TSTP Solution File: LCL756-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL756-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n016.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 : Sun Jul 17 07:57:35 EDT 2022
% Result : Unsatisfiable 0.90s 1.32s
% Output : Refutation 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL756-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jul 3 01:00:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.90/1.30 *** allocated 10000 integers for termspace/termends
% 0.90/1.30 *** allocated 10000 integers for clauses
% 0.90/1.30 *** allocated 10000 integers for justifications
% 0.90/1.30 *** allocated 15000 integers for termspace/termends
% 0.90/1.30 Bliksem 1.12
% 0.90/1.30
% 0.90/1.30
% 0.90/1.30 Automatic Strategy Selection
% 0.90/1.30
% 0.90/1.30 Clauses:
% 0.90/1.30 [
% 0.90/1.30 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 0.90/1.30 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.90/1.30 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.30 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.90/1.30 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.30 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.90/1.30 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.30 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.90/1.30 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.90/1.30 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.90/1.30 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.90/1.30 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.90/1.30 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.30 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.90/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.30 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 0.90/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.90/1.30 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.30 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.30 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.30 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.90/1.30 ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.30 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.90/1.30 ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.90/1.30 Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.30 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.90/1.30 ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.30 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.90/1.30 ],
% 0.90/1.30 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 0.90/1.30 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.90/1.30 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.90/1.30 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.90/1.30 , X ), W, X ), X ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 0.90/1.30 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.90/1.30 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.90/1.30 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.90/1.30 , X ), T, X ), W, X ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 0.90/1.30 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X, Y, 'tc_nat' ) ), X, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 0.90/1.30 'tc_nat' ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.90/1.30 , X, 'tc_nat' ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.90/1.30 ), 'tc_nat' ) ) ],
% 0.90/1.30 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OApp'( X, Y ), Z ),
% 0.90/1.30 'c_Lambda_OdB_OApp'( 'c_Lambda_Olift'( X, Z ), 'c_Lambda_Olift'( Y, Z ) )
% 0.90/1.30 ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 0.90/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.90/1.30 ) ],
% 0.90/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.30 ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.90/1.30 X ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.90/1.30 X ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 X, T, 'tc_nat' ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.90/1.30 X ) ) ],
% 0.90/1.30 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.30 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.30 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 0.90/1.30 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.30 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.30 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.30 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.30 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.90/1.30 , T, X ), X ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.30 , Z, X ), X ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.90/1.30 , T, X ), X ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.30 , Z, X ), X ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.30 ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.30 ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.90/1.30 ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.30 ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.30 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.90/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.90/1.30 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.90/1.30 , T, X ), X ), T, X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.90/1.30 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 0.90/1.30 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.90/1.30 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.90/1.30 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.90/1.30 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.90/1.30 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.30 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.90/1.30 ,
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.30 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.90/1.30 ,
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.90/1.30 T, X ) ) ],
% 0.90/1.30 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z,
% 0.90/1.30 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 0.90/1.30 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.30 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.30 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.30 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.90/1.30 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.90/1.30 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.90/1.30 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.90/1.30 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.90/1.30 , X ), W, X ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.90/1.30 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.90/1.30 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.90/1.30 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 0.90/1.30 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.90/1.30 ,
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.90/1.30 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.90/1.30 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.30 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 0.90/1.30 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.90/1.30 ,
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.90/1.30 ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 0.90/1.30 , X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.90/1.30 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.90/1.30 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.90/1.30 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.90/1.30 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 0.90/1.30 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 0.90/1.30 'tc_nat' ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ),
% 0.90/1.30 T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.90/1.30 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.30 T, X ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.30 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.90/1.30 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.90/1.30 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.90/1.30 ],
