:1, b:0),
% 20.95/21.37 'class_Ring__and__Field_Olordered__ring' [98, 1] (w:1, o:86, a:1, s:1
% 20.95/21.37 , b:0),
% 20.95/21.37 'class_Ring__and__Field_Odvd' [99, 1] (w:1, o:88, a:1, s:1, b:0),
% 20.95/21.37 'class_Ring__and__Field_Oordered__semidom' [100, 1] (w:1, o:74, a:1
% 20.95/21.37 , s:1, b:0),
% 20.95/21.37 'class_Ring__and__Field_Omult__mono1' [103, 1] (w:1, o:52, a:1, s:1
% 20.95/21.37 , b:0),
% 20.95/21.37 'class_Ring__and__Field_Omult__mono' [104, 1] (w:1, o:53, a:1, s:1
% 20.95/21.37 , b:0),
% 20.95/21.37 'class_Ring__and__Field_Osemiring__1' [105, 1] (w:1, o:90, a:1, s:1
% 20.95/21.37 , b:0),
% 20.95/21.37 'class_Ring__and__Field_Ocomm__ring' [106, 1] (w:1, o:62, a:1, s:1
% 20.95/21.37 , b:0),
% 20.95/21.37 'class_Ring__and__Field_Opordered__cancel__semiring' [109, 1] (w:1
% 20.95/21.37 , o:91, a:1, s:1, b:0),
% 20.95/21.37 'class_OrderedGroup_Oab__semigroup__mult' [110, 1] (w:1, o:92, a:1
% 20.95/21.37 , s:1, b:0),
% 20.95/21.37 'class_RealVector_Oreal__normed__algebra' [111, 1] (w:1, o:93, a:1
% 20.95/21.37 , s:1, b:0),
% 20.95/21.37 'class_Ring__and__Field_Ocomm__semiring' [115, 1] (w:1, o:87, a:1, s:
% 20.95/21.37 1, b:0),
% 20.95/21.37 'class_Ring__and__Field_Opordered__semiring' [117, 1] (w:1, o:94, a:1
% 20.95/21.37 , s:1, b:0),
% 20.95/21.37 'class_OrderedGroup_Ocancel__ab__semigroup__add' [118, 1] (w:1, o:95
% 20.95/21.37 , a:1, s:1, b:0),
% 20.95/21.37 'class_OrderedGroup_Ocancel__semigroup__add' [119, 1] (w:1, o:96, a:1
% 20.95/21.37 , s:1, b:0),
% 20.95/21.37 'class_OrderedGroup_Oab__group__add' [120, 1] (w:1, o:97, a:1, s:1
% 20.95/21.37 , b:0),
% 20.95/21.37 'class_OrderedGroup_Oab__semigroup__add' [121, 1] (w:1, o:98, a:1, s:
% 20.95/21.37 1, b:0),
% 20.95/21.37 'class_Ring__and__Field_Osemiring' [122, 1] (w:1, o:99, a:1, s:1, b:0
% 20.95/21.37 ),
% 20.95/21.37 'class_Ring__and__Field_Oordered__comm__semiring__strict' [123, 1]
% 20.95/21.37 (w:1, o:75, a:1, s:1, b:0),
% 20.95/21.37 'class_OrderedGroup_Omonoid__add' [126, 1] (w:1, o:100, a:1, s:1, b:0
% 20.95/21.37 ),
% 20.95/21.37 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [127, 1]
% 20.95/21.37 (w:1, o:101, a:1, s:1, b:0),
% 20.95/21.37 'class_Orderings_Opreorder' [128, 1] (w:1, o:102, a:1, s:1, b:0),
% 20.95/21.37 'class_Divides_Oring__div' [129, 1] (w:1, o:78, a:1, s:1, b:0),
% 20.95/21.37 'class_OrderedGroup_Opordered__ab__group__add' [130, 1] (w:1, o:103
% 20.95/21.37 , a:1, s:1, b:0),
% 20.95/21.37 'class_Ring__and__Field_Ocomm__ring__1' [133, 1] (w:1, o:63, a:1, s:1
% 20.95/21.37 , b:0),
% 20.95/21.37 'class_OrderedGroup_Ogroup__add' [134, 1] (w:1, o:104, a:1, s:1, b:0)
% 20.95/21.37 ,
% 20.95/21.37 'class_Ring__and__Field_Omult__zero' [135, 1] (w:1, o:54, a:1, s:1
% 20.95/21.37 , b:0),
% 20.95/21.37 'class_Ring__and__Field_Oabs__if' [137, 1] (w:1, o:105, a:1, s:1, b:0
% 20.95/21.37 ),
% 20.95/21.37 'class_Ring__and__Field_Oring__1' [138, 1] (w:1, o:89, a:1, s:1, b:0)
% 20.95/21.37 ,
% 20.95/21.37 'v_i' [139, 0] (w:1, o:44, a:1, s:1, b:0),
% 20.95/21.37 'v_n' [140, 0] (w:1, o:45, a:1, s:1, b:0),
% 20.95/21.37 'v_k' [141, 0] (w:1, o:46, a:1, s:1, b:0).
% 20.95/21.37
% 20.95/21.37
% 20.95/21.37 Starting Search:
% 20.95/21.37
% 20.95/21.37 Resimplifying inuse:
% 20.95/21.37 Done
% 20.95/21.37
% 20.95/21.37
% 20.95/21.37 Intermediate Status:
% 20.95/21.37 Generated: 5827
% 20.95/21.37 Kept: 2013
% 20.95/21.37 Inuse: 141
% 20.95/21.37 Deleted: 8
% 20.95/21.37 Deletedinuse: 0
% 20.95/21.37
% 20.95/21.37 Resimplifying inuse:
% 20.95/21.37 Done
% 20.95/21.37
% 20.95/21.37 Resimplifying inuse:
% 20.95/21.37 Done
% 20.95/21.37
% 20.95/21.37
% 20.95/21.37 Intermediate Status:
% 20.95/21.37 Generated: 15202
% 20.95/21.37 Kept: 4023
% 20.95/21.37 Inuse: 291
% 20.95/21.37 Deleted: 13
% 20.95/21.37 Deletedinuse: 0
% 20.95/21.37
% 20.95/21.37 Resimplifying inuse:
% 20.95/21.37 Done
% 20.95/21.37
% 20.95/21.37 Resimplifying inuse:
% 20.95/21.37 Done
% 20.95/21.37
% 20.95/21.37
% 20.95/21.37 Intermediate Status:
% 20.95/21.37 Generated: 27101
% 20.95/21.37 Kept: 6097
% 20.95/21.37 Inuse: 313
% 20.95/21.37 Deleted: 13
% 20.95/21.37 Deletedinuse: 0
% 20.95/21.37
% 20.95/21.37 Resimplifying inuse:
% 20.95/21.37 Done
% 20.95/21.37
% 20.95/21.37 Resimplifying inuse:
% 20.95/21.37 Done
% 20.95/21.37
% 20.95/21.37
% 20.95/21.37 Intermediate Status:
% 20.95/21.37 Generated: 38776
% 20.95/21.37 Kept: 8407
% 20.95/21.37 Inuse: 348
% 20.95/21.37 Deleted: 19
% 20.95/21.37 Deletedinuse: 6
% 20.95/21.37
% 20.95/21.37 Resimplifying inuse:
% 20.95/21.37 Done
% 20.95/21.37
% 20.95/21.37 Resimplifying inuse:
% 20.95/21.37 Done
% 20.95/21.37
% 20.95/21.37
% 20.95/21.37 Intermediate Status:
% 20.95/21.37 Generated: 48112
% 20.95/21.37 Kept: 10520
% 20.95/21.37 Inuse: 387
% 20.95/21.37 Deleted: 20
% 20.95/21.37 Deletedinuse: 6
% 20.95/21.37
% 20.95/21.37 Resimplifying inuse:
% 20.95/21.37 Done
% 20.95/21.37
% 20.95/21.37 Resimplifying inuse:
% 20.95/21.37 Done
% 20.95/21.37
% 20.95/21.37
% 20.95/21.37 Intermediate Status:
% 20.95/21.37 Generated: 57283
% 20.95/21.37 Kept: 12538
% 20.95/21.37 Inuse: 409
% 20.95/21.37 Deleted: 20
% 20.95/21.37 Deletedinuse: 6
% 20.95/21.37
% 20.95/21.37 Resimplifying inuse:
% 20.95/21.37 Done
% 20.95/21.37
% 20.95/21.37
% 20.95/21.37 Intermediate Status:
% 20.95/21.37 Generated: 66924
% 20.95/21.37 Kept: 14715
% 20.95/21.37 Inuse: 450
% 20.95/21.37 Deleted: 22
% 20.95/21.37 Deletedinuse: 6
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 76187
% 32.52/32.93 Kept: 16717
% 32.52/32.93 Inuse: 498
% 32.52/32.93 Deleted: 22
% 32.52/32.93 Deletedinuse: 6
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 86616
% 32.52/32.93 Kept: 18717
% 32.52/32.93 Inuse: 542
% 32.52/32.93 Deleted: 22
% 32.52/32.93 Deletedinuse: 6
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying clauses:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 97915
% 32.52/32.93 Kept: 21165
% 32.52/32.93 Inuse: 598
% 32.52/32.93 Deleted: 912
% 32.52/32.93 Deletedinuse: 7
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 111846
% 32.52/32.93 Kept: 23166
% 32.52/32.93 Inuse: 663
% 32.52/32.93 Deleted: 913
% 32.52/32.93 Deletedinuse: 7
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 125368
% 32.52/32.93 Kept: 25176
% 32.52/32.93 Inuse: 713
% 32.52/32.93 Deleted: 914
% 32.52/32.93 Deletedinuse: 8
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 153121
% 32.52/32.93 Kept: 27369
% 32.52/32.93 Inuse: 722
% 32.52/32.93 Deleted: 914
% 32.52/32.93 Deletedinuse: 8
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 166338
% 32.52/32.93 Kept: 29468
% 32.52/32.93 Inuse: 742
% 32.52/32.93 Deleted: 914
% 32.52/32.93 Deletedinuse: 8
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 181735
% 32.52/32.93 Kept: 31550
% 32.52/32.93 Inuse: 777
% 32.52/32.93 Deleted: 914
% 32.52/32.93 Deletedinuse: 8
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 204047
% 32.52/32.93 Kept: 33746
% 32.52/32.93 Inuse: 787
% 32.52/32.93 Deleted: 914
% 32.52/32.93 Deletedinuse: 8
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 218267
% 32.52/32.93 Kept: 35816
% 32.52/32.93 Inuse: 830
% 32.52/32.93 Deleted: 916
% 32.52/32.93 Deletedinuse: 8
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 233380
% 32.52/32.93 Kept: 37838
% 32.52/32.93 Inuse: 883
% 32.52/32.93 Deleted: 919
% 32.52/32.93 Deletedinuse: 9
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 251421
% 32.52/32.93 Kept: 39941
% 32.52/32.93 Inuse: 927
% 32.52/32.93 Deleted: 923
% 32.52/32.93 Deletedinuse: 12
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying clauses:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 263897
% 32.52/32.93 Kept: 41942
% 32.52/32.93 Inuse: 954
% 32.52/32.93 Deleted: 2229
% 32.52/32.93 Deletedinuse: 13
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 284073
% 32.52/32.93 Kept: 45035
% 32.52/32.93 Inuse: 992
% 32.52/32.93 Deleted: 2229
% 32.52/32.93 Deletedinuse: 13
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 304817
% 32.52/32.93 Kept: 47074
% 32.52/32.93 Inuse: 1002
% 32.52/32.93 Deleted: 2233
% 32.52/32.93 Deletedinuse: 17
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 325737
% 32.52/32.93 Kept: 49085
% 32.52/32.93 Inuse: 1014
% 32.52/32.93 Deleted: 2233
% 32.52/32.93 Deletedinuse: 17
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 343546
% 32.52/32.93 Kept: 51118
% 32.52/32.93 Inuse: 1043
% 32.52/32.93 Deleted: 2233
% 32.52/32.93 Deletedinuse: 17
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 355812
% 32.52/32.93 Kept: 53131
% 32.52/32.93 Inuse: 1077
% 32.52/32.93 Deleted: 2236
% 32.52/32.93 Deletedinuse: 20
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 374074
% 32.52/32.93 Kept: 55211
% 32.52/32.93 Inuse: 1101
% 32.52/32.93 Deleted: 2242
% 32.52/32.93 Deletedinuse: 25
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 385444
% 32.52/32.93 Kept: 57406
% 32.52/32.93 Inuse: 1129
% 32.52/32.93 Deleted: 2244
% 32.52/32.93 Deletedinuse: 25
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 407345
% 32.52/32.93 Kept: 60022
% 32.52/32.93 Inuse: 1149
% 32.52/32.93 Deleted: 2244
% 32.52/32.93 Deletedinuse: 25
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying clauses:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 428288
% 32.52/32.93 Kept: 62812
% 32.52/32.93 Inuse: 1184
% 32.52/32.93 Deleted: 3330
% 32.52/32.93 Deletedinuse: 25
