TSTP Solution File: SWV689-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV689-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n008.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 34.44s 34.85s
% Output : Refutation 34.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV689-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Thu Jun 16 02:29:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.92/1.28 *** allocated 10000 integers for termspace/termends
% 0.92/1.28 *** allocated 10000 integers for clauses
% 0.92/1.28 *** allocated 10000 integers for justifications
% 0.92/1.28 *** allocated 15000 integers for termspace/termends
% 0.92/1.28 *** allocated 22500 integers for termspace/termends
% 0.92/1.28 Bliksem 1.12
% 0.92/1.28
% 0.92/1.28
% 0.92/1.28 Automatic Strategy Selection
% 0.92/1.28
% 0.92/1.28 Clauses:
% 0.92/1.28 [
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.92/1.28 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.28 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.28 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.28 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.92/1.28 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.28 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.92/1.28 ), X ) ],
% 0.92/1.28 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.28 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.92/1.28 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 0.92/1.28 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.28 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.92/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.92/1.28 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.92/1.28 ],
% 0.92/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.92/1.28 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 0.92/1.28 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ],
% 0.92/1.28 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.92/1.28 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.92/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.92/1.28 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.92/1.28 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 0.92/1.28 ,
% 0.92/1.28 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 0.92/1.28 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.28 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.92/1.28 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.28 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.92/1.28 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 0.92/1.28 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.28 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.92/1.28 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.28 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 0.92/1.28 , Y, 'tc_nat' ) ) ],
% 0.92/1.28 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.92/1.28 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.92/1.28 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.28 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.28 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.28 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.28 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) )
% 0.92/1.28 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 0.92/1.28 , 'tc_nat' ) ) ],
% 0.92/1.28 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.92/1.28 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.92/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 0.92/1.28 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.92/1.28 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.92/1.28 ,
% 0.92/1.28 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.92/1.28 'tc_nat' ), 'tc_nat' ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 0.92/1.28 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.28 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.28 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.28 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.28 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.92/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.92/1.28 ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.92/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.92/1.28 ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.28 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.92/1.28 X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.28 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.92/1.28 ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.28 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.92/1.28 X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.28 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.92/1.28 ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.92/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.92/1.28 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.92/1.28 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.92/1.28 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.92/1.28 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.92/1.28 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.92/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.92/1.28 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.28 , X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.28 , X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.92/1.28 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.28 , X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.92/1.28 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.28 , X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.28 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.92/1.28 ,
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.92/1.28 ,
% 0.92/1.28 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.92/1.28 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.28 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.28 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.28 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.28 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.28 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.28 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 0.92/1.28 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 0.92/1.28 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.28 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 0.92/1.28 'c_lessequals'( T, X, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 0.92/1.28 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U ) ],
% 0.92/1.28 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat'
% 0.92/1.28 ), 'tc_nat' ) ],
% 0.92/1.28 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.92/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.28 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.92/1.28 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.92/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.92/1.28 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.92/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.28 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.92/1.28 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.28 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.28 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.92/1.28 ,
% 0.92/1.28 [ =( 'c_Orderings_Oord__class_Omin'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.28 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.92/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.92/1.28 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.92/1.28 , T, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.28 , Z, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.92/1.28 , T, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.28 , Z, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.92/1.28 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.28 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.92/1.28 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.92/1.28 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.92/1.28 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 0.92/1.28 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.28 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.92/1.28 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 0.92/1.28 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.92/1.28 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.92/1.28 , X, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.92/1.28 , T, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.92/1.28 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.92/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.92/1.28 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.92/1.28 ,
% 0.92/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.92/1.28 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.92/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.92/1.28 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.92/1.28 , X ), W, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 0.92/1.28 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 0.92/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.92/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.92/1.28 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.92/1.28 , X ), T, X ), W, X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 0.92/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 0.92/1.28 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.28 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.92/1.28 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.92/1.28 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.28 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.92/1.28 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.28 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 0.92/1.28 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.28 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.92/1.28 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.92/1.28 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z,
% 0.92/1.28 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 0.92/1.28 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.28 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 0.92/1.28 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.92/1.28 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.92/1.28 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.92/1.28 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.92/1.28 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.92/1.28 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.92/1.28 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.92/1.28 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.92/1.28 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.92/1.28 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.92/1.28 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.92/1.28 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.92/1.28 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 0.92/1.28 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.92/1.28 ,
% 0.92/1.28 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.92/1.28 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.92/1.28 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.92/1.28 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.28 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 0.92/1.28 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.92/1.28 ,
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.92/1.28 ) ) ],
% 0.92/1.28 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.92/1.28 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.92/1.28 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 0.92/1.28 , X ), Z, X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.28 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.92/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.28 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.92/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 0.92/1.28 , X ) ) ],
% 0.92/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.92/1.28 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.92/1.28 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.92/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.92/1.28 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.92/1.28 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.92/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.92/1.28 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.92/1.28 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.92/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.92/1.28 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ],
% 0.92/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.92/1.28 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ],
% 0.92/1.28 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.28 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.92/1.28 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.92/1.28 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.92/1.28 , Y, X ), X ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.92/1.28 , Z, X ), X ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 0.92/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.92/1.28 , Z, X ), X ) ],
% 0.92/1.28 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.28 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.92/1.28 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.92/1.28 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 0.92/1.28 Z, 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.92/1.28 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 0.92/1.28 Y, X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.92/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.92/1.28 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.92/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.92/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.92/1.28 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.92/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.92/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.92/1.28 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.28 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.92/1.28 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.28 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.28 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.92/1.28 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.28 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.92/1.28 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.28 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.92/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.92/1.28 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.92/1.28 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 0.92/1.29 ), X ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.92/1.29 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 0.92/1.29 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 0.92/1.29 ],
% 0.92/1.29 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.92/1.29 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.92/1.29 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.92/1.29 , Y, X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.92/1.29 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.92/1.29 , Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.92/1.29 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.92/1.29 , T, X ), X ), T, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.92/1.29 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.92/1.29 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.92/1.29 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.92/1.29 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.92/1.29 , X ), Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.92/1.29 , X ), Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.92/1.29 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.92/1.29 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 0.92/1.29 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 0.92/1.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.92/1.29 , Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.92/1.29 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.92/1.29 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.92/1.29 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.92/1.29 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.29 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.92/1.29 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.92/1.29 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.92/1.29 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.29 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.92/1.29 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.92/1.29 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 0.92/1.29 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.92/1.29 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.92/1.29 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 0.92/1.29 ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.92/1.29 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 0.92/1.29 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 0.92/1.29 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 0.92/1.29 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.92/1.29 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.92/1.29 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.92/1.29 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.92/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.92/1.29 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.92/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 0.92/1.29 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.92/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.92/1.29 T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.92/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.92/1.29 X ), Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.92/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.92/1.29 T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.92/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.92/1.29 X ), T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.92/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.92/1.29 T, X ), X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.92/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.92/1.29 X ), T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.92/1.29 ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.29 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.92/1.29 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.92/1.29 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.29 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.92/1.29 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.92/1.29 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 0.92/1.29 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.92/1.29 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.92/1.29 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 0.92/1.29 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.92/1.29 Y, 'tc_nat' ), 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.92/1.29 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.92/1.29 Y, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.92/1.29 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ],
% 0.92/1.29 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.92/1.29 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.92/1.29 X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 0.92/1.29 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.29 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X
% 0.92/1.29 ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y