% 0.90/1.30 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.90/1.30 ), 'tc_nat' ), X ) ],
% 0.90/1.30 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 0.90/1.30 , X, 'tc_nat' ), X ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.90/1.30 ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.90/1.30 ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.90/1.30 ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.90/1.30 ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.90/1.30 ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.30 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.30 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.30 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.90/1.30 'tc_nat' ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.90/1.30 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.90/1.30 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 0.90/1.30 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.90/1.30 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.30 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.30 Z, X ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.30 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.90/1.30 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.30 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.90/1.30 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.30 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.90/1.30 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.30 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.90/1.30 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.90/1.30 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.90/1.30 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.90/1.30 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z,
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.90/1.30 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.90/1.30 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.90/1.30 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.90/1.30 ), Y ) ],
% 0.90/1.30 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.90/1.30 'tc_nat' ) ],
% 0.90/1.30 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.30 'tc_nat' ) ],
% 0.90/1.30 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.30 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.90/1.30 ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.90/1.30 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.90/1.30 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.90/1.30 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 0.90/1.30 'c_Suc'( X ), 'tc_nat' ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.90/1.30 , Y, X ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.90/1.30 ,
% 0.90/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.90/1.30 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.90/1.30 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.90/1.30 ,
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.90/1.30 , Y, X ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.30 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.90/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.30 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.90/1.30 , T, X ), X ), T, X ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.30 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.30 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.30 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 0.90/1.30 X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.90/1.30 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 0.90/1.30 ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.30 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 0.90/1.30 X ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.30 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.30 ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.30 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.90/1.30 ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.30 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.30 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.90/1.30 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.90/1.30 ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.30 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.90/1.30 ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.90/1.30 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.90/1.30 ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.30 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.30 ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.90/1.30 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.90/1.30 ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.30 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.90/1.30 ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.90/1.30 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.90/1.30 ) ) ],
% 0.90/1.30 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.30 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 0.90/1.30 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.30 ), 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.30 ), 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.90/1.30 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' )
% 0.90/1.30 ) ],
% 0.90/1.30 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.90/1.30 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.90/1.30 ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.30 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.90/1.30 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.90/1.30 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.90/1.30 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.90/1.30 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.90/1.30 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.90/1.30 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.90/1.30 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.90/1.30 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.90/1.30 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.90/1.30 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.90/1.30 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.30 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 0.90/1.30 X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.90/1.30 T, X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.90/1.30 T, X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.30 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.90/1.30 T, X ) ) ],
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.30 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.90/1.30 ,
% 0.90/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.30 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.90/1.30 ,
% 0.90/1.30 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.90/1.30 ,
% 0.90/1.30 [ =( 'c_Orderings_Oord__class_Omin'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.90/1.30 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.30 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.30 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.30 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.30 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.90/1.30 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.90/1.30 , X ), W, X ), X ) ) ],
% 0.90/1.30 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.90/1.31 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.90/1.31 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.90/1.31 W, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.90/1.31 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.90/1.31 , X ), T, X ), W, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.90/1.31 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.90/1.31 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.90/1.31 W, X ), X ) ) ],