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 442215
% 32.52/32.93 Kept: 64828
% 32.52/32.93 Inuse: 1201
% 32.52/32.93 Deleted: 3330
% 32.52/32.93 Deletedinuse: 25
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 464106
% 32.52/32.93 Kept: 67179
% 32.52/32.93 Inuse: 1224
% 32.52/32.93 Deleted: 3330
% 32.52/32.93 Deletedinuse: 25
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 490309
% 32.52/32.93 Kept: 70250
% 32.52/32.93 Inuse: 1239
% 32.52/32.93 Deleted: 3333
% 32.52/32.93 Deletedinuse: 28
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 509302
% 32.52/32.93 Kept: 72987
% 32.52/32.93 Inuse: 1254
% 32.52/32.93 Deleted: 3333
% 32.52/32.93 Deletedinuse: 28
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 527667
% 32.52/32.93 Kept: 75060
% 32.52/32.93 Inuse: 1289
% 32.52/32.93 Deleted: 3333
% 32.52/32.93 Deletedinuse: 28
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 546289
% 32.52/32.93 Kept: 77073
% 32.52/32.93 Inuse: 1321
% 32.52/32.93 Deleted: 3333
% 32.52/32.93 Deletedinuse: 28
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 565949
% 32.52/32.93 Kept: 79223
% 32.52/32.93 Inuse: 1344
% 32.52/32.93 Deleted: 3333
% 32.52/32.93 Deletedinuse: 28
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying clauses:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 583701
% 32.52/32.93 Kept: 81567
% 32.52/32.93 Inuse: 1354
% 32.52/32.93 Deleted: 4100
% 32.52/32.93 Deletedinuse: 31
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 600087
% 32.52/32.93 Kept: 83645
% 32.52/32.93 Inuse: 1389
% 32.52/32.93 Deleted: 4100
% 32.52/32.93 Deletedinuse: 31
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 612064
% 32.52/32.93 Kept: 86776
% 32.52/32.93 Inuse: 1404
% 32.52/32.93 Deleted: 4101
% 32.52/32.93 Deletedinuse: 32
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 636667
% 32.52/32.93 Kept: 89795
% 32.52/32.93 Inuse: 1444
% 32.52/32.93 Deleted: 4106
% 32.52/32.93 Deletedinuse: 37
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Intermediate Status:
% 32.52/32.93 Generated: 655366
% 32.52/32.93 Kept: 91996
% 32.52/32.93 Inuse: 1479
% 32.52/32.93 Deleted: 4108
% 32.52/32.93 Deletedinuse: 39
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93 Resimplifying inuse:
% 32.52/32.93 Done
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 Bliksems!, er is een bewijs:
% 32.52/32.93 % SZS status Unsatisfiable
% 32.52/32.93 % SZS output start Refutation
% 32.52/32.93
% 32.52/32.93 clause( 18, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 32.52/32.93 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 32.52/32.93 )
% 32.52/32.93 .
% 32.52/32.93 clause( 21, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 32.52/32.93 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 96, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.52/32.93 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 97, [ ~(
% 32.52/32.93 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 32.52/32.93 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 32.52/32.93 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 99, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' )
% 32.52/32.93 , Z, 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y
% 32.52/32.93 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 209, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 32.52/32.93 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 261, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.52/32.93 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 339, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 32.52/32.93 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 363, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 377, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 32.52/32.93 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 32.52/32.93 , T ), =( X, Z ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 449, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 32.52/32.93 , Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 453, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 32.52/32.93 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 537, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 32.52/32.93 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 547, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 559, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y )
% 32.52/32.93 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 567, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 615, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.52/32.93 'v_i', X, 'tc_nat' ), 'v_n', 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 620, [ 'c_HOL_Oord__class_Oless'( 'v_k', 'v_n', 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 621, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.52/32.93 'v_k', 'v_i', 'tc_nat' ), 'v_n', 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 623, [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 32.52/32.93 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 639, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 755, [ ~( =( X, Y ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat'
% 32.52/32.93 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 32.52/32.93 , Z ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 758, [ ~( =( X, Y ) ), =( Y, X ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 835, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( =( X,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 843, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( =( Y,
% 32.52/32.93 'c_Suc'( X ) ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 851, [ 'c_HOL_Oord__class_Oless'( X, 'v_n', 'tc_nat' ), ~( =( X,
% 32.52/32.93 'v_k' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 853, [ 'c_HOL_Oord__class_Oless'( 'v_k', 'v_n', X ), ~( =( X,
% 32.52/32.93 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 1878, [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'v_n', X, 'tc_nat' ),
% 32.52/32.93 'v_k' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 1972, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.52/32.93 'tc_nat' ), 'v_n', 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 2030, [ ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'v_k',
% 32.52/32.93 'v_i', 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 32.52/32.93 )
% 32.52/32.93 .
% 32.52/32.93 clause( 2513, [ 'c_lessequals'( 'v_k', 'v_n', 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 4642, [ ~( =( 'c_HOL_Ominus__class_Ominus'( 'v_k', 'v_i', 'tc_nat'
% 32.52/32.93 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 8411, [ ~( =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( 'v_k', 'v_i',
% 32.52/32.93 'tc_nat' ) ), 'v_n' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 9158, [ ~( =( Y, 'v_k' ) ), ~( =( 'c_Suc'(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'v_n', X, 'tc_nat' ) ), 'c_Suc'( Y ) ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 9271, [ ~( =( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( 'v_n', X,
% 32.52/32.93 'tc_nat' ) ), 'c_Suc'( 'v_k' ) ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 14991, [ ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 32.52/32.93 'v_k', 'v_i', 'tc_nat' ) ), 'v_n', 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 15259, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ),
% 32.52/32.93 'c_lessequals'( 'v_k', 'c_HOL_Oplus__class_Oplus'( 'v_n', X, 'tc_nat' ),
% 32.52/32.93 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 32.52/32.93 , 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 20100, [ 'c_lessequals'( 'v_k', 'c_HOL_Oplus__class_Oplus'( 'v_n',
% 32.52/32.93 X, 'tc_nat' ), 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 21452, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( 'v_n', Y,
% 32.52/32.93 'tc_nat' ), 'tc_nat' ), ~( =( 'c_Suc'( 'v_k' ), 'c_Suc'( X ) ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 32724, [ ~( =( 'c_Suc'( Y ), 'c_Suc'( 'v_k' ) ) ), ~(
% 32.52/32.93 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'v_n', X, 'tc_nat' ), Y,
% 32.52/32.93 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 32730, [ ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'v_n', X,
% 32.52/32.93 'tc_nat' ), 'v_k', 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 35451, [ 'c_lessequals'( 'v_n', 'c_Suc'(
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( 'v_k', 'v_i', 'tc_nat' ) ), 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 35616, [ 'c_lessequals'( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 32.52/32.93 'v_k', 'v_i', 'tc_nat' ) ), 'tc_nat' ), ~( =( X, 'v_n' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 41492, [ ~( =( X, 'v_n' ) ), 'c_lessequals'( X,
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( 'v_k', 'v_i', 'tc_nat' ), 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 41809, [ 'c_lessequals'( 'v_n', 'c_HOL_Ominus__class_Ominus'( 'v_k'
% 32.52/32.93 , 'v_i', 'tc_nat' ), 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 46388, [ ~( 'c_lessequals'( 'v_i', 'v_k', 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 47078, [ ~( 'c_HOL_Oord__class_Oless'( 'v_i', 'v_k', 'tc_nat' ) ) ]
% 32.52/32.93 )
% 32.52/32.93 .