% 0.92/1.29 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.92/1.29 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.92/1.29 X ) ) ), =( Z, T ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.92/1.29 X ) ) ), =( Z, T ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.92/1.29 X ) ) ), =( Y, T ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.92/1.29 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.92/1.29 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.92/1.29 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.92/1.29 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.92/1.29 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.92/1.29 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.92/1.29 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 0.92/1.29 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.92/1.29 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X )
% 0.92/1.29 , 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 0.92/1.29 ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.92/1.29 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.92/1.29 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.29 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.92/1.29 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ) ), =( Y, Z ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.92/1.29 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.92/1.29 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.92/1.29 , T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.29 , Z, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 0.92/1.29 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.29 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 X ), T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 0.92/1.29 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.29 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.92/1.29 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.92/1.29 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.92/1.29 'c_Suc'( X ), 'tc_nat' ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.92/1.29 'c_Suc'( X ), 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 0.92/1.29 Z, Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.92/1.29 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 0.92/1.29 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.92/1.29 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.92/1.29 ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 0.92/1.29 ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 X ), X ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 0.92/1.29 ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.92/1.29 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 0.92/1.29 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 0.92/1.29 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 0.92/1.29 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 0.92/1.29 , X, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 0.92/1.29 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.92/1.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.92/1.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.92/1.29 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ) ],
% 0.92/1.29 [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.92/1.29 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat' ) ) )
% 0.92/1.29 ],
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.92/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 0.92/1.29 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.29 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 X ), T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.29 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.92/1.29 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.92/1.29 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 0.92/1.29 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 0.92/1.29 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.92/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.92/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 0.92/1.29 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.92/1.29 ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.92/1.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.92/1.29 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.92/1.29 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.92/1.29 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.92/1.29 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.92/1.29 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 0.92/1.29 X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 0.92/1.29 ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 0.92/1.29 X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.92/1.29 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.92/1.29 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' )
% 0.92/1.29 ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.92/1.29 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.92/1.29 ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.92/1.29 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 0.92/1.29 'c_Suc'( X ), 'tc_nat' ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.92/1.29 ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.92/1.29 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.92/1.29 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.92/1.29 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.92/1.29 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z,
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.92/1.29 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, U,
% 0.92/1.29 X ), X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.29 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.92/1.29 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 0.92/1.29 'tc_nat' ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Z
% 0.92/1.29 , Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 0.92/1.29 , Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 0.92/1.29 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.92/1.29 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.92/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.92/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.92/1.29 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.92/1.29 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.92/1.29 , X ), W, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 X ) ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 0.92/1.29 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 0.92/1.29 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.92/1.29 ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.92/1.29 X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.92/1.29 X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.92/1.29 X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.92/1.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.92/1.29 , T, X ), X ), T, X ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.92/1.29 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.92/1.29 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.92/1.29 T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.92/1.29 T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.92/1.29 T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.92/1.29 T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.92/1.29 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.92/1.29 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.92/1.29 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.92/1.29 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.92/1.29 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.92/1.29 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.92/1.29 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 0.92/1.29 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 0.92/1.29 Z, X ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.92/1.29 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.92/1.29 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 0.92/1.29 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 0.92/1.29 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.92/1.29 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.92/1.29 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.92/1.29 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.92/1.29 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 0.92/1.29 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.92/1.29 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.92/1.29 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.92/1.29 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.92/1.29 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), Y,
% 0.92/1.29 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.92/1.29 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.92/1.29 , T ), =( X, Z ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.92/1.29 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.92/1.29 , T ), =( X, Z ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.92/1.29 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.92/1.29 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.92/1.29 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.92/1.29 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.92/1.29 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 0.92/1.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 0.92/1.29 X ), Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.92/1.29 , X ), X ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.92/1.29 , X ), X ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.92/1.29 ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.92/1.29 ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.92/1.29 ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.92/1.29 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.92/1.29 ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.92/1.29 ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.92/1.29 ],
% 0.92/1.29 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.92/1.29 ), 'tc_nat' ), X ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.92/1.29 , X, 'tc_nat' ), X ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.92/1.29 ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.92/1.29 ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.92/1.29 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.92/1.29 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.92/1.29 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.29 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.29 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.92/1.29 X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 Z, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.29 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 Z, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.92/1.29 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.92/1.29 X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.92/1.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.92/1.29 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.92/1.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.92/1.29 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.92/1.29 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.92/1.29 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.92/1.29 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.92/1.29 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.92/1.29 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.92/1.29 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.92/1.29 Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.92/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.92/1.29 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.92/1.29 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.92/1.29 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.92/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( T
% 0.92/1.29 , Z, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z
% 0.92/1.29 , T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.92/1.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.92/1.29 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.92/1.29 , X ), W, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.92/1.29 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.92/1.29 W, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.92/1.29 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.92/1.29 , X ), T, X ), W, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.92/1.29 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.92/1.29 W, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.92/1.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.92/1.29 , Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.92/1.29 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.92/1.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.92/1.29 X ), Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ),
% 0.92/1.29 T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.92/1.29 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.92/1.29 , T, X ), X ), T, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 0.92/1.29 ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.92/1.29 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.92/1.29 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 0.92/1.29 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.92/1.29 ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.92/1.29 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.92/1.29 ), Y ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 ) ), =( Y, Z ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 ) ), =( Y, Z ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.92/1.29 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.92/1.29 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.92/1.29 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.92/1.29 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.92/1.29 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.92/1.29 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.92/1.29 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.92/1.29 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.92/1.29 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.92/1.29 , U, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.92/1.29 ), Y ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.92/1.29 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.92/1.29 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.92/1.29 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 , X ) ],
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 0.92/1.29 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.92/1.29 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.92/1.29 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 0.92/1.29 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.92/1.29 , Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.92/1.29 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.92/1.29 Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.92/1.29 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 0.92/1.29 ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 0.92/1.29 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.92/1.29 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.92/1.29 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.92/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.92/1.29 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 0.92/1.29 ), X, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.92/1.29 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 0.92/1.29 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.92/1.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.92/1.29 , Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 0.92/1.29 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.92/1.29 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.92/1.29 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.92/1.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.92/1.29 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 0.92/1.29 , Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X
% 0.92/1.29 ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 0.92/1.29 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.92/1.29 ) ), X, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.92/1.29 ) ), X, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 0.92/1.29 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.92/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.92/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.92/1.29 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.92/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.92/1.29 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.92/1.29 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 0.92/1.29 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.92/1.29 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 0.92/1.29 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.92/1.29 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 0.92/1.29 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.92/1.29 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 0.92/1.29 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.92/1.29 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.92/1.29 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.92/1.29 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.92/1.29 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.92/1.29 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.92/1.29 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.92/1.29 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.92/1.29 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.92/1.29 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.92/1.29 ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.29 , Y, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.92/1.29 , T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.92/1.29 , T, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.92/1.29 , Y, X ), X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.92/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 0.92/1.29 Y, X ), X ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 0.92/1.29 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.92/1.29 'c_lessequals'( Z, Y, X ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.92/1.29 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 X, T, 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.92/1.29 ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.92/1.29 ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.92/1.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.92/1.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.92/1.29 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.92/1.29 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.92/1.29 ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.92/1.29 ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.92/1.29 Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.92/1.29 ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.92/1.29 ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.92/1.29 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.92/1.29 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 0.92/1.29 , Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.92/1.29 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.92/1.29 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.92/1.29 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.92/1.29 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.92/1.29 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.92/1.29 , 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 0.92/1.29 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.92/1.29 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.92/1.29 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.92/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.92/1.29 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.92/1.29 ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 0.92/1.29 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.92/1.29 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.92/1.29 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.92/1.29 , 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat'