% 0.90/1.31 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 0.90/1.31 'c_lessequals'( T, X, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 0.90/1.31 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 0.90/1.31 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 0.90/1.31 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.90/1.31 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.90/1.31 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.31 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.31 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.31 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.90/1.31 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 0.90/1.31 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 0.90/1.31 Z, X ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.31 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.31 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.90/1.31 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.31 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.31 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.90/1.31 X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.90/1.31 X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.90/1.31 X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.90/1.31 X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.31 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.31 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.90/1.31 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 0.90/1.31 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 0.90/1.31 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), 'c_HOL_Oord__class_Oless'( Y, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 Y, 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.90/1.31 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.90/1.31 ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.90/1.31 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.31 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.90/1.31 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.90/1.31 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.90/1.31 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.90/1.31 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 0.90/1.31 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.90/1.31 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.90/1.31 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), Y,
% 0.90/1.31 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.31 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.31 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.31 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.31 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.90/1.31 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.90/1.31 , T ), =( X, Z ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.90/1.31 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.90/1.31 , T ), =( X, Z ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.31 ), X ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.90/1.31 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 0.90/1.31 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 0.90/1.31 X ), Z, X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.90/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 0.90/1.31 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.31 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 0.90/1.31 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 0.90/1.31 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.90/1.31 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ), =( X
% 0.90/1.31 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.90/1.31 ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.31 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 0.90/1.31 ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 0.90/1.31 X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ),
% 0.90/1.31 T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.90/1.31 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.90/1.31 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.90/1.31 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.90/1.31 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.31 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.90/1.31 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.90/1.31 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.31 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.31 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.90/1.31 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.90/1.31 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.31 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.31 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.31 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 0.90/1.31 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.90/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.90/1.31 ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.90/1.31 , T, X ) ) ), =( Y, Z ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.90/1.31 , T, X ) ) ), =( Z, T ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.90/1.31 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.90/1.31 X ), X ), Y ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ) ), =( Y, Z ) ],
% 0.90/1.31 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.31 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.90/1.31 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.31 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 0.90/1.31 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.31 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 X ), T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 0.90/1.31 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.31 , Z, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.90/1.31 , T, X ), X ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.90/1.31 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.31 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.31 'c_Suc'( X ), 'tc_nat' ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.31 'c_Suc'( X ), 'tc_nat' ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, T
% 0.90/1.31 , X ), Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( T, Y
% 0.90/1.31 , X ), Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 0.90/1.31 Z, Y, X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 0.90/1.31 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.90/1.31 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.90/1.31 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 0.90/1.31 [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 0.90/1.31 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, T ), 'c_Lambda_Olift'( Y, T ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.31 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.31 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 0.90/1.31 ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.90/1.31 ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.31 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.31 ) ), =( Y, Z ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.31 ) ), =( Y, Z ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 X ), X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.90/1.31 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z
% 0.90/1.31 , T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( T
% 0.90/1.31 , Z, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.90/1.31 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 0.90/1.31 ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 0.90/1.31 , 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 0.90/1.31 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 0.90/1.31 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.90/1.31 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.31 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.90/1.31 X ) ) ), =( Z, T ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.31 , Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.31 , Y, X ) ) ],
% 0.90/1.31 [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.90/1.31 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 0.90/1.31 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 0.90/1.31 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.31 'tc_nat' ) ],