% 32.52/32.93 clause( 47079, [ 'c_lessequals'( 'v_k', 'v_i', 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 47132, [ ~( 'c_lessequals'( X, 'v_k', 'tc_nat' ) ), ~( =( X, 'v_i'
% 32.52/32.93 ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 47135, [ ~( 'c_lessequals'( 'c_Suc'( 'v_i' ), 'v_k', 'tc_nat' ) ) ]
% 32.52/32.93 )
% 32.52/32.93 .
% 32.52/32.93 clause( 47245, [ 'c_lessequals'( 'v_k', X, 'tc_nat' ), ~( =( X, 'v_i' ) ) ]
% 32.52/32.93 )
% 32.52/32.93 .
% 32.52/32.93 clause( 48088, [ ~( 'c_lessequals'( X, 'v_k', 'tc_nat' ) ), ~( =( X,
% 32.52/32.93 'c_Suc'( 'v_i' ) ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 50450, [ ~( =( 'v_k', 'v_i' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 50488, [ ~( =( X, 'v_i' ) ), ~( =( 'c_Suc'( 'v_k' ), 'c_Suc'( X ) )
% 32.52/32.93 ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 50496, [ ~( =( 'c_Suc'( 'v_k' ), 'c_Suc'( 'v_i' ) ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 50508, [ ~( =( X, 'c_Suc'( 'v_i' ) ) ), ~( 'c_lessequals'( X,
% 32.52/32.93 'c_Suc'( 'v_k' ), 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 50527, [ ~( 'c_lessequals'( 'c_Suc'( 'v_i' ), 'c_Suc'( 'v_k' ),
% 32.52/32.93 'tc_nat' ) ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 50889, [ 'c_lessequals'( 'c_Suc'( 'v_k' ), 'c_Suc'( 'v_i' ),
% 32.52/32.93 'tc_nat' ) ] )
% 32.52/32.93 .
% 32.52/32.93 clause( 93858, [] )
% 32.52/32.93 .
% 32.52/32.93
% 32.52/32.93
% 32.52/32.93 % SZS output end Refutation
% 32.52/32.93 found a proof!
% 32.52/32.93
% 32.52/32.93 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 32.52/32.93
% 32.52/32.93 initialclauses(
% 32.52/32.93 [ clause( 93860, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.52/32.93 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 32.52/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 32.52/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.52/32.93 , clause( 93861, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.52/32.93 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 32.52/32.93 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 32.52/32.93 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 32.52/32.93 , clause( 93862, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.52/32.93 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 32.52/32.93 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 32.52/32.93 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 32.52/32.93 , clause( 93863, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 32.52/32.93 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93864, [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ),
% 32.52/32.93 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93865, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.52/32.93 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 32.52/32.93 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93866, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ] )
% 32.52/32.93 , clause( 93867, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.52/32.93 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93868, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.52/32.93 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93869, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.52/32.93 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), X
% 32.52/32.93 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 32.52/32.93 , clause( 93870, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat'
% 32.52/32.93 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93871, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 32.52/32.93 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93872, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.52/32.93 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.52/32.93 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 32.52/32.93 , clause( 93873, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.52/32.93 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.52/32.93 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 32.52/32.93 , clause( 93874, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.52/32.93 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.52/32.93 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 32.52/32.93 , clause( 93875, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.52/32.93 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 32.52/32.93 ] )
% 32.52/32.93 , clause( 93876, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 32.52/32.93 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ] )
% 32.52/32.93 , clause( 93877, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 32.52/32.93 X ) ), 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 32.52/32.93 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ] )
% 32.52/32.93 , clause( 93878, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 32.52/32.93 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 32.52/32.93 )
% 32.52/32.93 , clause( 93879, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 32.52/32.93 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 32.52/32.93 , clause( 93880, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 32.52/32.93 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 32.52/32.93 , clause( 93881, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 32.52/32.93 ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y
% 32.52/32.93 , X ) ] )
% 32.52/32.93 , clause( 93882, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 32.52/32.93 ) ), =( Y, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 32.52/32.93 ) ) ] )
% 32.52/32.93 , clause( 93883, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 32.52/32.93 Y, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 32.52/32.93 ) ) ] )
% 32.52/32.93 , clause( 93884, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 32.52/32.93 X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 32.52/32.93 ) ) ] )
% 32.52/32.93 , clause( 93885, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 32.52/32.93 ) ), =( Y, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 32.52/32.93 ) ) ] )
% 32.52/32.93 , clause( 93886, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 32.52/32.93 X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 32.52/32.93 ) ) ] )
% 32.52/32.93 , clause( 93887, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 32.52/32.93 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93888, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 32.52/32.93 X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 32.52/32.93 ) ) ] )
% 32.52/32.93 , clause( 93889, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 32.52/32.93 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 32.52/32.93 , clause( 93890, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.52/32.93 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.52/32.93 , clause( 93891, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 32.52/32.93 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93892, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 32.52/32.93 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93893, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.52/32.93 'tc_nat' ), X, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y
% 32.52/32.93 , 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.52/32.93 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93894, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' )
% 32.52/32.93 ] )
% 32.52/32.93 , clause( 93895, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ] )
% 32.52/32.93 , clause( 93896, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 32.52/32.93 , clause( 93897, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 32.52/32.93 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 32.52/32.93 )
% 32.52/32.93 , clause( 93898, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.52/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 32.52/32.93 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ] )
% 32.52/32.93 , clause( 93899, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ] )
% 32.52/32.93 , clause( 93900, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ] )
% 32.52/32.93 , clause( 93901, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 32.52/32.93 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 32.52/32.93 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93902, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93903, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 32.52/32.93 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.52/32.93 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93904, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 32.52/32.93 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 32.52/32.93 ) ] )
% 32.52/32.93 , clause( 93905, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 32.52/32.93 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 32.52/32.93 ) ] )
% 32.52/32.93 , clause( 93906, [ ~(
% 32.52/32.93 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 32.52/32.93 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ) ) ] )
% 32.52/32.93 , clause( 93907, [ ~(
% 32.52/32.93 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 32.52/32.93 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 32.52/32.93 ) ] )
% 32.52/32.93 , clause( 93908, [ ~(
% 32.52/32.93 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 32.52/32.93 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 32.52/32.93 , clause( 93909, [ ~(
% 32.52/32.93 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 32.52/32.93 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 32.52/32.93 ) ] )
% 32.52/32.93 , clause( 93910, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 32.52/32.93 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 32.52/32.93 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 32.52/32.93 , clause( 93911, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 32.52/32.93 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 32.52/32.93 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 32.52/32.93 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.52/32.93 , clause( 93912, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 32.52/32.93 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 32.52/32.93 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 32.52/32.93 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.52/32.93 , clause( 93913, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 32.52/32.93 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 32.52/32.93 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 32.52/32.93 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93914, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 32.52/32.93 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 32.52/32.93 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 32.52/32.93 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93915, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 32.52/32.93 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 32.52/32.93 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 32.52/32.93 , clause( 93916, [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 32.52/32.93 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 32.52/32.93 , clause( 93917, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 32.52/32.93 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93918, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.52/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 32.52/32.93 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 32.52/32.93 , clause( 93919, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.52/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 32.52/32.93 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 32.52/32.93 , clause( 93920, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.52/32.93 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.52/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 32.52/32.93 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93921, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.52/32.93 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 32.52/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 32.52/32.93 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93922, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.52/32.93 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.52/32.93 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 32.52/32.93 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93923, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.52/32.93 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 32.52/32.93 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 32.52/32.93 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93924, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.52/32.93 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.52/32.93 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.52/32.93 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93925, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.52/32.93 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.52/32.93 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.52/32.93 , clause( 93926, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.52/32.93 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.52/32.93 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 32.52/32.93 , clause( 93927, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.52/32.93 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 32.52/32.93 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 32.52/32.93 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93928, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.52/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 32.52/32.93 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.52/32.93 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.52/32.93 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93929, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.52/32.93 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93930, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.52/32.93 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 32.52/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93931, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.52/32.93 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 32.52/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93932, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.52/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.52/32.93 , clause( 93933, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 32.52/32.93 ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 32.52/32.93 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.52/32.93 , clause( 93934, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 32.52/32.93 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 32.52/32.93 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.52/32.93 , clause( 93935, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 32.52/32.93 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 32.52/32.93 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.52/32.93 , clause( 93936, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93937, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 32.52/32.93 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z,
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 32.52/32.93 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93938, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 32.52/32.93 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ), =(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 32.52/32.93 'tc_nat' ), U ) ] )
% 32.52/32.93 , clause( 93939, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ), 'tc_nat' ) ]
% 32.52/32.93 )
% 32.52/32.93 , clause( 93940, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 32.52/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 32.52/32.93 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93941, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.52/32.93 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.52/32.93 , clause( 93942, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.52/32.93 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.52/32.93 , clause( 93943, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93944, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93945, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.52/32.93 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 32.52/32.93 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.52/32.93 , clause( 93946, [ =( 'c_Orderings_Oord__class_Omin'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93947, [ =( 'c_Orderings_Oord__class_Omin'( X,
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93948, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 32.52/32.93 ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 32.52/32.93 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93949, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.52/32.93 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 32.52/32.93 , T, X ), X ) ) ] )
% 32.52/32.93 , clause( 93950, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.52/32.93 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.52/32.93 , Z, X ), X ) ) ] )
% 32.52/32.93 , clause( 93951, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 32.52/32.93 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 32.52/32.93 , T, X ), X ) ) ] )
% 32.52/32.93 , clause( 93952, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 32.52/32.93 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.52/32.93 , Z, X ), X ) ) ] )
% 32.52/32.93 , clause( 93953, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.52/32.93 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 32.52/32.93 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.52/32.93 , clause( 93954, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) )
% 32.52/32.93 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93955, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X )
% 32.52/32.93 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93956, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 32.52/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.52/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 32.52/32.93 , clause( 93957, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 32.52/32.93 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93958, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.52/32.93 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.52/32.93 , clause( 93959, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.52/32.93 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.52/32.93 , clause( 93960, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.52/32.93 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ] )
% 32.52/32.93 , clause( 93961, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y,
% 32.52/32.93 'tc_nat' ), 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ),
% 32.52/32.93 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93962, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 32.52/32.93 , T, X ), X ) ) ] )
% 32.52/32.93 , clause( 93963, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 32.52/32.93 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 32.52/32.93 , clause( 93964, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 32.52/32.93 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 32.52/32.93 )
% 32.52/32.93 , clause( 93965, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 32.52/32.93 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 32.52/32.93 , clause( 93966, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.52/32.93 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 32.52/32.93 T, 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ), W, X ), X ) ) ] )