% 0.92/1.29 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.92/1.29 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.92/1.29 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 0.92/1.29 'tc_nat' ) ],
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.92/1.29 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.92/1.29 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.92/1.29 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 0.92/1.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.92/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.92/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 0.92/1.29 ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.92/1.29 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 0.92/1.29 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.92/1.29 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.92/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 0.92/1.29 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.92/1.29 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.92/1.29 ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.92/1.29 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.92/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.92/1.29 ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 0.92/1.29 , 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.92/1.29 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.92/1.29 ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.92/1.29 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.92/1.29 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.92/1.29 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.92/1.29 , Y, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.92/1.29 , Y, X ) ) ],
% 0.92/1.29 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.92/1.29 , X ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.92/1.29 ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.92/1.29 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.92/1.29 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.92/1.29 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.92/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.92/1.29 ), =( Z, Y ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.92/1.29 ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.92/1.29 ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.92/1.29 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'v_i', 'v_n', 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.92/1.29 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.92/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.92/1.29 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.92/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.92/1.29 , T, X ) ) ), =( Z, T ) ],
% 0.92/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.92/1.29 , T, X ) ) ), =( Y, Z ) ],
% 0.92/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.92/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.92/1.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.92/1.29 [ 'c_HOL_Oord__class_Oless'( 'v_i', 'v_n', 'tc_nat' ) ],
% 0.92/1.29 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( 'v_i',
% 0.92/1.29 'v_k', 'tc_nat' ), 'v_n', 'tc_nat' ) ) ],
% 0.92/1.29 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.92/1.29 ],
% 0.92/1.29 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.92/1.29 ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.92/1.29 ],
% 0.92/1.29 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 0.92/1.29 ,
% 0.92/1.29 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.92/1.29 [ 'class_Orderings_Oorder'( 'tc_nat' ) ]
% 0.92/1.29 ] .
% 0.92/1.29
% 0.92/1.29
% 0.92/1.29 percentage equality = 0.215066, percentage horn = 0.888726
% 0.92/1.29 This is a problem with some equality
% 2.23/2.61
% 2.23/2.61
% 2.23/2.61
% 2.23/2.61 Options Used:
% 2.23/2.61
% 2.23/2.61 useres = 1
% 2.23/2.61 useparamod = 1
% 2.23/2.61 useeqrefl = 1
% 2.23/2.61 useeqfact = 1
% 2.23/2.61 usefactor = 1
% 2.23/2.61 usesimpsplitting = 0
% 2.23/2.61 usesimpdemod = 5
% 2.23/2.61 usesimpres = 3
% 2.23/2.61
% 2.23/2.61 resimpinuse = 1000
% 2.23/2.61 resimpclauses = 20000
% 2.23/2.61 substype = eqrewr
% 2.23/2.61 backwardsubs = 1
% 2.23/2.61 selectoldest = 5
% 2.23/2.61
% 2.23/2.61 litorderings [0] = split
% 2.23/2.61 litorderings [1] = extend the termordering, first sorting on arguments
% 2.23/2.61
% 2.23/2.61 termordering = kbo
% 2.23/2.61
% 2.23/2.61 litapriori = 0
% 2.23/2.61 termapriori = 1
% 2.23/2.61 litaposteriori = 0
% 2.23/2.61 termaposteriori = 0
% 2.23/2.61 demodaposteriori = 0
% 2.23/2.61 ordereqreflfact = 0
% 2.23/2.61
% 2.23/2.61 litselect = negord
% 2.23/2.61
% 2.23/2.61 maxweight = 15
% 2.23/2.61 maxdepth = 30000
% 2.23/2.61 maxlength = 115
% 2.23/2.61 maxnrvars = 195
% 2.23/2.61 excuselevel = 1
% 2.23/2.61 increasemaxweight = 1
% 2.23/2.61
% 2.23/2.61 maxselected = 10000000
% 2.23/2.61 maxnrclauses = 10000000
% 2.23/2.61
% 2.23/2.61 showgenerated = 0
% 2.23/2.61 showkept = 0
% 2.23/2.61 showselected = 0
% 2.23/2.61 showdeleted = 0
% 2.23/2.61 showresimp = 1
% 2.23/2.61 showstatus = 2000
% 2.23/2.61
% 2.23/2.61 prologoutput = 1
% 2.23/2.61 nrgoals = 5000000
% 2.23/2.61 totalproof = 1
% 2.23/2.61
% 2.23/2.61 Symbols occurring in the translation:
% 2.23/2.62
% 2.23/2.62 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.23/2.62 . [1, 2] (w:1, o:106, a:1, s:1, b:0),
% 2.23/2.62 ! [4, 1] (w:0, o:47, a:1, s:1, b:0),
% 2.23/2.62 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.23/2.62 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.23/2.62 'class_Ring__and__Field_Oordered__semiring__strict' [40, 1] (w:1, o:
% 2.23/2.62 57, a:1, s:1, b:0),
% 2.23/2.62 'c_HOL_Ozero__class_Ozero' [41, 1] (w:1, o:58, a:1, s:1, b:0),
% 2.23/2.62 'c_HOL_Oord__class_Oless' [43, 3] (w:1, o:134, a:1, s:1, b:0),
% 2.23/2.62 'c_HOL_Otimes__class_Otimes' [45, 3] (w:1, o:135, a:1, s:1, b:0),
% 2.23/2.62 'c_Suc' [47, 1] (w:1, o:59, a:1, s:1, b:0),
% 2.23/2.62 'tc_nat' [49, 0] (w:1, o:18, a:1, s:1, b:0),
% 2.23/2.62 'c_HOL_Oplus__class_Oplus' [50, 3] (w:1, o:136, a:1, s:1, b:0),
% 2.23/2.62 'class_Ring__and__Field_Oordered__ring__strict' [51, 1] (w:1, o:56
% 2.23/2.62 , a:1, s:1, b:0),
% 2.23/2.62 'c_Ring__and__Field_Odvd__class_Odvd' [54, 3] (w:1, o:137, a:1, s:1
% 2.23/2.62 , b:0),
% 2.23/2.62 'class_OrderedGroup_Opordered__comm__monoid__add' [55, 1] (w:1, o:61
% 2.23/2.62 , a:1, s:1, b:0),
% 2.23/2.62 'c_lessequals' [56, 3] (w:1, o:138, a:1, s:1, b:0),
% 2.23/2.62 'c_HOL_Ominus__class_Ominus' [60, 3] (w:1, o:139, a:1, s:1, b:0),
% 2.23/2.62 'class_Ring__and__Field_Ocomm__semiring__1' [61, 1] (w:1, o:64, a:1
% 2.23/2.62 , s:1, b:0),
% 2.23/2.62 'class_OrderedGroup_Opordered__ab__group__add__abs' [66, 1] (w:1, o:
% 2.23/2.62 65, a:1, s:1, b:0),
% 2.23/2.62 'c_HOL_Oabs__class_Oabs' [67, 2] (w:1, o:131, a:1, s:1, b:0),
% 2.23/2.62 'class_Orderings_Olinorder' [68, 1] (w:1, o:66, a:1, s:1, b:0),
% 2.23/2.62 'c_Orderings_Oord__class_Omin' [69, 3] (w:1, o:140, a:1, s:1, b:0),
% 2.23/2.62 'class_OrderedGroup_Olordered__ab__group__add__abs' [70, 1] (w:1, o:
% 2.23/2.62 67, a:1, s:1, b:0),
% 2.23/2.62 'class_Orderings_Oorder' [72, 1] (w:1, o:68, a:1, s:1, b:0),
% 2.23/2.62 'class_Ring__and__Field_Oidom' [74, 1] (w:1, o:69, a:1, s:1, b:0),
% 2.23/2.62 'class_OrderedGroup_Opordered__ab__semigroup__add' [75, 1] (w:1, o:70
% 2.23/2.62 , a:1, s:1, b:0),
% 2.23/2.62 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [76, 1]
% 2.23/2.62 (w:1, o:71, a:1, s:1, b:0),
% 2.23/2.62 'class_Ring__and__Field_Oordered__idom' [77, 1] (w:1, o:72, a:1, s:1
% 2.23/2.62 , b:0),
% 2.23/2.62 'class_Ring__and__Field_Opordered__ring__abs' [78, 1] (w:1, o:76, a:1
% 2.23/2.62 , s:1, b:0),
% 2.23/2.62 'class_OrderedGroup_Oab__semigroup__idem__mult' [79, 1] (w:1, o:77
% 2.23/2.62 , a:1, s:1, b:0),
% 2.23/2.62 'c_Divides_Odiv__class_Omod' [80, 3] (w:1, o:141, a:1, s:1, b:0),
% 2.23/2.62 'c_Parity_Oeven__odd__class_Oeven' [81, 2] (w:1, o:132, a:1, s:1, b:0
% 2.23/2.62 ),
% 2.23/2.62 'class_Divides_Osemiring__div' [82, 1] (w:1, o:79, a:1, s:1, b:0),
% 2.23/2.62 'class_OrderedGroup_Olordered__ab__group__add' [83, 1] (w:1, o:80, a:
% 2.23/2.62 1, s:1, b:0),
% 2.23/2.62 'class_Ring__and__Field_Oring__no__zero__divisors' [84, 1] (w:1, o:81
% 2.23/2.62 , a:1, s:1, b:0),
% 2.23/2.62 'class_Ring__and__Field_Ono__zero__divisors' [85, 1] (w:1, o:55, a:1
% 2.23/2.62 , s:1, b:0),
% 2.23/2.62 'class_Ring__and__Field_Oordered__semiring' [88, 1] (w:1, o:73, a:1
% 2.23/2.62 , s:1, b:0),
% 2.23/2.62 'class_Int_Onumber__ring' [89, 1] (w:1, o:82, a:1, s:1, b:0),
% 2.23/2.62 'class_Nat_Osemiring__char__0' [90, 1] (w:1, o:60, a:1, s:1, b:0),
% 2.23/2.62 'c_Nat_Osemiring__1__class_Oof__nat' [91, 2] (w:1, o:133, a:1, s:1
% 23.41/23.79 , b:0),
% 23.41/23.79 'class_Ring__and__Field_Opordered__ring' [92, 1] (w:1, o:83, a:1, s:1
% 23.41/23.79 , b:0),
% 23.41/23.79 'class_OrderedGroup_Ocomm__monoid__add' [95, 1] (w:1, o:84, a:1, s:1
% 23.41/23.79 , b:0),
% 23.41/23.79 'class_Ring__and__Field_Oring' [96, 1] (w:1, o:85, a:1, s:1, b:0),
% 23.41/23.79 'class_Ring__and__Field_Olordered__ring' [98, 1] (w:1, o:86, a:1, s:1
% 23.41/23.79 , b:0),
% 23.41/23.79 'class_Ring__and__Field_Odvd' [99, 1] (w:1, o:88, a:1, s:1, b:0),
% 23.41/23.79 'class_Ring__and__Field_Oordered__semidom' [100, 1] (w:1, o:74, a:1
% 23.41/23.79 , s:1, b:0),
% 23.41/23.79 'class_Ring__and__Field_Omult__mono1' [103, 1] (w:1, o:52, a:1, s:1
% 23.41/23.79 , b:0),
% 23.41/23.79 'class_Ring__and__Field_Omult__mono' [104, 1] (w:1, o:53, a:1, s:1
% 23.41/23.79 , b:0),
% 23.41/23.79 'class_Ring__and__Field_Osemiring__1' [105, 1] (w:1, o:90, a:1, s:1
% 23.41/23.79 , b:0),
% 23.41/23.79 'class_Ring__and__Field_Ocomm__ring' [106, 1] (w:1, o:62, a:1, s:1
% 23.41/23.79 , b:0),
% 23.41/23.79 'class_Ring__and__Field_Opordered__cancel__semiring' [109, 1] (w:1
% 23.41/23.79 , o:91, a:1, s:1, b:0),
% 23.41/23.79 'class_OrderedGroup_Oab__semigroup__mult' [110, 1] (w:1, o:92, a:1
% 23.41/23.79 , s:1, b:0),
% 23.41/23.79 'class_RealVector_Oreal__normed__algebra' [111, 1] (w:1, o:93, a:1
% 23.41/23.79 , s:1, b:0),
% 23.41/23.79 'class_Ring__and__Field_Ocomm__semiring' [115, 1] (w:1, o:87, a:1, s:
% 23.41/23.79 1, b:0),
% 23.41/23.79 'class_Ring__and__Field_Opordered__semiring' [117, 1] (w:1, o:94, a:1
% 23.41/23.79 , s:1, b:0),
% 23.41/23.79 'class_OrderedGroup_Ocancel__ab__semigroup__add' [118, 1] (w:1, o:95
% 23.41/23.79 , a:1, s:1, b:0),
% 23.41/23.79 'class_OrderedGroup_Ocancel__semigroup__add' [119, 1] (w:1, o:96, a:1
% 23.41/23.79 , s:1, b:0),
% 23.41/23.79 'class_OrderedGroup_Oab__group__add' [120, 1] (w:1, o:97, a:1, s:1
% 23.41/23.79 , b:0),
% 23.41/23.79 'class_OrderedGroup_Oab__semigroup__add' [121, 1] (w:1, o:98, a:1, s:
% 23.41/23.79 1, b:0),
% 23.41/23.79 'class_Ring__and__Field_Osemiring' [122, 1] (w:1, o:99, a:1, s:1, b:0
% 23.41/23.79 ),
% 23.41/23.79 'class_Ring__and__Field_Oordered__comm__semiring__strict' [123, 1]
% 23.41/23.79 (w:1, o:75, a:1, s:1, b:0),
% 23.41/23.79 'class_OrderedGroup_Omonoid__add' [126, 1] (w:1, o:100, a:1, s:1, b:0
% 23.41/23.79 ),
% 23.41/23.79 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [127, 1]
% 23.41/23.79 (w:1, o:101, a:1, s:1, b:0),
% 23.41/23.79 'class_Orderings_Opreorder' [128, 1] (w:1, o:102, a:1, s:1, b:0),
% 23.41/23.79 'class_Divides_Oring__div' [129, 1] (w:1, o:78, a:1, s:1, b:0),
% 23.41/23.79 'class_OrderedGroup_Opordered__ab__group__add' [130, 1] (w:1, o:103
% 23.41/23.79 , a:1, s:1, b:0),
% 23.41/23.79 'class_Ring__and__Field_Ocomm__ring__1' [133, 1] (w:1, o:63, a:1, s:1
% 23.41/23.79 , b:0),
% 23.41/23.79 'class_OrderedGroup_Ogroup__add' [134, 1] (w:1, o:104, a:1, s:1, b:0)
% 23.41/23.79 ,
% 23.41/23.79 'class_Ring__and__Field_Omult__zero' [135, 1] (w:1, o:54, a:1, s:1
% 23.41/23.79 , b:0),
% 23.41/23.79 'class_Ring__and__Field_Oabs__if' [137, 1] (w:1, o:105, a:1, s:1, b:0
% 23.41/23.79 ),
% 23.41/23.79 'class_Ring__and__Field_Oring__1' [138, 1] (w:1, o:89, a:1, s:1, b:0)
% 23.41/23.79 ,
% 23.41/23.79 'v_i' [139, 0] (w:1, o:44, a:1, s:1, b:0),
% 23.41/23.79 'v_n' [140, 0] (w:1, o:45, a:1, s:1, b:0),
% 23.41/23.79 'v_k' [141, 0] (w:1, o:46, a:1, s:1, b:0).
% 23.41/23.79
% 23.41/23.79
% 23.41/23.79 Starting Search:
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79
% 23.41/23.79 Intermediate Status:
% 23.41/23.79 Generated: 5911
% 23.41/23.79 Kept: 2014
% 23.41/23.79 Inuse: 143
% 23.41/23.79 Deleted: 8
% 23.41/23.79 Deletedinuse: 0
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79
% 23.41/23.79 Intermediate Status:
% 23.41/23.79 Generated: 18246
% 23.41/23.79 Kept: 4493
% 23.41/23.79 Inuse: 300
% 23.41/23.79 Deleted: 11
% 23.41/23.79 Deletedinuse: 0
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79
% 23.41/23.79 Intermediate Status:
% 23.41/23.79 Generated: 29964
% 23.41/23.79 Kept: 6596
% 23.41/23.79 Inuse: 315
% 23.41/23.79 Deleted: 17
% 23.41/23.79 Deletedinuse: 6
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79
% 23.41/23.79 Intermediate Status:
% 23.41/23.79 Generated: 41479
% 23.41/23.79 Kept: 8973
% 23.41/23.79 Inuse: 350
% 23.41/23.79 Deleted: 17
% 23.41/23.79 Deletedinuse: 6
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79
% 23.41/23.79 Intermediate Status:
% 23.41/23.79 Generated: 55076
% 23.41/23.79 Kept: 11472
% 23.41/23.79 Inuse: 398
% 23.41/23.79 Deleted: 19
% 23.41/23.79 Deletedinuse: 6
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79
% 23.41/23.79 Intermediate Status:
% 23.41/23.79 Generated: 66456
% 23.41/23.79 Kept: 13481
% 23.41/23.79 Inuse: 437
% 23.41/23.79 Deleted: 20
% 23.41/23.79 Deletedinuse: 6
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79
% 23.41/23.79 Intermediate Status:
% 23.41/23.79 Generated: 75682
% 23.41/23.79 Kept: 15519
% 23.41/23.79 Inuse: 482
% 23.41/23.79 Deleted: 20
% 23.41/23.79 Deletedinuse: 6
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79 Resimplifying inuse:
% 23.41/23.79 Done
% 23.41/23.79
% 23.41/23.79
% 23.41/23.79 Intermediate Status:
% 23.41/23.79 Generated: 86022
% 34.44/34.85 Kept: 17527
% 34.44/34.85 Inuse: 530
% 34.44/34.85 Deleted: 20
% 34.44/34.85 Deletedinuse: 6
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 97215
% 34.44/34.85 Kept: 19538
% 34.44/34.85 Inuse: 597
% 34.44/34.85 Deleted: 23
% 34.44/34.85 Deletedinuse: 6
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying clauses:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 107128
% 34.44/34.85 Kept: 21568
% 34.44/34.85 Inuse: 628
% 34.44/34.85 Deleted: 978
% 34.44/34.85 Deletedinuse: 9
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 120417
% 34.44/34.85 Kept: 23612
% 34.44/34.85 Inuse: 690
% 34.44/34.85 Deleted: 982
% 34.44/34.85 Deletedinuse: 10
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 153068
% 34.44/34.85 Kept: 26646
% 34.44/34.85 Inuse: 719
% 34.44/34.85 Deleted: 985
% 34.44/34.85 Deletedinuse: 12
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 165982
% 34.44/34.85 Kept: 28658
% 34.44/34.85 Inuse: 743
% 34.44/34.85 Deleted: 985
% 34.44/34.85 Deletedinuse: 12
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 180659
% 34.44/34.85 Kept: 30714
% 34.44/34.85 Inuse: 773
% 34.44/34.85 Deleted: 986
% 34.44/34.85 Deletedinuse: 12
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 202396
% 34.44/34.85 Kept: 32852
% 34.44/34.85 Inuse: 783
% 34.44/34.85 Deleted: 986
% 34.44/34.85 Deletedinuse: 12
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 221054
% 34.44/34.85 Kept: 34853
% 34.44/34.85 Inuse: 834
% 34.44/34.85 Deleted: 986
% 34.44/34.85 Deletedinuse: 12
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 235608
% 34.44/34.85 Kept: 36890
% 34.44/34.85 Inuse: 878
% 34.44/34.85 Deleted: 986
% 34.44/34.85 Deletedinuse: 12
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 247420
% 34.44/34.85 Kept: 38896
% 34.44/34.85 Inuse: 917
% 34.44/34.85 Deleted: 990
% 34.44/34.85 Deletedinuse: 15
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 266383
% 34.44/34.85 Kept: 41501
% 34.44/34.85 Inuse: 952
% 34.44/34.85 Deleted: 990
% 34.44/34.85 Deletedinuse: 15
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying clauses:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 285515
% 34.44/34.85 Kept: 44670
% 34.44/34.85 Inuse: 987
% 34.44/34.85 Deleted: 2004
% 34.44/34.85 Deletedinuse: 15
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 305918
% 34.44/34.85 Kept: 46692
% 34.44/34.85 Inuse: 998
% 34.44/34.85 Deleted: 2006
% 34.44/34.85 Deletedinuse: 17
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 336197
% 34.44/34.85 Kept: 49337
% 34.44/34.85 Inuse: 1012
% 34.44/34.85 Deleted: 2006
% 34.44/34.85 Deletedinuse: 17
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 354076
% 34.44/34.85 Kept: 51377
% 34.44/34.85 Inuse: 1061
% 34.44/34.85 Deleted: 2009
% 34.44/34.85 Deletedinuse: 20
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 365735
% 34.44/34.85 Kept: 53453
% 34.44/34.85 Inuse: 1091
% 34.44/34.85 Deleted: 2010
% 34.44/34.85 Deletedinuse: 20
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 386288
% 34.44/34.85 Kept: 55648
% 34.44/34.85 Inuse: 1115
% 34.44/34.85 Deleted: 2013
% 34.44/34.85 Deletedinuse: 22
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 416096
% 34.44/34.85 Kept: 58887
% 34.44/34.85 Inuse: 1148
% 34.44/34.85 Deleted: 2015
% 34.44/34.85 Deletedinuse: 22
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 438418
% 34.44/34.85 Kept: 61263
% 34.44/34.85 Inuse: 1183
% 34.44/34.85 Deleted: 2015
% 34.44/34.85 Deletedinuse: 22
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying clauses:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 452642
% 34.44/34.85 Kept: 63290
% 34.44/34.85 Inuse: 1202
% 34.44/34.85 Deleted: 3096
% 34.44/34.85 Deletedinuse: 22
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 474571
% 34.44/34.85 Kept: 65659
% 34.44/34.85 Inuse: 1223
% 34.44/34.85 Deleted: 3096
% 34.44/34.85 Deletedinuse: 22
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 501710
% 34.44/34.85 Kept: 68696
% 34.44/34.85 Inuse: 1238
% 34.44/34.85 Deleted: 3096
% 34.44/34.85 Deletedinuse: 22
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 521555
% 34.44/34.85 Kept: 71379
% 34.44/34.85 Inuse: 1253
% 34.44/34.85 Deleted: 3096
% 34.44/34.85 Deletedinuse: 22
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 536892
% 34.44/34.85 Kept: 73488
% 34.44/34.85 Inuse: 1288
% 34.44/34.85 Deleted: 3096
% 34.44/34.85 Deletedinuse: 22
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 557480
% 34.44/34.85 Kept: 75686
% 34.44/34.85 Inuse: 1323
% 34.44/34.85 Deleted: 3096
% 34.44/34.85 Deletedinuse: 22
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 585278
% 34.44/34.85 Kept: 78819
% 34.44/34.85 Inuse: 1348
% 34.44/34.85 Deleted: 3096
% 34.44/34.85 Deletedinuse: 22
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 602065
% 34.44/34.85 Kept: 80826
% 34.44/34.85 Inuse: 1372
% 34.44/34.85 Deleted: 3096
% 34.44/34.85 Deletedinuse: 22
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 620884
% 34.44/34.85 Kept: 84489
% 34.44/34.85 Inuse: 1398
% 34.44/34.85 Deleted: 3096
% 34.44/34.85 Deletedinuse: 22
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying clauses:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 648167
% 34.44/34.85 Kept: 87508
% 34.44/34.85 Inuse: 1438
% 34.44/34.85 Deleted: 3847
% 34.44/34.85 Deletedinuse: 26
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Intermediate Status:
% 34.44/34.85 Generated: 666383
% 34.44/34.85 Kept: 89655
% 34.44/34.85 Inuse: 1473
% 34.44/34.85 Deleted: 3849
% 34.44/34.85 Deletedinuse: 28
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85 Resimplifying inuse:
% 34.44/34.85 Done
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 Bliksems!, er is een bewijs:
% 34.44/34.85 % SZS status Unsatisfiable
% 34.44/34.85 % SZS output start Refutation
% 34.44/34.85
% 34.44/34.85 clause( 17, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 34.44/34.85 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 34.44/34.85 )
% 34.44/34.85 .