% 0.90/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.90/1.31 'tc_nat' ) ],
% 0.90/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.31 'tc_nat' ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), Y, 'tc_nat' ), 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat'
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.90/1.31 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.31 ), =( Z, Y ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.31 ) ],
% 0.90/1.31 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 0.90/1.31 , Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.90/1.31 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.90/1.31 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.90/1.31 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.31 ) ],
% 0.90/1.31 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.90/1.31 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.90/1.31 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.90/1.31 X ), Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 0.90/1.31 'tc_nat' ), 'tc_nat' ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ],
% 0.90/1.31 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z, T ) ) ),
% 0.90/1.31 =( Y, T ) ],
% 0.90/1.31 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z, T ) ) ),
% 0.90/1.31 =( X, Z ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.90/1.31 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.90/1.31 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.31 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.90/1.31 ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.31 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.90/1.31 X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.31 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.90/1.31 ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.31 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.90/1.31 X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.90/1.31 ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.90/1.31 ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.90/1.31 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 0.90/1.31 ), X, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.90/1.31 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.90/1.31 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.31 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.90/1.31 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.31 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.90/1.31 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.90/1.31 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.90/1.31 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.31 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.31 ) ), X, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.31 ) ), X, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 0.90/1.31 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.90/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.90/1.31 ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.90/1.31 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.31 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.31 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.31 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.31 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 0.90/1.31 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 0.90/1.31 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.90/1.31 , Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.31 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.90/1.31 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.31 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.90/1.31 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.31 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.90/1.31 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.31 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.90/1.31 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.31 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.90/1.31 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.90/1.31 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.90/1.31 ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.31 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.31 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.90/1.31 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 0.90/1.31 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.90/1.31 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.90/1.31 X ) ) ), =( Z, T ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.90/1.31 X ) ) ), =( Y, T ) ],
% 0.90/1.31 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 0.90/1.31 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oplus__class_Oplus'( Z,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.31 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X
% 0.90/1.31 ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y
% 0.90/1.31 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~( 'c_lessequals'( Z,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~( 'c_lessequals'( Y,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.90/1.31 , T, X ), X ), T, X ) ) ],
% 0.90/1.31 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 0.90/1.31 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y, Z ),
% 0.90/1.31 'c_Suc'( T ) ), 'c_Lambda_Osubst'( U, Y, T ), Z ), 'c_Lambda_Osubst'(
% 0.90/1.31 'c_Lambda_Osubst'( X, U, Z ), Y, T ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( T, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.31 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.90/1.31 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.90/1.31 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 0.90/1.31 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.90/1.31 X ), X ) ) ],
% 0.90/1.31 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( X
% 0.90/1.31 , Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ],
% 0.90/1.31 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z
% 0.90/1.31 , Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 0.90/1.31 Z, Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.90/1.31 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 0.90/1.31 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.90/1.31 X ), X ), X ) ],
% 0.90/1.31 [ =( 'c_Orderings_Oord__class_Omax'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.90/1.31 [ =( 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 'tc_nat' ), X, 'tc_nat' ), X ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.90/1.31 X ), X ), Y ) ],
% 0.90/1.31 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 0.90/1.31 'tc_nat' ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.31 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.90/1.31 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.31 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.90/1.31 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.90/1.31 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 0.90/1.31 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.90/1.31 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ), 'c_Lambda_Olift'( Z, Y ) )
% 0.90/1.31 , ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.90/1.31 [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 0.90/1.31 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( T,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), 'c_Lambda_Olift'( Y,
% 0.90/1.31 T ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 T, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Y ), 'c_Suc'( Z ) ),
% 0.90/1.31 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Z ), Y ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 0.90/1.31 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.90/1.31 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.90/1.31 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.31 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.31 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.31 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 X ), T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.31 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X