% 32.52/32.93 , clause( 93967, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.52/32.93 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 32.52/32.93 , X ), W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X
% 32.52/32.93 ), X ) ) ] )
% 32.52/32.93 , clause( 93968, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.52/32.93 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W, X ) ) ] )
% 32.52/32.93 , clause( 93969, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.52/32.93 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 32.52/32.93 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ] )
% 32.52/32.93 , clause( 93970, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 32.52/32.93 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93971, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.52/32.93 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93972, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 32.52/32.93 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93973, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.52/32.93 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93974, [ ~(
% 32.52/32.93 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 32.52/32.93 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 32.52/32.93 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 32.52/32.93 , clause( 93975, [ ~(
% 32.52/32.93 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 32.52/32.93 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 32.52/32.93 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 32.52/32.93 , clause( 93976, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 32.52/32.93 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 32.52/32.93 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93977, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 32.52/32.93 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X
% 32.52/32.93 , Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 32.52/32.93 )
% 32.52/32.93 , clause( 93978, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 32.52/32.93 , clause( 93979, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 32.52/32.93 , clause( 93980, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 32.52/32.93 , clause( 93981, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 32.52/32.93 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 32.52/32.93 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93982, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 32.52/32.93 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 32.52/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 32.52/32.93 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 32.52/32.93 )
% 32.52/32.93 , clause( 93983, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 32.52/32.93 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 32.52/32.93 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93984, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 32.52/32.93 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 32.52/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.52/32.93 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 32.52/32.93 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 32.52/32.93 )
% 32.52/32.93 , clause( 93985, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 32.52/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 32.52/32.93 ) ) ] )
% 32.52/32.93 , clause( 93986, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 32.52/32.93 ) ) ) ] )
% 32.52/32.93 , clause( 93987, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 32.52/32.93 ) ) ) ] )
% 32.52/32.93 , clause( 93988, [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ),
% 32.52/32.93 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y
% 32.52/32.93 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y
% 32.52/32.93 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ] )
% 32.52/32.93 , clause( 93989, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.52/32.93 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 32.52/32.93 , clause( 93990, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.52/32.93 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.52/32.93 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.52/32.93 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.52/32.93 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 32.52/32.93 , clause( 93991, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.52/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 32.52/32.93 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 32.52/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 32.52/32.93 , X ) ) ] )
% 32.52/32.93 , clause( 93992, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 32.52/32.93 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 32.52/32.93 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 32.52/32.93 , clause( 93993, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 32.52/32.93 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 32.52/32.93 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 32.52/32.93 , clause( 93994, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 32.52/32.93 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 32.52/32.93 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 32.52/32.93 , clause( 93995, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 32.52/32.93 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ] )
% 32.52/32.93 , clause( 93996, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 32.52/32.93 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ] )
% 32.52/32.93 , clause( 93997, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 32.52/32.93 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( Y
% 32.52/32.93 , Z, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 32.52/32.93 , clause( 93998, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 32.52/32.93 , Y, X ), X ) ] )
% 32.52/32.93 , clause( 93999, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.52/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 32.56/32.93 , Z, X ), X ) ] )
% 32.56/32.93 , clause( 94000, [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 32.56/32.93 , Z, X ), X ) ] )
% 32.56/32.93 , clause( 94001, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.56/32.93 ) ] )
% 32.56/32.93 , clause( 94002, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.56/32.93 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.56/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 32.56/32.93 Z, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94003, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.56/32.93 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 32.56/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.56/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 32.56/32.93 , clause( 94004, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.93 , clause( 94005, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.56/32.93 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 32.56/32.93 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 32.56/32.93 , clause( 94006, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.56/32.93 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 32.56/32.93 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 32.56/32.93 , clause( 94007, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 32.56/32.93 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94008, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 32.56/32.93 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94009, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94010, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.93 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 32.56/32.93 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ] )
% 32.56/32.93 , clause( 94011, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 32.56/32.93 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ] )
% 32.56/32.93 , clause( 94012, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 32.56/32.93 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 32.56/32.93 ] )
% 32.56/32.93 , clause( 94013, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 32.56/32.93 'tc_nat' ), 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ),
% 32.56/32.93 =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ] )
% 32.56/32.93 , clause( 94014, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.56/32.93 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94015, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.56/32.93 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94016, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.56/32.93 ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 32.56/32.93 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 32.56/32.93 )
% 32.56/32.93 , clause( 94017, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 Z, Y, X ) ) ] )
% 32.56/32.93 , clause( 94018, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94019, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.56/32.93 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 32.56/32.93 )
% 32.56/32.93 , clause( 94020, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94021, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 Z, Y, X ) ) ] )
% 32.56/32.93 , clause( 94022, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 32.56/32.93 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 32.56/32.93 , T, X ), X ), T, X ) ) ] )
% 32.56/32.93 , clause( 94023, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.93 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 32.56/32.93 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.93 , clause( 94024, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 32.56/32.93 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94025, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 32.56/32.93 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94026, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 32.56/32.93 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 32.56/32.93 , X ) ) ] )
% 32.56/32.93 , clause( 94027, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 32.56/32.93 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 32.56/32.93 , clause( 94028, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 32.56/32.93 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 32.56/32.93 , clause( 94029, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 32.56/32.93 , X ), Z, X ) ) ] )
% 32.56/32.93 , clause( 94030, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 32.56/32.93 , X ), Z, X ) ) ] )
% 32.56/32.93 , clause( 94031, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.56/32.93 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 32.56/32.93 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 32.56/32.93 , clause( 94032, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94033, [ =( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94034, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 32.56/32.93 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 32.56/32.93 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 32.56/32.93 , Z, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94035, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 32.56/32.93 ] )
% 32.56/32.93 , clause( 94036, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 32.56/32.93 ] )
% 32.56/32.93 , clause( 94037, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 32.56/32.93 ] )
% 32.56/32.93 , clause( 94038, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 32.56/32.93 )
% 32.56/32.93 , clause( 94039, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 32.56/32.93 )
% 32.56/32.93 , clause( 94040, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y, T,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94041, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.56/32.93 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.93 , clause( 94042, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 32.56/32.93 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94043, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 32.56/32.93 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94044, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 32.56/32.93 , clause( 94045, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94046, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 32.56/32.93 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 32.56/32.93 , clause( 94047, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.56/32.93 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.56/32.93 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 32.56/32.93 , clause( 94048, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94049, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94050, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94051, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94052, [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) )
% 32.56/32.93 , =( Y, Z ) ] )
% 32.56/32.93 , clause( 94053, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 32.56/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 32.56/32.93 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.56/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 32.56/32.93 , clause( 94054, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94055, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94056, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 32.56/32.93 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 32.56/32.93 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ] )
% 32.56/32.93 , clause( 94057, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 32.56/32.93 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 32.56/32.93 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ] )
% 32.56/32.93 , clause( 94058, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94059, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.56/32.93 , clause( 94060, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94061, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94062, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94063, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ] )
% 32.56/32.93 , clause( 94064, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94065, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94066, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 32.56/32.93 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94067, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.93 X ) ), 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.93 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 32.56/32.93 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X
% 32.56/32.93 ) ] )
% 32.56/32.93 , clause( 94068, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 32.56/32.93 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 32.56/32.93 T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94069, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.56/32.93 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 32.56/32.93 T, X ), Z, X ) ) ] )
% 32.56/32.93 , clause( 94070, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.56/32.93 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 Z, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94071, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 32.56/32.93 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 32.56/32.93 , X ), T, X ) ) ] )
% 32.56/32.93 , clause( 94072, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 32.56/32.93 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 32.56/32.93 , T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94073, [ =( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94074, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 32.56/32.93 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 32.56/32.93 , X ), T, X ) ) ] )
% 32.56/32.93 , clause( 94075, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 32.56/32.93 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 32.56/32.93 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94076, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 32.56/32.93 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94077, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 32.56/32.93 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94078, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 32.56/32.93 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94079, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 32.56/32.93 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94080, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 32.56/32.93 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94081, [ =( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 32.56/32.93 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94082, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 32.56/32.93 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 32.56/32.93 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94083, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 32.56/32.93 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94084, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94085, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94086, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.56/32.93 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 32.56/32.93 , clause( 94087, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.56/32.93 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94088, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 32.56/32.93 , clause( 94089, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 32.56/32.93 , clause( 94090, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 32.56/32.93 , clause( 94091, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 32.56/32.93 , clause( 94092, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 32.56/32.93 , clause( 94093, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94094, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat'
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94095, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 32.56/32.93 )
% 32.56/32.93 , clause( 94096, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 32.56/32.93 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 32.56/32.93 , clause( 94097, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 32.56/32.93 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 32.56/32.93 , clause( 94098, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94099, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94100, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94101, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94102, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94103, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94104, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94105, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94106, [ ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ) ),
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94107, [ ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94108, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94109, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 32.56/32.93 ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94110, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ),
% 32.56/32.93 ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94111, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94112, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 32.56/32.93 , clause( 94113, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 32.56/32.93 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 32.56/32.93 , clause( 94114, [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94115, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94116, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 32.56/32.93 X ), X ) ) ] )