% 34.44/34.85 clause( 20, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 34.44/34.85 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 96, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.85 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 97, [ ~(
% 34.44/34.85 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 34.44/34.85 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 34.44/34.85 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 99, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' )
% 34.44/34.85 , Z, 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y
% 34.44/34.85 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 208, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 34.44/34.85 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 261, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 34.44/34.85 'tc_nat' ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 338, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 34.44/34.85 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 376, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 34.44/34.85 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 34.44/34.85 , T ), =( X, Z ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 449, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 34.44/34.85 , Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 453, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 537, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 34.44/34.85 'tc_nat' ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 539, [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 547, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 615, [ 'c_HOL_Oord__class_Oless'( 'v_i', 'v_n', 'tc_nat' ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 619, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.85 'v_i', 'v_k', 'tc_nat' ), 'v_n', 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 621, [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 34.44/34.85 'tc_nat' ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 637, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 753, [ ~( =( X, Y ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat'
% 34.44/34.85 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 34.44/34.85 , Z ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 756, [ ~( =( X, Y ) ), =( Y, X ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 832, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( =( Y,
% 34.44/34.85 'c_Suc'( X ) ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 837, [ 'c_HOL_Oord__class_Oless'( X, 'v_n', 'tc_nat' ), ~( =( X,
% 34.44/34.85 'v_i' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 839, [ 'c_HOL_Oord__class_Oless'( 'v_i', 'v_n', X ), ~( =( X,
% 34.44/34.85 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 1075, [ ~( 'c_lessequals'( 'v_n', 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 1271, [ ~( 'c_lessequals'( 'v_n', X, 'tc_nat' ) ), ~( =( X,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 1773, [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'v_n', X, 'tc_nat' ),
% 34.44/34.85 'v_i' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 1794, [ ~( =( Y, 'v_i' ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'v_n', X, 'tc_nat' ) ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 2288, [ 'c_lessequals'( 'v_i', 'v_n', 'tc_nat' ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 4497, [ ~( =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( 'v_i', 'v_k',
% 34.44/34.85 'tc_nat' ) ), 'v_n' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 14581, [ ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.85 'v_i', 'v_k', 'tc_nat' ) ), 'v_n', 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 14832, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ),
% 34.44/34.85 'c_lessequals'( 'v_i', 'c_HOL_Oplus__class_Oplus'( 'v_n', X, 'tc_nat' ),
% 34.44/34.85 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 34.44/34.85 , 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 19012, [ 'c_lessequals'( 'v_n', 'c_Suc'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( 'v_i', 'v_k', 'tc_nat' ) ), 'tc_nat' ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 19058, [ 'c_lessequals'( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.85 'v_i', 'v_k', 'tc_nat' ) ), 'tc_nat' ), ~( =( X, 'v_n' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 20559, [ 'c_lessequals'( 'v_i', 'c_HOL_Oplus__class_Oplus'( 'v_n',
% 34.44/34.85 X, 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 20958, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( 'v_n', Y,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ), ~( =( X, 'v_i' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 28598, [ ~( =( X, 'v_i' ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'v_n', Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 28610, [ ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'v_n', X,
% 34.44/34.85 'tc_nat' ), 'v_i', 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 41207, [ ~( =( X, 'v_n' ) ), 'c_lessequals'( X,
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( 'v_i', 'v_k', 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 41459, [ 'c_lessequals'( 'v_n', 'c_HOL_Ominus__class_Ominus'( 'v_i'
% 34.44/34.85 , 'v_k', 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 41926, [ ~( 'c_lessequals'( 'v_k', 'v_i', 'tc_nat' ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 41927, [ ~( =( 'c_HOL_Ominus__class_Ominus'( 'v_i', 'v_k', 'tc_nat'
% 34.44/34.85 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 42151, [ 'c_lessequals'( 'v_i', 'v_k', 'tc_nat' ) ] )
% 34.44/34.85 .
% 34.44/34.85 clause( 91656, [] )
% 34.44/34.85 .
% 34.44/34.85
% 34.44/34.85
% 34.44/34.85 % SZS output end Refutation
% 34.44/34.85 found a proof!
% 34.44/34.85
% 34.44/34.85 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 34.44/34.85
% 34.44/34.85 initialclauses(
% 34.44/34.85 [ clause( 91658, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.85 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 34.44/34.85 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 34.44/34.85 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 34.44/34.85 , clause( 91659, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.85 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 34.44/34.85 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 34.44/34.85 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 34.44/34.85 , clause( 91660, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 34.44/34.85 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91661, [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ),
% 34.44/34.85 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91662, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 34.44/34.85 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91663, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91664, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 34.44/34.85 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91665, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 34.44/34.85 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91666, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), X
% 34.44/34.85 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 34.44/34.85 , clause( 91667, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat'
% 34.44/34.85 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91668, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91669, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.85 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 34.44/34.85 , clause( 91670, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.85 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 34.44/34.85 , clause( 91671, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.85 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 34.44/34.85 , clause( 91672, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.85 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 34.44/34.85 ] )
% 34.44/34.85 , clause( 91673, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 34.44/34.85 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ] )
% 34.44/34.85 , clause( 91674, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 34.44/34.85 X ) ), 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ] )
% 34.44/34.85 , clause( 91675, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 34.44/34.85 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 34.44/34.85 )
% 34.44/34.85 , clause( 91676, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 34.44/34.85 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 34.44/34.85 , clause( 91677, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 34.44/34.85 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 34.44/34.85 , clause( 91678, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 34.44/34.85 ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y
% 34.44/34.85 , X ) ] )
% 34.44/34.85 , clause( 91679, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 34.44/34.85 ) ), =( Y, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91680, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 34.44/34.85 Y, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91681, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 34.44/34.85 X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91682, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 34.44/34.85 ) ), =( Y, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91683, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 34.44/34.85 X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91684, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 34.44/34.85 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91685, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 34.44/34.85 X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91686, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 34.44/34.85 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 34.44/34.85 , clause( 91687, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.85 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.85 , clause( 91688, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 34.44/34.85 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91689, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 34.44/34.85 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91690, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), X, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y
% 34.44/34.85 , 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91691, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' )
% 34.44/34.85 ] )
% 34.44/34.85 , clause( 91692, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ] )
% 34.44/34.85 , clause( 91693, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 34.44/34.85 , clause( 91694, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 34.44/34.85 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 34.44/34.85 )
% 34.44/34.85 , clause( 91695, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 34.44/34.85 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91696, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ] )
% 34.44/34.85 , clause( 91697, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ] )
% 34.44/34.85 , clause( 91698, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 34.44/34.85 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.85 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91699, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91700, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 34.44/34.85 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.85 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91701, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 34.44/34.85 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 34.44/34.85 ) ] )
% 34.44/34.85 , clause( 91702, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 34.44/34.85 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 34.44/34.85 ) ] )
% 34.44/34.85 , clause( 91703, [ ~(
% 34.44/34.85 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 34.44/34.85 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ) ) ] )
% 34.44/34.85 , clause( 91704, [ ~(
% 34.44/34.85 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 34.44/34.85 ) ] )
% 34.44/34.85 , clause( 91705, [ ~(
% 34.44/34.85 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 34.44/34.85 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91706, [ ~(
% 34.44/34.85 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 34.44/34.85 ) ] )
% 34.44/34.85 , clause( 91707, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 34.44/34.85 , clause( 91708, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 34.44/34.85 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 34.44/34.85 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.85 , clause( 91709, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 34.44/34.85 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 34.44/34.85 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.85 , clause( 91710, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 34.44/34.85 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 34.44/34.85 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91711, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 34.44/34.85 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 34.44/34.85 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91712, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 34.44/34.85 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 34.44/34.85 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 34.44/34.85 , clause( 91713, [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91714, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91715, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 34.44/34.85 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 34.44/34.85 , clause( 91716, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 34.44/34.85 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 34.44/34.85 , clause( 91717, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 34.44/34.85 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91718, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 34.44/34.85 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91719, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.85 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 34.44/34.85 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91720, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 34.44/34.85 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 34.44/34.85 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91721, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.85 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.85 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91722, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.85 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.85 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.85 , clause( 91723, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.85 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.85 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 34.44/34.85 , clause( 91724, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.85 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.85 , clause( 91725, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91726, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 34.44/34.85 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91727, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 34.44/34.85 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91728, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 34.44/34.85 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91729, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 34.44/34.85 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91730, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91731, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 34.44/34.85 ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 34.44/34.85 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.85 , clause( 91732, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 34.44/34.85 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.85 , clause( 91733, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 34.44/34.85 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.85 , clause( 91734, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91735, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 34.44/34.85 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z,
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 34.44/34.85 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91736, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 34.44/34.85 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ), =(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 34.44/34.85 'tc_nat' ), U ) ] )
% 34.44/34.85 , clause( 91737, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ), 'tc_nat' ) ]
% 34.44/34.85 )
% 34.44/34.85 , clause( 91738, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 34.44/34.85 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91739, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 34.44/34.85 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.85 , clause( 91740, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 34.44/34.85 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.85 , clause( 91741, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91742, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91743, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 34.44/34.85 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.85 , clause( 91744, [ =( 'c_Orderings_Oord__class_Omin'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91745, [ =( 'c_Orderings_Oord__class_Omin'( X,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91746, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 34.44/34.85 ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91747, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.85 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 34.44/34.85 , T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91748, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.85 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 34.44/34.85 , Z, X ), X ) ) ] )
% 34.44/34.85 , clause( 91749, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 34.44/34.85 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 34.44/34.85 , T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91750, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 34.44/34.85 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 34.44/34.85 , Z, X ), X ) ) ] )
% 34.44/34.85 , clause( 91751, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 34.44/34.85 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 34.44/34.85 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.85 , clause( 91752, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) )
% 34.44/34.85 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91753, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X )
% 34.44/34.85 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91754, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 34.44/34.85 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 34.44/34.85 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 34.44/34.85 , clause( 91755, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 34.44/34.85 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91756, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 34.44/34.85 , clause( 91757, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 34.44/34.85 , clause( 91758, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ] )
% 34.44/34.85 , clause( 91759, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y,
% 34.44/34.85 'tc_nat' ), 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ),
% 34.44/34.85 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91760, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 34.44/34.85 , T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91761, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 34.44/34.85 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 34.44/34.85 , clause( 91762, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 34.44/34.85 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 34.44/34.85 )
% 34.44/34.85 , clause( 91763, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 34.44/34.85 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 34.44/34.85 , clause( 91764, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 T, 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ), W, X ), X ) ) ] )
% 34.44/34.85 , clause( 91765, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.85 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 34.44/34.85 , X ), W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X
% 34.44/34.85 ), X ) ) ] )
% 34.44/34.85 , clause( 91766, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W, X ) ) ] )
% 34.44/34.85 , clause( 91767, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 34.44/34.85 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ] )
% 34.44/34.85 , clause( 91768, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91769, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.85 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91770, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91771, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.85 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91772, [ ~(
% 34.44/34.85 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 34.44/34.85 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 34.44/34.85 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 34.44/34.85 , clause( 91773, [ ~(
% 34.44/34.85 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 34.44/34.85 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 34.44/34.85 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 34.44/34.85 , clause( 91774, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 34.44/34.85 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 34.44/34.85 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91775, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X
% 34.44/34.85 , Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 34.44/34.85 )
% 34.44/34.85 , clause( 91776, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91777, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91778, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91779, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 34.44/34.85 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91780, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 34.44/34.85 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 34.44/34.85 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 34.44/34.85 )
% 34.44/34.85 , clause( 91781, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 34.44/34.85 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 34.44/34.85 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91782, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 34.44/34.85 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 34.44/34.85 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 34.44/34.85 )
% 34.44/34.85 , clause( 91783, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91784, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 34.44/34.85 ) ) ) ] )