% 0.90/1.31 ), T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y
% 0.90/1.31 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.90/1.31 ],
% 0.90/1.31 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.31 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.90/1.31 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.90/1.31 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.31 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.90/1.31 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.31 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.90/1.31 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.90/1.31 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.90/1.31 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.90/1.31 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 0.90/1.31 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.90/1.31 ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.90/1.31 ],
% 0.90/1.31 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.90/1.31 , X, 'tc_nat' ), X ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.31 ), 'tc_nat' ), X ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.31 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.31 ), X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.90/1.31 ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.90/1.31 ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.90/1.31 ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.90/1.31 ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.90/1.31 ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 0.90/1.31 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.90/1.31 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.90/1.31 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.31 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.31 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.90/1.31 ), Y ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.90/1.31 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 Y, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.31 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 Y, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.31 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.90/1.31 X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 Z, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.31 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 Z, T, X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.31 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.90/1.31 X ), X ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.90/1.31 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.90/1.31 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 0.90/1.31 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.31 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.31 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.31 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.31 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.31 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.90/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 0.90/1.31 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.31 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 0.90/1.31 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 0.90/1.31 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OApp'( Y, Z ) ) ) ],
% 0.90/1.31 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.90/1.31 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.90/1.31 , 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 0.90/1.31 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.90/1.31 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.90/1.31 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.90/1.31 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.31 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.31 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.90/1.31 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OAbs'( Z ) ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.31 , Y, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.31 , T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.31 , T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.31 , Y, X ), X ) ) ],
% 0.90/1.31 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.90/1.31 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.90/1.31 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.90/1.31 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.90/1.31 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.90/1.31 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.90/1.31 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 0.90/1.31 ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.90/1.31 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.90/1.31 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.90/1.31 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.31 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.90/1.31 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.90/1.31 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.31 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.31 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.90/1.31 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.90/1.31 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.31 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.31 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.31 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.90/1.31 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.31 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.31 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.31 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.31 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.31 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 0.90/1.31 , X ) ) ],
% 0.90/1.31 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 0.90/1.31 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.90/1.31 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.90/1.31 T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.90/1.31 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.90/1.31 X ), Z, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.90/1.31 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.90/1.31 T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.90/1.31 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.90/1.31 X ), T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.90/1.31 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.90/1.31 T, X ), X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.90/1.31 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.90/1.31 X ), T, X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.31 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.31 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.31 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.90/1.31 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.31 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.31 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.90/1.31 'c_lessequals'( Z, Y, X ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.31 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.90/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.31 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 0.90/1.31 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 0.90/1.31 ],
% 0.90/1.31 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T ),
% 0.90/1.31 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubst'( X, Z, T ), 'c_Lambda_Osubst'( Y,
% 0.90/1.31 Z, T ) ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.90/1.31 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.90/1.31 ) ],