% 32.56/32.93 , clause( 94117, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 32.56/32.93 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 32.56/32.93 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ] )
% 32.56/32.93 , clause( 94118, [ ~(
% 32.56/32.93 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T
% 32.56/32.93 , X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 32.56/32.93 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94119, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 32.56/32.93 , clause( 94120, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 32.56/32.93 , clause( 94121, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 32.56/32.93 , clause( 94122, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.56/32.93 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 32.56/32.93 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 32.56/32.93 , clause( 94123, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 32.56/32.93 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 32.56/32.93 , clause( 94124, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 32.56/32.93 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 Y, T, X ) ) ), =( Z, T ) ] )
% 32.56/32.93 , clause( 94125, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 32.56/32.93 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 T, Z, X ) ) ), =( Y, T ) ] )
% 32.56/32.93 , clause( 94126, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 32.56/32.93 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94127, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 32.56/32.93 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94128, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat'
% 32.56/32.93 ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94129, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 32.56/32.93 ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94130, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 32.56/32.93 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94131, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 32.56/32.93 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 32.56/32.93 , X ) ) ] )
% 32.56/32.93 , clause( 94132, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 32.56/32.93 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 32.56/32.93 , X ) ) ] )
% 32.56/32.93 , clause( 94133, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 32.56/32.93 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 32.56/32.93 , X ) ) ] )
% 32.56/32.93 , clause( 94134, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 32.56/32.93 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 32.56/32.93 , X ) ) ] )
% 32.56/32.93 , clause( 94135, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94136, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94137, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.93 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 32.56/32.93 X ) ] )
% 32.56/32.93 , clause( 94138, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94139, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94140, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94141, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94142, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94143, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94144, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 32.56/32.93 ] )
% 32.56/32.93 , clause( 94145, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 32.56/32.93 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 32.56/32.93 , clause( 94146, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 32.56/32.93 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 32.56/32.93 , clause( 94147, [ ~(
% 32.56/32.93 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 32.56/32.93 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 32.56/32.93 , clause( 94148, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94149, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.56/32.93 'tc_nat' ) ), =( Y, Z ) ] )
% 32.56/32.93 , clause( 94150, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94151, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94152, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.56/32.93 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 32.56/32.93 , T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94153, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.56/32.93 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.56/32.93 , Z, X ), X ) ) ] )
% 32.56/32.93 , clause( 94154, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 32.56/32.93 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94155, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.56/32.93 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 X ), T, X ) ) ] )
% 32.56/32.93 , clause( 94156, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 32.56/32.93 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94157, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.56/32.93 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94158, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94159, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94160, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 32.56/32.93 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) )
% 32.56/32.93 ] )
% 32.56/32.93 , clause( 94161, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 32.56/32.93 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 32.56/32.93 ] )
% 32.56/32.93 , clause( 94162, [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.56/32.93 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94163, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 32.56/32.93 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.93 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ] )
% 32.56/32.93 , clause( 94164, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94165, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94166, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 32.56/32.93 Z, Y, X ) ) ] )
% 32.56/32.93 , clause( 94167, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 32.56/32.93 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 32.56/32.93 , clause( 94168, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 32.56/32.93 ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 32.56/32.93 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94169, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 32.56/32.93 Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94170, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 32.56/32.93 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94171, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.56/32.93 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94172, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 X ), X ) ) ] )
% 32.56/32.93 , clause( 94173, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 X ), X ) ) ] )
% 32.56/32.93 , clause( 94174, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 32.56/32.93 X, 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94175, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 32.56/32.93 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94176, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_Suc'( X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 32.56/32.93 Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 32.56/32.93 ) ] )
% 32.56/32.93 , clause( 94177, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 32.56/32.93 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94178, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94179, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), X, 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X,
% 32.56/32.93 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94180, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 32.56/32.93 'tc_nat' ), X, 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94181, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94182, [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 32.56/32.93 'tc_nat' ) ), Y ) ), =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94183, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.93 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94184, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 32.56/32.93 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 32.56/32.93 , clause( 94185, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 32.56/32.93 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 32.56/32.93 , clause( 94186, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.56/32.93 , clause( 94187, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94188, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 32.56/32.93 )
% 32.56/32.93 , clause( 94189, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X
% 32.56/32.93 ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94190, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.93 , clause( 94191, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.93 , clause( 94192, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.56/32.93 ~( 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X
% 32.56/32.93 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94193, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ]
% 32.56/32.93 )
% 32.56/32.93 , clause( 94194, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 32.56/32.93 ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94195, [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ),
% 32.56/32.93 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94196, [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.56/32.93 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94197, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94198, [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'(
% 32.56/32.93 Y ), 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat'
% 32.56/32.93 ) ) ) ] )
% 32.56/32.93 , clause( 94199, [ =( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 32.56/32.93 ] )
% 32.56/32.93 , clause( 94200, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 32.56/32.93 ] )
% 32.56/32.93 , clause( 94201, [ ~(
% 32.56/32.93 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 32.56/32.93 , clause( 94202, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94203, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 32.56/32.93 , clause( 94204, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.56/32.93 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.56/32.93 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 32.56/32.93 , clause( 94205, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 32.56/32.93 , clause( 94206, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94207, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94208, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.56/32.93 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.56/32.93 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 32.56/32.93 , clause( 94209, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 32.56/32.93 , clause( 94210, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94211, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.56/32.93 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 X ), T, X ) ) ] )
% 32.56/32.93 , clause( 94212, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94213, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.56/32.93 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94214, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 32.56/32.93 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94215, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 32.56/32.93 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94216, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 32.56/32.93 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94217, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 32.56/32.93 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94218, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 32.56/32.93 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94219, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 32.56/32.93 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94220, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 32.56/32.93 , clause( 94221, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ] )
% 32.56/32.93 , clause( 94222, [ =( 'c_Divides_Odiv__class_Omod'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 32.56/32.93 ), Z, 'tc_nat' ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y,
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94223, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 32.56/32.93 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94224, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 32.56/32.93 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 32.56/32.93 , clause( 94225, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 32.56/32.93 , =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 32.56/32.93 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 32.56/32.93 ) ] )
% 32.56/32.93 , clause( 94226, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 32.56/32.93 , clause( 94227, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94228, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.93 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94229, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 32.56/32.93 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94230, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 32.56/32.93 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94231, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 32.56/32.93 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94232, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 32.56/32.93 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.93 , clause( 94233, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 32.56/32.93 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 32.56/32.93 , clause( 94234, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.93 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 32.56/32.93 ) ] )
% 32.56/32.93 , clause( 94235, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.56/32.93 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94236, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.56/32.93 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94237, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.93 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 32.56/32.93 , clause( 94238, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.93 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ] )
% 32.56/32.93 , clause( 94239, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 32.56/32.93 , X ) ) ] )
% 32.56/32.93 , clause( 94240, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 32.56/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.93 , clause( 94241, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 32.56/32.93 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.56/32.93 ) ), Y, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94242, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 32.56/32.93 ), 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94243, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.56/32.93 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94244, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.56/32.93 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.56/32.93 , clause( 94245, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 32.56/32.93 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94246, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 32.56/32.93 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94247, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 32.56/32.93 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94248, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 32.56/32.93 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94249, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'(
% 32.56/32.93 X, Y, 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94250, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 32.56/32.93 X ) ) ] )
% 32.56/32.93 , clause( 94251, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 32.56/32.93 ) ] )
% 32.56/32.93 , clause( 94252, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 32.56/32.93 X ) ) ] )
% 32.56/32.93 , clause( 94253, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 32.56/32.93 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 32.56/32.93 , clause( 94254, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y
% 32.56/32.93 , X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94255, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 32.56/32.93 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94256, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.56/32.93 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94257, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 32.56/32.93 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94258, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 32.56/32.93 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94259, [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ),
% 32.56/32.93 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94260, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 32.56/32.93 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.93 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 32.56/32.93 ] )
% 32.56/32.93 , clause( 94261, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 32.56/32.93 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 32.56/32.93 ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 32.56/32.93 , clause( 94262, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 32.56/32.93 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 32.56/32.93 , 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 32.56/32.93 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94263, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 32.56/32.93 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 32.56/32.93 , 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 32.56/32.93 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 32.56/32.93 X, T, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94264, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.56/32.93 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 32.56/32.93 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 32.56/32.93 , clause( 94265, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.56/32.93 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.93 , clause( 94266, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 32.56/32.93 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 32.56/32.93 , clause( 94267, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.93 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ] )
% 32.56/32.93 , clause( 94268, [ ~(
% 32.56/32.93 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 32.56/32.93 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 32.56/32.93 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X
% 32.56/32.93 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 32.56/32.93 ) ) ] )
% 32.56/32.93 , clause( 94269, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 32.56/32.93 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94270, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 32.56/32.93 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94271, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 32.56/32.93 , ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Z
% 32.56/32.93 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94272, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 32.56/32.93 , ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 32.56/32.93 , Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94273, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 32.56/32.93 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 32.56/32.93 , clause( 94274, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94275, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 32.56/32.93 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ] )