% 34.44/34.85 , clause( 91785, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 34.44/34.85 ) ) ) ] )
% 34.44/34.85 , clause( 91786, [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y
% 34.44/34.85 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y
% 34.44/34.85 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ] )
% 34.44/34.85 , clause( 91787, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.85 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 34.44/34.85 , clause( 91788, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.85 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.85 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 34.44/34.85 , clause( 91789, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 34.44/34.85 , X ) ) ] )
% 34.44/34.85 , clause( 91790, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.85 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 34.44/34.85 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 34.44/34.85 , clause( 91791, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.85 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 34.44/34.85 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 34.44/34.85 , clause( 91792, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.85 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 34.44/34.85 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 34.44/34.85 , clause( 91793, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 34.44/34.85 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ] )
% 34.44/34.85 , clause( 91794, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 34.44/34.85 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ] )
% 34.44/34.85 , clause( 91795, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( Y
% 34.44/34.85 , Z, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91796, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 34.44/34.85 , Y, X ), X ) ] )
% 34.44/34.85 , clause( 91797, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 34.44/34.85 , Z, X ), X ) ] )
% 34.44/34.85 , clause( 91798, [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 34.44/34.85 , Z, X ), X ) ] )
% 34.44/34.85 , clause( 91799, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 34.44/34.85 ) ] )
% 34.44/34.85 , clause( 91800, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 34.44/34.85 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 34.44/34.85 Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91801, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 34.44/34.85 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 34.44/34.85 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 34.44/34.85 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 34.44/34.85 , clause( 91802, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.85 , clause( 91803, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 34.44/34.85 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 34.44/34.85 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 34.44/34.85 , clause( 91804, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 34.44/34.85 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 34.44/34.85 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 34.44/34.85 , clause( 91805, [ =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 34.44/34.85 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91806, [ =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 34.44/34.85 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91807, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91808, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.85 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ] )
% 34.44/34.85 , clause( 91809, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 34.44/34.85 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 34.44/34.85 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ] )
% 34.44/34.85 , clause( 91810, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 34.44/34.85 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 34.44/34.85 ] )
% 34.44/34.85 , clause( 91811, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 34.44/34.85 'tc_nat' ), 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ),
% 34.44/34.85 =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ] )
% 34.44/34.85 , clause( 91812, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 34.44/34.85 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 34.44/34.85 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91813, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 34.44/34.85 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 34.44/34.85 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91814, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 34.44/34.85 ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 34.44/34.85 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 34.44/34.85 )
% 34.44/34.85 , clause( 91815, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 Z, Y, X ) ) ] )
% 34.44/34.85 , clause( 91816, [ =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91817, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 34.44/34.85 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 34.44/34.85 )
% 34.44/34.85 , clause( 91818, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91819, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 Z, Y, X ) ) ] )
% 34.44/34.85 , clause( 91820, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 34.44/34.85 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 34.44/34.85 , T, X ), X ), T, X ) ) ] )
% 34.44/34.85 , clause( 91821, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.85 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 34.44/34.85 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.85 , clause( 91822, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 34.44/34.85 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91823, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 34.44/34.85 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91824, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 34.44/34.85 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 34.44/34.85 , clause( 91825, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 34.44/34.85 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 34.44/34.85 , clause( 91826, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 34.44/34.85 , X ), Z, X ) ) ] )
% 34.44/34.85 , clause( 91827, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 34.44/34.85 , X ), Z, X ) ) ] )
% 34.44/34.85 , clause( 91828, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 34.44/34.85 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 34.44/34.85 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 34.44/34.85 , clause( 91829, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 34.44/34.85 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91830, [ =( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 34.44/34.85 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91831, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 34.44/34.85 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 34.44/34.85 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 34.44/34.85 , Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91832, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 34.44/34.85 ] )
% 34.44/34.85 , clause( 91833, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 34.44/34.85 ] )
% 34.44/34.85 , clause( 91834, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 34.44/34.85 ] )
% 34.44/34.85 , clause( 91835, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 34.44/34.85 )
% 34.44/34.85 , clause( 91836, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 34.44/34.85 )
% 34.44/34.85 , clause( 91837, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y, T,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91838, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 34.44/34.85 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.85 , clause( 91839, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 34.44/34.85 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91840, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 34.44/34.85 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91841, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 34.44/34.85 , clause( 91842, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91843, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 34.44/34.85 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 34.44/34.85 , clause( 91844, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.85 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.85 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 34.44/34.85 , clause( 91845, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 34.44/34.85 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91846, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 34.44/34.85 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91847, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 34.44/34.85 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91848, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 34.44/34.85 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91849, [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 34.44/34.85 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) )
% 34.44/34.85 , =( Y, Z ) ] )
% 34.44/34.85 , clause( 91850, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 34.44/34.85 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 34.44/34.85 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 34.44/34.85 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 34.44/34.85 , clause( 91851, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91852, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91853, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 34.44/34.85 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 34.44/34.85 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ] )
% 34.44/34.85 , clause( 91854, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 34.44/34.85 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 34.44/34.85 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ] )
% 34.44/34.85 , clause( 91855, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91856, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 34.44/34.85 , clause( 91857, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.85 , clause( 91858, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91859, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91860, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ] )
% 34.44/34.85 , clause( 91861, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.85 , clause( 91862, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91863, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 34.44/34.85 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.85 , clause( 91864, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.85 X ) ), 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X
% 34.44/34.85 ) ] )
% 34.44/34.85 , clause( 91865, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 34.44/34.85 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 34.44/34.85 T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91866, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.85 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 34.44/34.85 T, X ), Z, X ) ) ] )
% 34.44/34.85 , clause( 91867, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.85 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 Z, T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91868, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 34.44/34.85 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 34.44/34.85 , X ), T, X ) ) ] )
% 34.44/34.85 , clause( 91869, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 34.44/34.85 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 34.44/34.85 , T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91870, [ =( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91871, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 34.44/34.85 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 34.44/34.85 , X ), T, X ) ) ] )
% 34.44/34.85 , clause( 91872, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 34.44/34.85 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 34.44/34.85 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91873, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 34.44/34.85 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91874, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 34.44/34.85 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91875, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 34.44/34.85 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91876, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 34.44/34.85 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91877, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 34.44/34.85 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91878, [ =( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 34.44/34.85 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91879, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 34.44/34.85 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 34.44/34.85 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91880, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 34.44/34.85 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91881, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 34.44/34.85 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91882, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 34.44/34.85 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91883, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 34.44/34.85 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 34.44/34.85 , clause( 91884, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 34.44/34.85 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.85 , clause( 91885, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 34.44/34.85 , clause( 91886, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 34.44/34.85 , clause( 91887, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 34.44/34.85 , clause( 91888, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 34.44/34.85 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 34.44/34.85 , clause( 91889, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 34.44/34.85 , clause( 91890, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91891, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 34.44/34.85 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat'
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91892, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 34.44/34.85 )
% 34.44/34.85 , clause( 91893, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 34.44/34.85 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 34.44/34.85 , clause( 91894, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 34.44/34.85 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 34.44/34.85 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 34.44/34.85 , clause( 91895, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91896, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91897, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91898, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91899, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91900, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91901, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91902, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91903, [ ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ) ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91904, [ ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91905, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91906, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 34.44/34.85 ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91907, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ),
% 34.44/34.85 ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91908, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91909, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 34.44/34.85 , clause( 91910, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 34.44/34.85 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 34.44/34.85 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 34.44/34.85 , clause( 91911, [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91912, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 34.44/34.85 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91913, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 34.44/34.85 X ), X ) ) ] )
% 34.44/34.85 , clause( 91914, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 34.44/34.85 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ] )
% 34.44/34.85 , clause( 91915, [ ~(
% 34.44/34.85 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T
% 34.44/34.85 , X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 34.44/34.85 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91916, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 34.44/34.85 , clause( 91917, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 34.44/34.85 , clause( 91918, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 34.44/34.85 , clause( 91919, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 34.44/34.85 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 34.44/34.85 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 34.44/34.85 , clause( 91920, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 34.44/34.85 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 34.44/34.85 , clause( 91921, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 34.44/34.85 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 Y, T, X ) ) ), =( Z, T ) ] )
% 34.44/34.85 , clause( 91922, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 34.44/34.85 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 T, Z, X ) ) ), =( Y, T ) ] )
% 34.44/34.85 , clause( 91923, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 34.44/34.85 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.85 , clause( 91924, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 34.44/34.85 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 34.44/34.85 , X ) ) ] )
% 34.44/34.85 , clause( 91925, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 34.44/34.85 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91926, [ =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat'
% 34.44/34.85 ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91927, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 34.44/34.85 ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91928, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 34.44/34.85 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91929, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 34.44/34.85 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 34.44/34.85 , X ) ) ] )
% 34.44/34.85 , clause( 91930, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 34.44/34.85 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 34.44/34.85 , X ) ) ] )
% 34.44/34.85 , clause( 91931, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 34.44/34.85 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 34.44/34.85 , X ) ) ] )
% 34.44/34.85 , clause( 91932, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.85 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 34.44/34.85 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 34.44/34.85 , X ) ) ] )
% 34.44/34.85 , clause( 91933, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91934, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ] )
% 34.44/34.85 , clause( 91935, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.85 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 34.44/34.85 X ) ] )
% 34.44/34.85 , clause( 91936, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91937, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91938, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91939, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91940, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91941, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 34.44/34.85 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91942, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 34.44/34.85 ] )
% 34.44/34.85 , clause( 91943, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 34.44/34.85 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 34.44/34.85 , clause( 91944, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 34.44/34.85 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.85 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 34.44/34.85 , clause( 91945, [ ~(
% 34.44/34.85 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 34.44/34.85 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 34.44/34.85 , clause( 91946, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 34.44/34.85 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91947, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 34.44/34.85 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 34.44/34.85 'tc_nat' ) ), =( Y, Z ) ] )
% 34.44/34.85 , clause( 91948, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91949, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.85 , clause( 91950, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.85 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 34.44/34.85 , T, X ), X ) ) ] )
% 34.44/34.85 , clause( 91951, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.85 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.85 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 34.44/34.85 , Z, X ), X ) ) ] )
% 34.44/34.85 , clause( 91952, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 34.44/34.85 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 34.44/34.85 ) ) ] )
% 34.44/34.85 , clause( 91953, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.85 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 34.44/34.85 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 34.44/34.85 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.85 X ), T, X ) ) ] )
% 34.44/34.85 , clause( 91954, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 34.44/34.86 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 34.44/34.86 ) ) ] )
% 34.44/34.86 , clause( 91955, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 34.44/34.86 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 91956, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 34.44/34.86 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91957, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91958, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 34.44/34.86 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X,
% 34.44/34.86 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 91959, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 34.44/34.86 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 34.44/34.86 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 91960, [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 34.44/34.86 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91961, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 34.44/34.86 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ] )