% 32.56/32.93 , clause( 94276, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 32.56/32.93 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 32.56/32.93 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 32.56/32.93 , clause( 94277, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.93 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X )
% 32.56/32.93 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 32.56/32.93 , clause( 94278, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 32.56/32.93 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 32.56/32.93 , clause( 94279, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat'
% 32.56/32.93 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 32.56/32.93 , clause( 94280, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 32.56/32.93 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 32.56/32.93 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 32.56/32.93 , clause( 94281, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 32.56/32.93 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 32.56/32.93 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 32.56/32.93 , X ), W, X ) ) ] )
% 32.56/32.93 , clause( 94282, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.93 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.93 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 X ) ) ] )
% 32.56/32.93 , clause( 94283, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94284, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.93 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94285, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 32.56/32.93 ) ] )
% 32.56/32.93 , clause( 94286, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.93 ) ] )
% 32.56/32.93 , clause( 94287, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 32.56/32.93 Y, X ) ) ] )
% 32.56/32.93 , clause( 94288, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94289, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.93 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 32.56/32.93 Y, X ) ) ] )
% 32.56/32.93 , clause( 94290, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 32.56/32.93 X ) ) ] )
% 32.56/32.93 , clause( 94291, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 32.56/32.93 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 32.56/32.93 , T, X ), X ), T, X ) ) ] )
% 32.56/32.93 , clause( 94292, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 32.56/32.93 , clause( 94293, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 32.56/32.93 , clause( 94294, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94295, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 32.56/32.93 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X )
% 32.56/32.93 , X ) ) ] )
% 32.56/32.93 , clause( 94296, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 32.56/32.93 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X )
% 32.56/32.93 , X ) ) ] )
% 32.56/32.93 , clause( 94297, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 32.56/32.93 T, X ) ) ] )
% 32.56/32.93 , clause( 94298, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 32.56/32.93 T, X ) ) ] )
% 32.56/32.93 , clause( 94299, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 32.56/32.93 T, X ) ) ] )
% 32.56/32.93 , clause( 94300, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 32.56/32.93 T, X ) ) ] )
% 32.56/32.93 , clause( 94301, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 32.56/32.93 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X )
% 32.56/32.93 , X ) ) ] )
% 32.56/32.93 , clause( 94302, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 32.56/32.93 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X )
% 32.56/32.93 , X ) ) ] )
% 32.56/32.93 , clause( 94303, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 32.56/32.93 , clause( 94304, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 32.56/32.93 , clause( 94305, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.93 X ) ), 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 32.56/32.93 , clause( 94306, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 32.56/32.93 , Z, X ), 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 32.56/32.93 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ] )
% 32.56/32.93 , clause( 94307, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 32.56/32.93 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94308, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 32.56/32.93 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 32.56/32.93 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 32.56/32.93 Z, X ) ) ] )
% 32.56/32.93 , clause( 94309, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.93 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 32.56/32.93 ] )
% 32.56/32.93 , clause( 94310, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.56/32.93 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94311, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.56/32.93 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.56/32.93 , clause( 94312, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 32.56/32.93 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94313, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.93 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94314, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 32.56/32.93 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 32.56/32.93 , clause( 94315, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 32.56/32.93 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 32.56/32.93 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 32.56/32.93 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94316, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 32.56/32.93 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 32.56/32.93 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94317, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 32.56/32.93 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 32.56/32.93 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 32.56/32.93 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94318, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 32.56/32.93 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 32.56/32.93 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94319, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 32.56/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 32.56/32.93 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.56/32.93 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 32.56/32.93 , clause( 94320, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 32.56/32.93 ), Z, 'tc_nat' ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 32.56/32.93 Z ), Y, 'tc_nat' ) ) ] )
% 32.56/32.93 , clause( 94321, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 32.56/32.93 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 32.56/32.93 , T ), =( X, Z ) ] )
% 32.56/32.93 , clause( 94322, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.93 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 32.56/32.93 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 32.56/32.93 , T ), =( X, Z ) ] )
% 32.56/32.93 , clause( 94323, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.56/32.93 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.56/32.93 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 32.56/32.93 =( Y, T ) ] )
% 32.56/32.93 , clause( 94324, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.56/32.93 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.56/32.93 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.93 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 32.56/32.93 =( Y, T ) ] )
% 32.56/32.93 , clause( 94325, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 32.56/32.93 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 32.56/32.93 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 32.56/32.93 , X ) ) ] )
% 32.56/32.93 , clause( 94326, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 32.56/32.93 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 32.56/32.93 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 32.56/32.94 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 32.56/32.94 X ), Z, X ) ) ] )
% 32.56/32.94 , clause( 94327, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.56/32.94 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.94 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 32.56/32.94 , clause( 94328, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94329, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94330, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94331, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.56/32.94 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.94 , clause( 94332, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.94 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 32.56/32.94 ) ] )
% 32.56/32.94 , clause( 94333, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94334, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94335, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 32.56/32.94 , clause( 94336, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 32.56/32.94 , clause( 94337, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.94 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 32.56/32.94 ) ] )
% 32.56/32.94 , clause( 94338, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.94 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 32.56/32.94 ) ] )
% 32.56/32.94 , clause( 94339, [ ~(
% 32.56/32.94 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 32.56/32.94 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 32.56/32.94 , clause( 94340, [ ~(
% 32.56/32.94 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 32.56/32.94 , clause( 94341, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 32.56/32.94 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94342, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 32.56/32.94 ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94343, [ ~( 'class_Orderings_Oorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 32.56/32.94 , clause( 94344, [ ~( 'class_Orderings_Oorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 32.56/32.94 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 32.56/32.94 , clause( 94345, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 32.56/32.94 , clause( 94346, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 32.56/32.94 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 32.56/32.94 , clause( 94347, [ ~(
% 32.56/32.94 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 Y, T, X ) ) ] )
% 32.56/32.94 , clause( 94348, [ ~(
% 32.56/32.94 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 Y, T, X ) ) ] )
% 32.56/32.94 , clause( 94349, [ ~(
% 32.56/32.94 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 32.56/32.94 X ), X ) ) ] )
% 32.56/32.94 , clause( 94350, [ ~(
% 32.56/32.94 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 Z, T, X ) ) ] )
% 32.56/32.94 , clause( 94351, [ ~(
% 32.56/32.94 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 Z, T, X ) ) ] )
% 32.56/32.94 , clause( 94352, [ ~(
% 32.56/32.94 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 32.56/32.94 X ), X ) ) ] )
% 32.56/32.94 , clause( 94353, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 32.56/32.94 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 32.56/32.94 , clause( 94354, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 32.56/32.94 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 32.56/32.94 , clause( 94355, [ ~(
% 32.56/32.94 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 32.56/32.94 , clause( 94356, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 32.56/32.94 'c_lessequals'( Y, Z, X ) ) ] )
% 32.56/32.94 , clause( 94357, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( T, Z, X
% 32.56/32.94 ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( T, Y, X
% 32.56/32.94 ), Z, X ) ) ] )
% 32.56/32.94 , clause( 94358, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 32.56/32.94 , clause( 94359, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.94 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 32.56/32.94 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 32.56/32.94 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 32.56/32.94 , clause( 94360, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.94 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 32.56/32.94 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 32.56/32.94 X ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 32.56/32.94 , clause( 94361, [ ~( 'class_Orderings_Oorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 32.56/32.94 , X ) ) ] )
% 32.56/32.94 , clause( 94362, [ ~( 'class_Orderings_Oorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 32.56/32.94 Z, Y ) ] )
% 32.56/32.94 , clause( 94363, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 32.56/32.94 , clause( 94364, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 32.56/32.94 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 32.56/32.94 , clause( 94365, [ ~( 'class_Orderings_Oorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 32.56/32.94 Y, Z ) ] )
% 32.56/32.94 , clause( 94366, [ ~( 'class_Orderings_Oorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 32.56/32.94 , X ) ) ] )
% 32.56/32.94 , clause( 94367, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 32.56/32.94 , clause( 94368, [ ~( 'class_Orderings_Oorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 32.56/32.94 , X ) ) ] )
% 32.56/32.94 , clause( 94369, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ),
% 32.56/32.94 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 32.56/32.94 , clause( 94370, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 32.56/32.94 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 32.56/32.94 , clause( 94371, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 32.56/32.94 , clause( 94372, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 32.56/32.94 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 32.56/32.94 , clause( 94373, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 32.56/32.94 , clause( 94374, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94375, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 32.56/32.94 , Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 32.56/32.94 , clause( 94376, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 32.56/32.94 , clause( 94377, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 32.56/32.94 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 32.56/32.94 , clause( 94378, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 32.56/32.94 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 32.56/32.94 , clause( 94379, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 32.56/32.94 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 32.56/32.94 , clause( 94380, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.56/32.94 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ] )
% 32.56/32.94 , clause( 94381, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.56/32.94 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 32.56/32.94 , clause( 94382, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 32.56/32.94 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 32.56/32.94 , clause( 94383, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 32.56/32.94 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 32.56/32.94 , clause( 94384, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 32.56/32.94 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ] )
% 32.56/32.94 , clause( 94385, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 32.56/32.94 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 32.56/32.94 , X ), W, X ), X ) ) ] )
% 32.56/32.94 , clause( 94386, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 32.56/32.94 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 32.56/32.94 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 32.56/32.94 W, X ), X ) ) ] )
% 32.56/32.94 , clause( 94387, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 32.56/32.94 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 32.56/32.94 , X ), T, X ), W, X ) ) ] )
% 32.56/32.94 , clause( 94388, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 32.56/32.94 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 32.56/32.94 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 32.56/32.94 W, X ), X ) ) ] )
% 32.56/32.94 , clause( 94389, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 32.56/32.94 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 32.56/32.94 , Y, X ) ) ] )
% 32.56/32.94 , clause( 94390, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 32.56/32.94 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 32.56/32.94 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 32.56/32.94 X ), Z, X ) ) ] )
% 32.56/32.94 , clause( 94391, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.56/32.94 , =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z,
% 32.56/32.94 X ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ] )
% 32.56/32.94 , clause( 94392, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 32.56/32.94 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 32.56/32.94 , clause( 94393, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 32.56/32.94 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 32.56/32.94 , clause( 94394, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 32.56/32.94 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 32.56/32.94 , T, X ), X ), T, X ) ) ] )
% 32.56/32.94 , clause( 94395, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.94 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 32.56/32.94 ), X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X
% 32.56/32.94 ), X ) ) ] )
% 32.56/32.94 , clause( 94396, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.56/32.94 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 32.56/32.94 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 32.56/32.94 , clause( 94397, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.56/32.94 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 32.56/32.94 ~( 'c_lessequals'( U, T, X ) ) ] )
% 32.56/32.94 , clause( 94398, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 32.56/32.94 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 32.56/32.94 , clause( 94399, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.94 ) ] )
% 32.56/32.94 , clause( 94400, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.94 ) ] )
% 32.56/32.94 , clause( 94401, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 32.56/32.94 ) ] )
% 32.56/32.94 , clause( 94402, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.94 ) ] )
% 32.56/32.94 , clause( 94403, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.56/32.94 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 32.56/32.94 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94404, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 32.56/32.94 ), Y ) ] )
% 32.56/32.94 , clause( 94405, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.94 ) ), =( Y, Z ) ] )
% 32.56/32.94 , clause( 94406, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.94 ) ), =( Y, Z ) ] )
% 32.56/32.94 , clause( 94407, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.56/32.94 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 32.56/32.94 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 32.56/32.94 , clause( 94408, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 32.56/32.94 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 32.56/32.94 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 32.56/32.94 , clause( 94409, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 32.56/32.94 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 32.56/32.94 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 32.56/32.94 , clause( 94410, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 32.56/32.94 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 32.56/32.94 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 32.56/32.94 , clause( 94411, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 32.56/32.94 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 32.56/32.94 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 32.56/32.94 , clause( 94412, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 32.56/32.94 , U, X ), X ) ) ] )
% 32.56/32.94 , clause( 94413, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 32.56/32.94 ), Y ) ] )
% 32.56/32.94 , clause( 94414, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 32.56/32.94 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 32.56/32.94 , ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94415, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94416, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 32.56/32.94 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 32.56/32.94 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94417, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94418, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94419, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.94 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94420, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.94 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94421, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94422, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94423, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 32.56/32.94 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' )
% 32.56/32.94 , ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94424, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 32.56/32.94 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94425, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X )
% 32.56/32.94 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94426, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 32.56/32.94 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94427, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94428, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.94 , X ) ] )
% 32.56/32.94 , clause( 94429, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.56/32.94 , clause( 94430, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.94 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 32.56/32.94 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94431, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.94 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 32.56/32.94 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94432, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94433, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94434, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94435, [ =( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94436, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94437, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94438, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.94 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 32.56/32.94 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94439, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94440, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94441, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 32.56/32.94 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 32.56/32.94 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94442, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 32.56/32.94 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.94 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94443, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 32.56/32.94 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94444, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94445, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 32.56/32.94 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 32.56/32.94 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 32.56/32.94 , clause( 94446, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94447, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 32.56/32.94 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94448, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 32.56/32.94 Z, X ) ) ] )
% 32.56/32.94 , clause( 94449, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 32.56/32.94 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 32.56/32.94 , clause( 94450, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 32.56/32.94 ), X ) ) ] )
% 32.56/32.94 , clause( 94451, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 32.56/32.94 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 32.56/32.94 , clause( 94452, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.56/32.94 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94453, [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 32.56/32.94 'tc_nat' ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 32.56/32.94 , clause( 94454, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.56/32.94 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.56/32.94 , clause( 94455, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 32.56/32.94 'tc_nat' ), 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94456, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 32.56/32.94 'tc_nat' ), 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94457, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 32.56/32.94 'tc_nat' ), 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94458, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 32.56/32.94 'tc_nat' ), 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94459, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 32.56/32.94 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94460, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.56/32.94 , 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 32.56/32.94 , clause( 94461, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.56/32.94 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.94 , X ) ) ] )
% 32.56/32.94 , clause( 94462, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.56/32.94 ) ) ) ] )
% 32.56/32.94 , clause( 94463, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.56/32.94 ) ) ) ] )
% 32.56/32.94 , clause( 94464, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.94 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.94 , clause( 94465, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ), ~(
% 32.56/32.94 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94466, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 32.56/32.94 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94467, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 32.56/32.94 ), X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94468, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 32.56/32.94 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z
% 32.56/32.94 , 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94469, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 32.56/32.94 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.94 Z, X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 32.56/32.94 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.94 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94470, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94471, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 32.56/32.94 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94472, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 32.56/32.94 ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94473, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( T, 'c_HOL_Otimes__class_Otimes'( Y, U,
% 32.56/32.94 'tc_nat' ), 'tc_nat' ) ) ), =( 'c_Divides_Odiv__class_Omod'( X, Y,
% 32.56/32.94 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94474, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.56/32.94 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.94 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 32.56/32.94 , clause( 94475, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.94 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94476, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.56/32.94 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.56/32.94 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 32.56/32.94 , clause( 94477, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.56/32.94 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.56/32.94 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 32.56/32.94 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 32.56/32.94 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94478, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.94 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 32.56/32.94 X ) ] )
% 32.56/32.94 , clause( 94479, [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 32.56/32.94 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94480, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 32.56/32.94 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94481, [ 'c_HOL_Oord__class_Oless'( X,
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.56/32.94 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94482, [ 'c_HOL_Oord__class_Oless'( X,
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.56/32.94 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94483, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94484, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 32.56/32.94 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ] )
% 32.56/32.94 , clause( 94485, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.56/32.94 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 32.56/32.94 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.94 , clause( 94486, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.56/32.94 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.94 , clause( 94487, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 32.56/32.94 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 32.56/32.94 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 32.56/32.94 , clause( 94488, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 32.56/32.94 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 32.56/32.94 , clause( 94489, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 32.56/32.94 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 32.56/32.94 , clause( 94490, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94491, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.94 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 32.56/32.94 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 32.56/32.94 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 32.56/32.94 , clause( 94492, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 32.56/32.94 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94493, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.94 X ) ), ~( =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.94 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94494, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.94 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.94 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94495, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.94 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 32.56/32.94 , ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y
% 32.56/32.94 , 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.94 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94496, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 32.56/32.94 , Y, X ) ] )
% 32.56/32.94 , clause( 94497, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y
% 32.56/32.94 , X ) ] )
% 32.56/32.94 , clause( 94498, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94499, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z,
% 32.56/32.94 Y, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94500, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94501, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.56/32.94 , 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 32.56/32.94 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ] )
% 32.56/32.94 , clause( 94502, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 32.56/32.94 , Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94503, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.56/32.94 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.56/32.94 , clause( 94504, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 32.56/32.94 , X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94505, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 32.56/32.94 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 32.56/32.94 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94506, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.56/32.94 , clause( 94507, [ =( 'c_Divides_Odiv__class_Omod'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), X, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94508, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 32.56/32.94 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94509, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 32.56/32.94 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.56/32.94 , clause( 94510, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 32.56/32.94 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94511, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.94 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 32.56/32.94 ) ) ] )
% 32.56/32.94 , clause( 94512, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.94 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.56/32.94 , Y, X ), X ) ) ] )
% 32.56/32.94 , clause( 94513, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.94 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 32.56/32.94 , T, X ), X ) ) ] )
% 32.56/32.94 , clause( 94514, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.94 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 32.56/32.94 , T, X ), X ) ) ] )
% 32.56/32.94 , clause( 94515, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.56/32.94 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.56/32.94 , Y, X ), X ) ) ] )
% 32.56/32.94 , clause( 94516, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 32.56/32.94 , X ) ) ] )
% 32.56/32.94 , clause( 94517, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 32.56/32.94 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 32.56/32.94 , X ) ) ] )
% 32.56/32.94 , clause( 94518, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.56/32.94 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 32.56/32.94 ) ] )
% 32.56/32.94 , clause( 94519, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 32.56/32.94 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.56/32.94 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 32.56/32.94 , clause( 94520, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ),
% 32.56/32.94 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94521, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 32.56/32.94 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94522, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 32.56/32.94 =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 32.56/32.94 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ] )
% 32.56/32.94 , clause( 94523, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 32.56/32.94 , Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 32.56/32.94 , clause( 94524, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 32.56/32.94 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94525, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 32.56/32.94 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94526, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 32.56/32.94 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94527, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 X, T, 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94528, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94529, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94530, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94531, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94532, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94533, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 32.56/32.94 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94534, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 32.56/32.94 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94535, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 32.56/32.94 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94536, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94537, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 32.56/32.94 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94538, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 32.56/32.94 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94539, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 32.56/32.94 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94540, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94541, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94542, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 32.56/32.94 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94543, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ),
% 32.56/32.94 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94544, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94545, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94546, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 32.56/32.94 Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94547, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94548, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94549, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 32.56/32.94 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94550, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 32.56/32.94 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94551, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94552, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 32.56/32.94 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94553, [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 32.56/32.94 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 32.56/32.94 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.56/32.94 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 32.56/32.94 , Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94554, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 X, 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94555, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94556, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'(
% 32.56/32.94 Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94557, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 X, Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94558, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.94 Z, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94559, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 32.56/32.94 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 32.56/32.94 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94560, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 32.56/32.94 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94561, [ =( 'c_Orderings_Oord__class_Omin'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 32.56/32.94 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94562, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 32.56/32.94 , clause( 94563, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94564, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94565, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 32.56/32.94 , clause( 94566, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 32.56/32.94 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94567, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 32.56/32.94 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.94 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat'