% 34.44/34.86 , clause( 91962, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 91963, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 91964, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 34.44/34.86 Z, Y, X ) ) ] )
% 34.44/34.86 , clause( 91965, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 34.44/34.86 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 34.44/34.86 , clause( 91966, [ =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 34.44/34.86 ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 34.44/34.86 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91967, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 34.44/34.86 Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91968, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 34.44/34.86 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91969, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 34.44/34.86 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 91970, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 X ), X ) ) ] )
% 34.44/34.86 , clause( 91971, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 X ), X ) ) ] )
% 34.44/34.86 , clause( 91972, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 34.44/34.86 X, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 91973, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 34.44/34.86 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91974, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_Suc'( X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 34.44/34.86 Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 91975, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 34.44/34.86 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 91976, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 34.44/34.86 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91977, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), X, 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X,
% 34.44/34.86 'tc_nat' ) ] )
% 34.44/34.86 , clause( 91978, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 34.44/34.86 'tc_nat' ), X, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 91979, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91980, [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 34.44/34.86 'tc_nat' ) ), Y ) ), =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 34.44/34.86 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91981, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.86 , clause( 91982, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 34.44/34.86 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 34.44/34.86 , clause( 91983, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 34.44/34.86 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 34.44/34.86 , clause( 91984, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 34.44/34.86 , clause( 91985, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91986, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 91987, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X
% 34.44/34.86 ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91988, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 91989, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 91990, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 34.44/34.86 ~( 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X
% 34.44/34.86 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 91991, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 91992, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 34.44/34.86 ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91993, [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ),
% 34.44/34.86 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 91994, [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 34.44/34.86 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91995, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 91996, [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'(
% 34.44/34.86 Y ), 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat'
% 34.44/34.86 ) ) ) ] )
% 34.44/34.86 , clause( 91997, [ =( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 34.44/34.86 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 91998, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 34.44/34.86 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 91999, [ ~(
% 34.44/34.86 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 34.44/34.86 , clause( 92000, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 92001, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 34.44/34.86 , clause( 92002, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.86 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.86 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92003, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 34.44/34.86 , clause( 92004, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 92005, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.86 , clause( 92006, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.86 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.86 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 34.44/34.86 , clause( 92007, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 34.44/34.86 , clause( 92008, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.86 , clause( 92009, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 34.44/34.86 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 X ), T, X ) ) ] )
% 34.44/34.86 , clause( 92010, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 92011, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 34.44/34.86 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 92012, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 34.44/34.86 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92013, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 34.44/34.86 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92014, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 34.44/34.86 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 34.44/34.86 ) ) ] )
% 34.44/34.86 , clause( 92015, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 34.44/34.86 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 34.44/34.86 ) ) ] )
% 34.44/34.86 , clause( 92016, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 34.44/34.86 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92017, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 34.44/34.86 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92018, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92019, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92020, [ =( 'c_Divides_Odiv__class_Omod'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 34.44/34.86 ), Z, 'tc_nat' ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92021, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 34.44/34.86 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92022, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 34.44/34.86 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 34.44/34.86 , clause( 92023, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 34.44/34.86 , =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 34.44/34.86 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92024, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.86 , clause( 92025, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 92026, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 34.44/34.86 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.86 , clause( 92027, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 34.44/34.86 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 92028, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 34.44/34.86 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.86 , clause( 92029, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 34.44/34.86 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 92030, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 34.44/34.86 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 34.44/34.86 , clause( 92031, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92032, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 34.44/34.86 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.86 , clause( 92033, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 34.44/34.86 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.86 , clause( 92034, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 34.44/34.86 , clause( 92035, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ] )
% 34.44/34.86 , clause( 92036, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.86 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92037, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92038, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 34.44/34.86 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 34.44/34.86 ) ), Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92039, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 34.44/34.86 ), 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92040, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 34.44/34.86 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92041, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 34.44/34.86 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 34.44/34.86 , clause( 92042, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 34.44/34.86 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92043, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 34.44/34.86 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92044, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 34.44/34.86 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92045, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 34.44/34.86 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92046, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'(
% 34.44/34.86 X, Y, 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92047, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 34.44/34.86 X ) ) ] )
% 34.44/34.86 , clause( 92048, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92049, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 34.44/34.86 X ) ) ] )
% 34.44/34.86 , clause( 92050, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 34.44/34.86 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 34.44/34.86 , clause( 92051, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y
% 34.44/34.86 , X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92052, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 34.44/34.86 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92053, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 34.44/34.86 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.86 , clause( 92054, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 34.44/34.86 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92055, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92056, [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92057, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 34.44/34.86 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.86 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92058, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 34.44/34.86 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 34.44/34.86 ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92059, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 34.44/34.86 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 34.44/34.86 , 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 34.44/34.86 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92060, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 34.44/34.86 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 34.44/34.86 , 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 34.44/34.86 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 34.44/34.86 X, T, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92061, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 34.44/34.86 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 34.44/34.86 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 34.44/34.86 , clause( 92062, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 34.44/34.86 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.86 , clause( 92063, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 34.44/34.86 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92064, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ] )
% 34.44/34.86 , clause( 92065, [ ~(
% 34.44/34.86 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 34.44/34.86 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X
% 34.44/34.86 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 34.44/34.86 ) ) ] )
% 34.44/34.86 , clause( 92066, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92067, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 34.44/34.86 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92068, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 34.44/34.86 , ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Z
% 34.44/34.86 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92069, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 34.44/34.86 , ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 34.44/34.86 , Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92070, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 34.44/34.86 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92071, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92072, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 34.44/34.86 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ] )
% 34.44/34.86 , clause( 92073, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 34.44/34.86 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92074, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X )
% 34.44/34.86 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 34.44/34.86 , clause( 92075, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 34.44/34.86 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 34.44/34.86 , clause( 92076, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat'
% 34.44/34.86 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 34.44/34.86 , clause( 92077, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 34.44/34.86 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 34.44/34.86 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 34.44/34.86 , clause( 92078, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 34.44/34.86 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 34.44/34.86 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 34.44/34.86 , X ), W, X ) ) ] )
% 34.44/34.86 , clause( 92079, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 X ) ) ] )
% 34.44/34.86 , clause( 92080, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.86 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92081, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.86 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92082, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92083, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92084, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.86 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 34.44/34.86 Y, X ) ) ] )
% 34.44/34.86 , clause( 92085, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92086, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.86 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 34.44/34.86 Y, X ) ) ] )
% 34.44/34.86 , clause( 92087, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 34.44/34.86 X ) ) ] )
% 34.44/34.86 , clause( 92088, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 34.44/34.86 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 34.44/34.86 , T, X ), X ), T, X ) ) ] )
% 34.44/34.86 , clause( 92089, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 34.44/34.86 , clause( 92090, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 34.44/34.86 , clause( 92091, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92092, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.86 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X )
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92093, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.86 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X )
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92094, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 34.44/34.86 T, X ) ) ] )
% 34.44/34.86 , clause( 92095, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 34.44/34.86 T, X ) ) ] )
% 34.44/34.86 , clause( 92096, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 34.44/34.86 T, X ) ) ] )
% 34.44/34.86 , clause( 92097, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 34.44/34.86 T, X ) ) ] )
% 34.44/34.86 , clause( 92098, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.86 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X )
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92099, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.86 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X )
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92100, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 34.44/34.86 , clause( 92101, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 34.44/34.86 , clause( 92102, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 34.44/34.86 , clause( 92103, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.86 , Z, X ), 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ] )
% 34.44/34.86 , clause( 92104, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 34.44/34.86 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92105, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 34.44/34.86 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 34.44/34.86 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 34.44/34.86 Z, X ) ) ] )
% 34.44/34.86 , clause( 92106, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92107, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 34.44/34.86 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92108, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 34.44/34.86 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 34.44/34.86 , clause( 92109, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 34.44/34.86 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92110, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92111, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92112, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 34.44/34.86 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 34.44/34.86 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 34.44/34.86 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92113, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 34.44/34.86 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 34.44/34.86 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92114, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 34.44/34.86 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 34.44/34.86 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 34.44/34.86 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92115, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 34.44/34.86 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92116, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 34.44/34.86 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 34.44/34.86 , clause( 92117, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 34.44/34.86 ), Z, 'tc_nat' ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 34.44/34.86 Z ), Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92118, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 34.44/34.86 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 34.44/34.86 , T ), =( X, Z ) ] )
% 34.44/34.86 , clause( 92119, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 34.44/34.86 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 34.44/34.86 , T ), =( X, Z ) ] )
% 34.44/34.86 , clause( 92120, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 34.44/34.86 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 34.44/34.86 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 34.44/34.86 =( Y, T ) ] )
% 34.44/34.86 , clause( 92121, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 34.44/34.86 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 34.44/34.86 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 34.44/34.86 =( Y, T ) ] )
% 34.44/34.86 , clause( 92122, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 34.44/34.86 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92123, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 34.44/34.86 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 34.44/34.86 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 34.44/34.86 X ), Z, X ) ) ] )
% 34.44/34.86 , clause( 92124, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 34.44/34.86 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 34.44/34.86 , clause( 92125, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 34.44/34.86 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 34.44/34.86 , clause( 92126, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92127, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92128, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92129, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 34.44/34.86 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 92130, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.86 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92131, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92132, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92133, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 34.44/34.86 , clause( 92134, [ =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 34.44/34.86 , clause( 92135, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.86 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92136, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.86 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92137, [ ~(
% 34.44/34.86 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 34.44/34.86 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92138, [ ~(
% 34.44/34.86 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92139, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 34.44/34.86 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92140, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 34.44/34.86 ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92141, [ ~( 'class_Orderings_Oorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 34.44/34.86 , clause( 92142, [ ~( 'class_Orderings_Oorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 34.44/34.86 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 34.44/34.86 , clause( 92143, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92144, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 34.44/34.86 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92145, [ ~(
% 34.44/34.86 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92146, [ ~(
% 34.44/34.86 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92147, [ ~(
% 34.44/34.86 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 34.44/34.86 X ), X ) ) ] )
% 34.44/34.86 , clause( 92148, [ ~(
% 34.44/34.86 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 Z, T, X ) ) ] )
% 34.44/34.86 , clause( 92149, [ ~(
% 34.44/34.86 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 Z, T, X ) ) ] )
% 34.44/34.86 , clause( 92150, [ ~(
% 34.44/34.86 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 34.44/34.86 X ), X ) ) ] )
% 34.44/34.86 , clause( 92151, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.86 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92152, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 34.44/34.86 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92153, [ ~(
% 34.44/34.86 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92154, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 34.44/34.86 'c_lessequals'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92155, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( T, Z, X
% 34.44/34.86 ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( T, Y, X
% 34.44/34.86 ), Z, X ) ) ] )
% 34.44/34.86 , clause( 92156, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 34.44/34.86 , clause( 92157, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 34.44/34.86 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 34.44/34.86 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92158, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 34.44/34.86 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 34.44/34.86 X ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 34.44/34.86 , clause( 92159, [ ~( 'class_Orderings_Oorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92160, [ ~( 'class_Orderings_Oorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 34.44/34.86 Z, Y ) ] )
% 34.44/34.86 , clause( 92161, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92162, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 34.44/34.86 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 34.44/34.86 , clause( 92163, [ ~( 'class_Orderings_Oorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 34.44/34.86 Y, Z ) ] )
% 34.44/34.86 , clause( 92164, [ ~( 'class_Orderings_Oorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92165, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92166, [ ~( 'class_Orderings_Oorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92167, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ),
% 34.44/34.86 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92168, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 34.44/34.86 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 34.44/34.86 , clause( 92169, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 34.44/34.86 , clause( 92170, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 34.44/34.86 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 34.44/34.86 , clause( 92171, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 34.44/34.86 , clause( 92172, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92173, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.86 , Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 34.44/34.86 , clause( 92174, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 34.44/34.86 , clause( 92175, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 34.44/34.86 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 34.44/34.86 , clause( 92176, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 34.44/34.86 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 34.44/34.86 , clause( 92177, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 34.44/34.86 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92178, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ] )
% 34.44/34.86 , clause( 92179, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 34.44/34.86 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92180, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 34.44/34.86 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 34.44/34.86 , clause( 92181, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 34.44/34.86 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92182, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 34.44/34.86 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ] )
% 34.44/34.86 , clause( 92183, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 34.44/34.86 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 34.44/34.86 , X ), W, X ), X ) ) ] )
% 34.44/34.86 , clause( 92184, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 34.44/34.86 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 34.44/34.86 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 34.44/34.86 W, X ), X ) ) ] )
% 34.44/34.86 , clause( 92185, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 34.44/34.86 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 34.44/34.86 , X ), T, X ), W, X ) ) ] )
% 34.44/34.86 , clause( 92186, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 34.44/34.86 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 34.44/34.86 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 34.44/34.86 W, X ), X ) ) ] )
% 34.44/34.86 , clause( 92187, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 34.44/34.86 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 34.44/34.86 , Y, X ) ) ] )
% 34.44/34.86 , clause( 92188, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 34.44/34.86 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 34.44/34.86 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 34.44/34.86 X ), Z, X ) ) ] )
% 34.44/34.86 , clause( 92189, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 34.44/34.86 , =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z,
% 34.44/34.86 X ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92190, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 34.44/34.86 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 34.44/34.86 , clause( 92191, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 34.44/34.86 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 34.44/34.86 , clause( 92192, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 34.44/34.86 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 34.44/34.86 , T, X ), X ), T, X ) ) ] )
% 34.44/34.86 , clause( 92193, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 34.44/34.86 ), X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X
% 34.44/34.86 ), X ) ) ] )
% 34.44/34.86 , clause( 92194, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 34.44/34.86 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 34.44/34.86 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 34.44/34.86 , clause( 92195, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 34.44/34.86 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 34.44/34.86 ~( 'c_lessequals'( U, T, X ) ) ] )
% 34.44/34.86 , clause( 92196, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 34.44/34.86 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92197, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92198, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92199, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92200, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92201, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 34.44/34.86 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 34.44/34.86 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92202, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 34.44/34.86 ), Y ) ] )
% 34.44/34.86 , clause( 92203, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 ) ), =( Y, Z ) ] )
% 34.44/34.86 , clause( 92204, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 ) ), =( Y, Z ) ] )
% 34.44/34.86 , clause( 92205, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 34.44/34.86 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 34.44/34.86 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 34.44/34.86 , clause( 92206, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 34.44/34.86 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 34.44/34.86 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92207, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 34.44/34.86 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 34.44/34.86 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92208, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 34.44/34.86 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 34.44/34.86 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92209, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 34.44/34.86 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 34.44/34.86 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92210, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 34.44/34.86 , U, X ), X ) ) ] )
% 34.44/34.86 , clause( 92211, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 34.44/34.86 ), Y ) ] )
% 34.44/34.86 , clause( 92212, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 34.44/34.86 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 34.44/34.86 , ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92213, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92214, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 34.44/34.86 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 34.44/34.86 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92215, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92216, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92217, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92218, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92219, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92220, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92221, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 34.44/34.86 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' )
% 34.44/34.86 , ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92222, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 34.44/34.86 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92223, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X )
% 34.44/34.86 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92224, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92225, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 , X ) ] )
% 34.44/34.86 , clause( 92226, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 34.44/34.86 , clause( 92227, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.86 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 34.44/34.86 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92228, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.86 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 34.44/34.86 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92229, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92230, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92231, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92232, [ =( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92233, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92234, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92235, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.86 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 34.44/34.86 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92236, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92237, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92238, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 34.44/34.86 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 34.44/34.86 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92239, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 34.44/34.86 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92240, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 34.44/34.86 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92241, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92242, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 34.44/34.86 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 34.44/34.86 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 34.44/34.86 , clause( 92243, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92244, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 34.44/34.86 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92245, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 34.44/34.86 Z, X ) ) ] )
% 34.44/34.86 , clause( 92246, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 34.44/34.86 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92247, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 34.44/34.86 ), X ) ) ] )
% 34.44/34.86 , clause( 92248, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 34.44/34.86 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92249, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 34.44/34.86 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92250, [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 34.44/34.86 , clause( 92251, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 34.44/34.86 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 34.44/34.86 , clause( 92252, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92253, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92254, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92255, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92256, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 34.44/34.86 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92257, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 34.44/34.86 , 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92258, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 34.44/34.86 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92259, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 34.44/34.86 ) ) ) ] )
% 34.44/34.86 , clause( 92260, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 34.44/34.86 ) ) ) ] )
% 34.44/34.86 , clause( 92261, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 92262, [ =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ), ~(
% 34.44/34.86 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92263, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 34.44/34.86 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92264, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 34.44/34.86 ), X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92265, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 34.44/34.86 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z
% 34.44/34.86 , 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92266, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 34.44/34.86 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 Z, X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 34.44/34.86 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92267, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92268, [ =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 34.44/34.86 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92269, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 34.44/34.86 ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92270, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( T, 'c_HOL_Otimes__class_Otimes'( Y, U,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ) ) ), =( 'c_Divides_Odiv__class_Omod'( X, Y,
% 34.44/34.86 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92271, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 34.44/34.86 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 34.44/34.86 , clause( 92272, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92273, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.86 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.86 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92274, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.86 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 34.44/34.86 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 34.44/34.86 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 34.44/34.86 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92275, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 34.44/34.86 X ) ] )
% 34.44/34.86 , clause( 92276, [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 34.44/34.86 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92277, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 34.44/34.86 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92278, [ 'c_HOL_Oord__class_Oless'( X,
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 34.44/34.86 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92279, [ 'c_HOL_Oord__class_Oless'( X,
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 34.44/34.86 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92280, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92281, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 34.44/34.86 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ] )
% 34.44/34.86 , clause( 92282, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 34.44/34.86 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 34.44/34.86 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 92283, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 34.44/34.86 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 92284, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 34.44/34.86 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 34.44/34.86 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 34.44/34.86 , clause( 92285, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 34.44/34.86 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 34.44/34.86 , clause( 92286, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 34.44/34.86 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92287, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92288, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 34.44/34.86 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 34.44/34.86 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 34.44/34.86 , clause( 92289, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 34.44/34.86 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92290, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), ~( =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92291, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92292, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 34.44/34.86 , ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y
% 34.44/34.86 , 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92293, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.86 , Y, X ) ] )
% 34.44/34.86 , clause( 92294, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y
% 34.44/34.86 , X ) ] )
% 34.44/34.86 , clause( 92295, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92296, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z,
% 34.44/34.86 Y, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92297, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92298, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 34.44/34.86 , 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 34.44/34.86 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ] )
% 34.44/34.86 , clause( 92299, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.86 , Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92300, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 34.44/34.86 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 34.44/34.86 , clause( 92301, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 34.44/34.86 , X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92302, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 34.44/34.86 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92303, [ =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 34.44/34.86 , clause( 92304, [ =( 'c_Divides_Odiv__class_Omod'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), X, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92305, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 34.44/34.86 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92306, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 34.44/34.86 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 34.44/34.86 , clause( 92307, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 34.44/34.86 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92308, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 34.44/34.86 ) ) ] )
% 34.44/34.86 , clause( 92309, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 34.44/34.86 , Y, X ), X ) ) ] )
% 34.44/34.86 , clause( 92310, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 34.44/34.86 , T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92311, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 34.44/34.86 , T, X ), X ) ) ] )
% 34.44/34.86 , clause( 92312, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 34.44/34.86 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 34.44/34.86 , Y, X ), X ) ) ] )
% 34.44/34.86 , clause( 92313, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92314, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 34.44/34.86 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92315, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 34.44/34.86 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92316, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 34.44/34.86 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 34.44/34.86 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 34.44/34.86 , clause( 92317, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ),
% 34.44/34.86 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92318, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 34.44/34.86 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92319, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 34.44/34.86 =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 34.44/34.86 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ] )
% 34.44/34.86 , clause( 92320, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 34.44/34.86 , Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 34.44/34.86 , clause( 92321, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 34.44/34.86 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92322, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 34.44/34.86 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92323, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 34.44/34.86 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92324, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 34.44/34.86 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92325, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 X, T, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92326, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92327, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92328, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92329, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92330, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92331, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 34.44/34.86 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92332, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 34.44/34.86 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92333, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 34.44/34.86 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92334, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92335, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 34.44/34.86 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92336, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 34.44/34.86 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92337, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 34.44/34.86 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92338, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92339, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92340, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 34.44/34.86 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92341, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ),