% 32.56/32.94 ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94568, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 32.56/32.94 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.94 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94569, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 32.56/32.94 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.94 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94570, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 32.56/32.94 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94571, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 32.56/32.94 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ] )
% 32.56/32.94 , clause( 94572, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94573, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.94 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 32.56/32.94 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94574, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.94 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94575, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 32.56/32.94 'tc_nat' ), X, 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94576, [ =( 'c_HOL_Otimes__class_Otimes'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 32.56/32.94 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94577, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 32.56/32.94 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94578, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 32.56/32.94 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94579, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 32.56/32.94 , clause( 94580, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ) ] )
% 32.56/32.94 , clause( 94581, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.56/32.94 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.56/32.94 , X ) ) ] )
% 32.56/32.94 , clause( 94582, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.56/32.94 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 32.56/32.94 , X ) ) ] )
% 32.56/32.94 , clause( 94583, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 32.56/32.94 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ] )
% 32.56/32.94 , clause( 94584, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.56/32.94 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94585, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.56/32.94 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 32.56/32.94 , clause( 94586, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94587, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94588, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 32.56/32.94 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 32.56/32.94 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94589, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 32.56/32.94 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 32.56/32.94 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 32.56/32.94 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94590, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 32.56/32.94 , Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94591, [ 'c_HOL_Oord__class_Oless'( X,
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 32.56/32.94 Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94592, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 32.56/32.94 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 32.56/32.94 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94593, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 32.56/32.94 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94594, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 X, Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94595, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94596, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.56/32.94 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.94 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94597, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 32.56/32.94 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 32.56/32.94 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94598, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 32.56/32.94 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94599, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94600, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.56/32.94 Y, X ) ) ] )
% 32.56/32.94 , clause( 94601, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.56/32.94 Y, X ) ) ] )
% 32.56/32.94 , clause( 94602, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.56/32.94 Y, X ) ) ] )
% 32.56/32.94 , clause( 94603, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.56/32.94 Y, X ) ) ] )
% 32.56/32.94 , clause( 94604, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 32.56/32.94 , clause( 94605, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 32.56/32.94 , clause( 94606, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94607, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94608, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 32.56/32.94 , clause( 94609, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94610, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 32.56/32.94 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94611, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.56/32.94 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 32.56/32.94 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 32.56/32.94 , clause( 94612, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.56/32.94 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 32.56/32.94 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 32.56/32.94 , clause( 94613, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 32.56/32.94 ), =( Z, Y ) ] )
% 32.56/32.94 , clause( 94614, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 32.56/32.94 ) ] )
% 32.56/32.94 , clause( 94615, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 32.56/32.94 ) ] )
% 32.56/32.94 , clause( 94616, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 32.56/32.94 , clause( 94617, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 32.56/32.94 , clause( 94618, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 32.56/32.94 , clause( 94619, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 32.56/32.94 ), =( Z, Y ) ] )
% 32.56/32.94 , clause( 94620, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'v_i', X, 'tc_nat' ), 'v_n', 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94621, [ 'c_HOL_Oord__class_Oless'( 'v_i', 'v_n', 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94622, [ ~( 'class_Orderings_Oorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 32.56/32.94 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 32.56/32.94 , clause( 94623, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 32.56/32.94 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 32.56/32.94 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 32.56/32.94 , clause( 94624, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 32.56/32.94 , T, X ) ) ), =( Z, T ) ] )
% 32.56/32.94 , clause( 94625, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 32.56/32.94 , T, X ) ) ), =( Y, Z ) ] )
% 32.56/32.94 , clause( 94626, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 32.56/32.94 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94627, [ 'c_HOL_Oord__class_Oless'( 'v_k', 'v_n', 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94628, [ ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( 'v_k', 'v_i', 'tc_nat' ), 'v_n', 'tc_nat' )
% 32.56/32.94 ) ] )
% 32.56/32.94 , clause( 94629, [
% 32.56/32.94 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94630, [
% 32.56/32.94 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94631, [
% 32.56/32.94 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94632, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 32.56/32.94 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94633, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.56/32.94 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94634, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 32.56/32.94 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94635, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 32.56/32.94 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94636, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 32.56/32.94 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94637, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94638, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94639, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94640, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94641, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94642, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 32.56/32.94 ] )
% 32.56/32.94 , clause( 94643, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94644, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94645, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 94646, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94647, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94648, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94649, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94650, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94651, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94652, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94653, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94654, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94655, [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94656, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94657, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94658, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 32.56/32.94 ] ).
% 32.56/32.94
% 32.56/32.94
% 32.56/32.94
% 32.56/32.94 subsumption(
% 32.56/32.94 clause( 18, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 32.56/32.94 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 32.56/32.94 )
% 32.56/32.94 , clause( 93878, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 32.56/32.94 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 32.56/32.94 )
% 32.56/32.94 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 32.56/32.94 1 )] ) ).
% 32.56/32.94
% 32.56/32.94
% 32.56/32.94 subsumption(
% 32.56/32.94 clause( 21, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 93887, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 32.56/32.94 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 32.56/32.94 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 32.56/32.94
% 32.56/32.94
% 32.56/32.94 subsumption(
% 32.56/32.94 clause( 96, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 93971, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 32.56/32.94 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 32.56/32.94 ), ==>( 1, 1 )] ) ).
% 32.56/32.94
% 32.56/32.94
% 32.56/32.94 subsumption(
% 32.56/32.94 clause( 97, [ ~(
% 32.56/32.94 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 32.56/32.94 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 32.56/32.94 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 32.56/32.94 , clause( 93974, [ ~(
% 32.56/32.94 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 32.56/32.94 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 32.56/32.94 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 32.56/32.94 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 32.56/32.94 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 32.56/32.94 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 ),
% 32.56/32.94 ==>( 4, 4 )] ) ).
% 32.56/32.94
% 32.56/32.94
% 32.56/32.94 subsumption(
% 32.56/32.94 clause( 99, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' )
% 32.56/32.94 , Z, 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y
% 32.56/32.94 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 93976, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 32.56/32.94 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 32.56/32.94 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 32.56/32.94 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 32.56/32.94 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 32.56/32.94 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 32.56/32.94
% 32.56/32.94
% 32.56/32.94 subsumption(
% 32.56/32.94 clause( 209, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 32.56/32.94 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94110, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ),
% 32.56/32.94 ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.56/32.94 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 32.56/32.94 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 32.56/32.94
% 32.56/32.94
% 32.56/32.94 subsumption(
% 32.56/32.94 clause( 261, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.56/32.94 'tc_nat' ) ] )
% 32.56/32.94 , clause( 94174, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 32.56/32.94 X, 'tc_nat' ) ] )
% 32.56/32.94 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.56/32.94
% 32.56/32.94
% 32.56/32.94 subsumption(
% 32.56/32.94 clause( 339, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , clause( 94269, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 32.56/32.94 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 32.56/32.94 'tc_nat' ) ) ] )
% 32.56/32.94 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 32.56/32.98 ), ==>( 1, 1 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 363, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 32.56/32.98 , clause( 94303, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 32.56/32.98 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 32.56/32.98 ), ==>( 1, 1 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 377, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 32.56/32.98 , T ), =( X, Z ) ] )
% 32.56/32.98 , clause( 94321, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 32.56/32.98 , T ), =( X, Z ) ] )
% 32.56/32.98 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 32.56/32.98 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 449, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 32.56/32.98 , Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 32.56/32.98 , clause( 94417, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.98 X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 32.56/32.98 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 32.56/32.98 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 453, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 32.56/32.98 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.98 , clause( 94421, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 32.56/32.98 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.98 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 32.56/32.98 ), ==>( 1, 1 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 537, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 32.56/32.98 'tc_nat' ) ] )
% 32.56/32.98 , clause( 94526, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 32.56/32.98 'tc_nat' ) ] )
% 32.56/32.98 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 32.56/32.98 ), ==>( 1, 1 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 547, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 32.56/32.98 , clause( 94540, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 32.56/32.98 )
% 32.56/32.98 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 559, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y )
% 32.56/32.98 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.98 , clause( 94556, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'(
% 32.56/32.98 Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 32.56/32.98 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 32.56/32.98 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 567, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 32.56/32.98 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.98 , clause( 94564, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 32.56/32.98 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.56/32.98 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 615, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.98 'v_i', X, 'tc_nat' ), 'v_n', 'tc_nat' ) ] )
% 32.56/32.98 , clause( 94620, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.98 'v_i', X, 'tc_nat' ), 'v_n', 'tc_nat' ) ] )
% 32.56/32.98 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 620, [ 'c_HOL_Oord__class_Oless'( 'v_k', 'v_n', 'tc_nat' ) ] )
% 32.56/32.98 , clause( 94627, [ 'c_HOL_Oord__class_Oless'( 'v_k', 'v_n', 'tc_nat' ) ] )
% 32.56/32.98 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 621, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.56/32.98 'v_k', 'v_i', 'tc_nat' ), 'v_n', 'tc_nat' ) ) ] )
% 32.56/32.98 , clause( 94628, [ ~( 'c_HOL_Oord__class_Oless'(
% 32.56/32.98 'c_HOL_Ominus__class_Ominus'( 'v_k', 'v_i', 'tc_nat' ), 'v_n', 'tc_nat' )
% 32.56/32.98 ) ] )
% 32.56/32.98 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 623, [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 32.56/32.98 'tc_nat' ) ] )
% 32.56/32.98 , clause( 94630, [
% 32.56/32.98 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 32.56/32.98 )
% 32.56/32.98 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 subsumption(
% 32.56/32.98 clause( 639, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 32.56/32.98 , clause( 94646, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 32.56/32.98 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 eqswap(
% 32.56/32.98 clause( 104673, [ =( Y, X ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 32.56/32.98 , T ) ] )
% 32.56/32.98 , clause( 377, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 32.56/32.98 , T ), =( X, Z ) ] )
% 32.56/32.98 , 2, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] )
% 32.56/32.98 ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 eqswap(
% 32.56/32.98 clause( 104674, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat' ),
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 32.56/32.98 , X ), =( Y, T ) ] )
% 32.56/32.98 , clause( 104673, [ =( Y, X ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 32.56/32.98 , T ) ] )
% 32.56/32.98 , 1, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] )
% 32.56/32.98 ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 eqfact(
% 32.56/32.98 clause( 104692, [ ~( =( X, Y ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 32.56/32.98 , Y ) ] )
% 32.56/32.98 , clause( 104674, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat' ),
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 32.56/32.98 , X ), =( Y, T ) ] )
% 32.56/32.98 , 2, 1, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, Z ), :=( T, X )] )
% 32.56/32.98 ).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 eqswap(
% 32.56/32.98 clause( 104695, [ =( Y, X ), ~( =( Z, Y ) ), ~( =(
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ) ] )
% 32.56/32.98 , clause( 104692, [ ~( =( X, Y ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 32.56/32.98 , Y ) ] )
% 32.56/32.98 , 2, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] )).
% 32.56/32.98
% 32.56/32.98
% 32.56/32.98 eqswap(
% 32.56/32.98 clause( 104697, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 32.56/32.98 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( X
% 32.56/32.98 , Z ), ~( =( Y, X ) ) ] )
% 32.56/32.98 , clause( 104695, [ =( Y, X ), ~( =( Z, Y ) ), ~( =(
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ),
% 32.56/32.98 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat'
% 32.56/32.98 ), 'c_HOL_OtimesCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------