% 34.44/34.86 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92342, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92343, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92344, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 34.44/34.86 Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92345, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92346, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92347, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 34.44/34.86 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92348, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 34.44/34.86 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92349, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92350, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 34.44/34.86 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92351, [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 34.44/34.86 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 34.44/34.86 , Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92352, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 X, 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92353, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92354, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'(
% 34.44/34.86 Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92355, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 X, Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92356, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.86 Z, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92357, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 34.44/34.86 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 34.44/34.86 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92358, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 34.44/34.86 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92359, [ =( 'c_Orderings_Oord__class_Omin'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 34.44/34.86 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92360, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 34.44/34.86 , clause( 92361, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92362, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92363, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 34.44/34.86 , clause( 92364, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 34.44/34.86 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92365, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 34.44/34.86 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat'
% 34.44/34.86 ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92366, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 34.44/34.86 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92367, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 34.44/34.86 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92368, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92369, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 34.44/34.86 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ] )
% 34.44/34.86 , clause( 92370, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92371, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 34.44/34.86 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92372, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.86 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92373, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 34.44/34.86 'tc_nat' ), X, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92374, [ =( 'c_HOL_Otimes__class_Otimes'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 34.44/34.86 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92375, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 34.44/34.86 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92376, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 34.44/34.86 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92377, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 34.44/34.86 , clause( 92378, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ) ] )
% 34.44/34.86 , clause( 92379, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 34.44/34.86 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92380, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 34.44/34.86 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 34.44/34.86 , X ) ) ] )
% 34.44/34.86 , clause( 92381, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 34.44/34.86 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ] )
% 34.44/34.86 , clause( 92382, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92383, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 34.44/34.86 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 34.44/34.86 , clause( 92384, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92385, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92386, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 34.44/34.86 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92387, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 34.44/34.86 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 34.44/34.86 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 34.44/34.86 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92388, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 34.44/34.86 , Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92389, [ 'c_HOL_Oord__class_Oless'( X,
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 34.44/34.86 Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92390, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 34.44/34.86 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 34.44/34.86 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92391, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 34.44/34.86 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92392, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 X, Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92393, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92394, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.86 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.86 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92395, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 34.44/34.86 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92396, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 34.44/34.86 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92397, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92398, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 34.44/34.86 Y, X ) ) ] )
% 34.44/34.86 , clause( 92399, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 34.44/34.86 Y, X ) ) ] )
% 34.44/34.86 , clause( 92400, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 34.44/34.86 Y, X ) ) ] )
% 34.44/34.86 , clause( 92401, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 34.44/34.86 Y, X ) ) ] )
% 34.44/34.86 , clause( 92402, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 34.44/34.86 , clause( 92403, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 34.44/34.86 , clause( 92404, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92405, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92406, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 34.44/34.86 , clause( 92407, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 34.44/34.86 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92408, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 34.44/34.86 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92409, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 34.44/34.86 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 34.44/34.86 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 34.44/34.86 , clause( 92410, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 34.44/34.86 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 34.44/34.86 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 34.44/34.86 , clause( 92411, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 34.44/34.86 ), =( Z, Y ) ] )
% 34.44/34.86 , clause( 92412, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92413, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92414, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 34.44/34.86 , clause( 92415, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 34.44/34.86 , clause( 92416, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 34.44/34.86 , clause( 92417, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 34.44/34.86 ), =( Z, Y ) ] )
% 34.44/34.86 , clause( 92418, [ 'c_HOL_Oord__class_Oless'( 'v_i', 'v_n', 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92419, [ ~( 'class_Orderings_Oorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 34.44/34.86 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 34.44/34.86 , clause( 92420, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 34.44/34.86 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 34.44/34.86 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 34.44/34.86 , clause( 92421, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 34.44/34.86 , T, X ) ) ), =( Z, T ) ] )
% 34.44/34.86 , clause( 92422, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 34.44/34.86 , T, X ) ) ), =( Y, Z ) ] )
% 34.44/34.86 , clause( 92423, [ =( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 34.44/34.86 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 92424, [ 'c_HOL_Oord__class_Oless'( 'v_i', 'v_n', 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92425, [ ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.86 'c_HOL_Ominus__class_Ominus'( 'v_i', 'v_k', 'tc_nat' ), 'v_n', 'tc_nat' )
% 34.44/34.86 ) ] )
% 34.44/34.86 , clause( 92426, [
% 34.44/34.86 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92427, [
% 34.44/34.86 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92428, [
% 34.44/34.86 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92429, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 34.44/34.86 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92430, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 34.44/34.86 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92431, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 34.44/34.86 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92432, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 34.44/34.86 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92433, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 34.44/34.86 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92434, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92435, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92436, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92437, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92438, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92439, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 34.44/34.86 ] )
% 34.44/34.86 , clause( 92440, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92441, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92442, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 92443, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92444, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92445, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92446, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92447, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92448, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92449, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92450, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92451, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92452, [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92453, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92454, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 34.44/34.86 , clause( 92455, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 34.44/34.86 ] ).
% 34.44/34.86
% 34.44/34.86
% 34.44/34.86
% 34.44/34.86 subsumption(
% 34.44/34.86 clause( 17, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 34.44/34.86 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 34.44/34.86 )
% 34.44/34.86 , clause( 91675, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 34.44/34.86 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 34.44/34.86 )
% 34.44/34.86 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 34.44/34.86 1 )] ) ).
% 34.44/34.86
% 34.44/34.86
% 34.44/34.86 subsumption(
% 34.44/34.86 clause( 20, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91684, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 34.44/34.86 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 34.44/34.86 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 34.44/34.86
% 34.44/34.86
% 34.44/34.86 subsumption(
% 34.44/34.86 clause( 96, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , clause( 91769, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 34.44/34.86 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 34.44/34.86 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 34.44/34.86 ), ==>( 1, 1 )] ) ).
% 34.44/34.86
% 34.44/34.86
% 34.44/34.86 subsumption(
% 34.44/34.86 clause( 97, [ ~(
% 34.44/34.86 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 34.44/34.86 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 34.44/34.86 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 34.44/34.86 , clause( 91772, [ ~(
% 34.44/34.86 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 34.44/34.86 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 34.44/34.86 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 34.44/34.86 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 34.44/34.88 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 34.44/34.88 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 ),
% 34.44/34.88 ==>( 4, 4 )] ) ).
% 34.44/34.88
% 34.44/34.88
% 34.44/34.88 subsumption(
% 34.44/34.88 clause( 99, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' )
% 34.44/34.88 , Z, 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y
% 34.44/34.88 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.88 , clause( 91774, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 34.44/34.88 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 34.44/34.88 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 34.44/34.88 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 34.44/34.88 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 34.44/34.88 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 34.44/34.88
% 34.44/34.88
% 34.44/34.88 subsumption(
% 34.44/34.88 clause( 208, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 34.44/34.88 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 34.44/34.88 , clause( 91907, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ),
% 34.44/34.88 ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 34.44/34.88 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 34.44/34.88 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 34.44/34.88
% 34.44/34.88
% 34.44/34.88 subsumption(
% 34.44/34.88 clause( 261, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 34.44/34.88 'tc_nat' ) ] )
% 34.44/34.88 , clause( 91972, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 34.44/34.88 X, 'tc_nat' ) ] )
% 34.44/34.88 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 34.44/34.88
% 34.44/34.88
% 34.44/34.88 subsumption(
% 34.44/34.88 clause( 338, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 34.44/34.88 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 34.44/34.88 'tc_nat' ) ) ] )
% 34.44/34.88 , clause( 92066, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 34.44/34.88 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 34.44/34.88 'tc_nat' ) ) ] )
% 34.44/34.88 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 34.44/34.88 ), ==>( 1, 1 )] ) ).
% 34.44/34.88
% 34.44/34.88
% 34.44/34.88 subsumption(
% 34.44/34.88 clause( 376, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.88 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.88 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.88 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 34.44/34.88 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 34.44/34.88 , T ), =( X, Z ) ] )
% 34.44/34.88 , clause( 92118, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.88 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.88 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.88 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 34.44/34.88 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 34.44/34.88 , T ), =( X, Z ) ] )
% 34.44/34.88 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 34.44/34.88 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 34.44/34.88
% 34.44/34.88
% 34.44/34.88 subsumption(
% 34.44/34.88 clause( 449, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 34.44/34.88 , Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 34.44/34.88 , clause( 92215, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.88 X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 34.44/34.88 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 34.44/34.88 )] ) ).
% 34.44/34.88
% 34.44/34.88
% 34.44/34.88 subsumption(
% 34.44/34.88 clause( 453, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 34.44/34.88 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.88 , clause( 92219, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 34.44/34.88 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 34.44/34.88 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 34.44/34.88 ), ==>( 1, 1 )] ) ).
% 34.44/34.88
% 34.44/34.88
% 34.44/34.88 subsumption(
% 34.44/34.88 clause( 537, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 34.44/34.88 'tc_nat' ) ] )
% 34.44/34.88 , clause( 92323, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 34.44/34.88 'tc_nat' ) ] )
% 34.44/34.88 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 34.44/34.88 ), ==>( 1, 1 )] ) ).
% 34.44/34.88
% 34.44/34.88
% 34.44/34.88 subsumption(
% 34.44/34.88 clause( 539, [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'(
% 34.44/34.88 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.88 , clause( 92326, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 34.44/34.88 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 34.44/34.88 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 34.44/34.88
% 34.44/34.88
% 34.44/34.88 subsumption(
% 34.44/34.88 clause( 547, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 34.44/34.89 , clause( 92338, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 34.44/34.89 )
% 34.44/34.89 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 34.44/34.89
% 34.44/34.89
% 34.44/34.89 subsumption(
% 34.44/34.89 clause( 615, [ 'c_HOL_Oord__class_Oless'( 'v_i', 'v_n', 'tc_nat' ) ] )
% 34.44/34.89 , clause( 92418, [ 'c_HOL_Oord__class_Oless'( 'v_i', 'v_n', 'tc_nat' ) ] )
% 34.44/34.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 34.44/34.89
% 34.44/34.89
% 34.44/34.89 subsumption(
% 34.44/34.89 clause( 619, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 34.44/34.89 'v_i', 'v_k', 'tc_nat' ), 'v_n', 'tc_nat' ) ) ] )
% 34.44/34.89 , clause( 92425, [ ~( 'c_HOL_Oord__class_Oless'(
% 34.44/34.89 'c_HOL_Ominus__class_Ominus'( 'v_i', 'v_k', 'tc_nat' ), 'v_n', 'tc_nat' )
% 34.44/34.89 ) ] )
% 34.44/34.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 34.44/34.89
% 34.44/34.89
% 34.44/34.89 subsumption(
% 34.44/34.89 clause( 621, [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 34.44/34.89 'tc_nat' ) ] )
% 34.44/34.89 , clause( 92427, [
% 34.44/34.89 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 34.44/34.89 )
% 34.44/34.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 34.44/34.89
% 34.44/34.89
% 34.44/34.89 subsumption(
% 34.44/34.89 clause( 637, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 34.44/34.89 , clause( 92443, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 34.44/34.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 34.44/34.89
% 34.44/34.89
% 34.44/34.89 eqswap(
% 34.44/34.89 clause( 100580, [ =( Y, X ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.89 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 34.44/34.89 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.89 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 34.44/34.89 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 34.44/34.89 , T ) ] )
% 34.44/34.89 , clause( 376, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.89 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 34.44/34.89 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.89 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 34.44/34.89 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 34.44/34.89 , T ), =( X, Z ) ] )
% 34.44/34.89 , 2, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] )
% 34.44/34.89 ).
% 34.44/34.89
% 34.44/34.89
% 34.44/34.89 eqswap(
% 34.44/34.89 clause( 100581, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.89 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat' ),
% 34.44/34.90 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.90 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 34.44/34.90 ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 34.44/34.90 , X ), =( Y, T ) ] )
% 34.44/34.90 , clause( 100580, [ =( Y, X ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.90 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 34.44/34.90 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.90 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 34.44/34.90 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 34.44/34.90 , T ) ] )
% 34.44/34.90 , 1, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] )
% 34.44/34.90 ).
% 34.44/34.90
% 34.44/34.90
% 34.44/34.90 eqfact(
% 34.44/34.90 clause( 100599, [ ~( =( X, Y ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.90 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 34.44/34.90 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.90 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 34.44/34.90 ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 34.44/34.90 , Y ) ] )
% 34.44/34.90 , clause( 100581, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.90 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat' ),
% 34.44/34.90 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.90 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 34.44/34.90 ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 34.44/34.90 , X ), =( Y, T ) ] )
% 34.44/34.90 , 2, 1, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, Z ), :=( T, X )] )
% 34.44/34.90 ).
% 34.44/34.90
% 34.44/34.90
% 34.44/34.90 eqswap(
% 34.44/34.90 clause( 100602, [ =( Y, X ), ~( =( Z, Y ) ), ~( =(
% 34.44/34.90 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 34.44/34.90 ), 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.90 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat'
% 34.44/34.90 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ) ] )
% 34.44/34.90 , clause( 100599, [ ~( =( X, Y ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 34.44/34.90 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 34.44/34.90 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ),
% 34.44/34.90 'c_HOL_Oplus__class_Oplus'Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------