% 0.90/1.31 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.90/1.31 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 0.90/1.31 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.90/1.31 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.90/1.31 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.90/1.31 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.90/1.31 ) ) ],
% 0.90/1.31 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 0.90/1.31 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.90/1.31 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.90/1.31 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.90/1.31 [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ],
% 0.90/1.31 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.31 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.31 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.90/1.31 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.90/1.31 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.90/1.31 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.90/1.31 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OApp'( Y, Z ) ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.90/1.31 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 0.90/1.31 'c_InductTermi_OIT'( X ) ) ],
% 0.90/1.31 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.90/1.31 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.90/1.31 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.90/1.31 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.90/1.31 [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ), 'c_Lambda_Osubst'( T,
% 0.90/1.31 Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ],
% 0.90/1.31 [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.90/1.31 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) )
% 0.90/1.31 ],
% 0.90/1.31 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.90/1.31 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.90/1.31 'tc_nat' ) ],
% 0.90/1.31 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 0.90/1.31 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubst'(
% 0.90/1.31 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.90/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.90/1.31 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 0.90/1.31 , X, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 0.90/1.31 'tc_nat' ) ],
% 0.90/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.90/1.31 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.90/1.31 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.31 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 0.90/1.31 'c_InductTermi_OIT'( X ) ) ],
% 0.90/1.31 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.90/1.31 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X ) ],
% 0.90/1.31 [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.90/1.31 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat' ) ) )
% 0.90/1.31 ],
% 0.90/1.31 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.31 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.90/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.90/1.31 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.90/1.31 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OVar'( Z ) ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.90/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.90/1.31 [ 'c_InductTermi_OIT'( 'v_ra' ) ],
% 0.90/1.31 [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra', 'c_Lambda_OdB_OVar'( X
% 0.90/1.31 ), Y ) ) ],
% 0.90/1.31 [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra', 'c_Lambda_OdB_OVar'(
% 0.90/1.31 'c_Suc'( 'v_ia' ) ), 'c_Suc'( 'v_ja' ) ) ) ) ],
% 0.90/1.31 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.90/1.31 ],
% 0.90/1.31 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.90/1.31 ) ],
% 0.90/1.31 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.90/1.31 ],
% 0.90/1.31 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 0.90/1.31 ,
% 0.90/1.31 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.90/1.31 [ 'class_Orderings_Oorder'( 'tc_nat' ) ]
% 0.90/1.31 ] .
% 0.90/1.31
% 0.90/1.31
% 0.90/1.31 percentage equality = 0.256875, percentage horn = 0.896499
% 0.90/1.31 This is a problem with some equality
% 0.90/1.31
% 0.90/1.31
% 0.90/1.31
% 0.90/1.31 Options Used:
% 0.90/1.31
% 0.90/1.31 useres = 1
% 0.90/1.31 useparamod = 1
% 0.90/1.31 useeqrefl = 1
% 0.90/1.31 useeqfact = 1
% 0.90/1.31 usefactor = 1
% 0.90/1.31 usesimpsplitting = 0
% 0.90/1.31 usesimpdemod = 5
% 0.90/1.31 usesimpres = 3
% 0.90/1.31
% 0.90/1.31 resimpinuse = 1000
% 0.90/1.31 resimpclauses = 20000
% 0.90/1.31 substype = eqrewr
% 0.90/1.31 backwardsubs = 1
% 0.90/1.31 selectoldest = 5
% 0.90/1.31
% 0.90/1.31 litorderings [0] = split
% 0.90/1.31 litorderings [1] = extend the termordering, first sorting on arguments
% 0.90/1.31
% 0.90/1.31 termordering = kbo
% 0.90/1.31
% 0.90/1.31 litapriori = 0
% 0.90/1.31 termapriori = 1
% 0.90/1.31 litaposteriori = 0
% 0.90/1.31 termaposteriori = 0
% 0.90/1.31 demodaposteriori = 0
% 0.90/1.32 ordereqreflfact = 0
% 0.90/1.32
% 0.90/1.32 litselect = negord
% 0.90/1.32
% 0.90/1.32 maxweight = 15
% 0.90/1.32 maxdepth = 30000
% 0.90/1.32 maxlength = 115
% 0.90/1.32 maxnrvars = 195
% 0.90/1.32 excuselevel = 1
% 0.90/1.32 increasemaxweight = 1
% 0.90/1.32
% 0.90/1.32 maxselected = 10000000
% 0.90/1.32 maxnrclauses = 10000000
% 0.90/1.32
% 0.90/1.32 showgenerated = 0
% 0.90/1.32 showkept = 0
% 0.90/1.32 showselected = 0
% 0.90/1.32 showdeleted = 0
% 0.90/1.32 showresimp = 1
% 0.90/1.32 showstatus = 2000
% 0.90/1.32
% 0.90/1.32 prologoutput = 1
% 0.90/1.32 nrgoals = 5000000
% 0.90/1.32 totalproof = 1
% 0.90/1.32
% 0.90/1.32 Symbols occurring in the translation:
% 0.90/1.32
% 0.90/1.32 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.90/1.32 . [1, 2] (w:1, o:107, a:1, s:1, b:0),
% 0.90/1.32 ! [4, 1] (w:0, o:53, a:1, s:1, b:0),
% 0.90/1.32 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.90/1.32 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.90/1.32 'tc_nat' [42, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus' [43, 3] (w:1, o:135, a:1, s:1, b:0),
% 0.90/1.32 'c_lessequals' [44, 3] (w:1, o:136, a:1, s:1, b:0),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus' [45, 3] (w:1, o:138, a:1, s:1, b:0),
% 0.90/1.32 'class_Orderings_Olinorder' [47, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.90/1.32 'c_Orderings_Oord__class_Omax' [50, 3] (w:1, o:139, a:1, s:1, b:0),
% 0.90/1.32 'c_Orderings_Oord__class_Omin' [54, 3] (w:1, o:140, a:1, s:1, b:0),
% 0.90/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [55, 1]
% 0.90/1.32 (w:1, o:59, a:1, s:1, b:0),
% 0.90/1.32 'class_OrderedGroup_Ocomm__monoid__add' [56, 1] (w:1, o:60, a:1, s:1
% 0.90/1.32 , b:0),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero' [58, 1] (w:1, o:61, a:1, s:1, b:0),
% 0.90/1.32 'c_Suc' [60, 1] (w:1, o:62, a:1, s:1, b:0),
% 0.90/1.32 'c_HOL_Oord__class_Oless' [62, 3] (w:1, o:137, a:1, s:1, b:0),
% 0.90/1.32 'c_HOL_Oone__class_Oone' [63, 1] (w:1, o:63, a:1, s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Opordered__ring' [64, 1] (w:1, o:74, a:1, s:1
% 0.90/1.32 , b:0),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes' [66, 3] (w:1, o:141, a:1, s:1, b:0),
% 0.90/1.32 'c_Divides_Odiv__class_Omod' [68, 3] (w:1, o:142, a:1, s:1, b:0),
% 0.90/1.32 'c_Lambda_OdB_OApp' [71, 2] (w:1, o:132, a:1, s:1, b:0),
% 0.90/1.32 'c_Lambda_Olift' [72, 2] (w:1, o:133, a:1, s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Oordered__ring__strict' [73, 1] (w:1, o:68
% 0.90/1.32 , a:1, s:1, b:0),
% 0.90/1.32 'class_Divides_Osemiring__div' [74, 1] (w:1, o:76, a:1, s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Ocomm__semiring__1' [75, 1] (w:1, o:77, a:1
% 0.90/1.32 , s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Oidom' [77, 1] (w:1, o:78, a:1, s:1, b:0),
% 0.90/1.32 'class_Int_Onumber__ring' [78, 1] (w:1, o:79, a:1, s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Oordered__semiring__strict' [79, 1] (w:1, o:
% 0.90/1.32 69, a:1, s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Oordered__semiring' [80, 1] (w:1, o:70, a:1
% 0.90/1.32 , s:1, b:0),
% 0.90/1.32 'class_OrderedGroup_Oab__group__add' [81, 1] (w:1, o:80, a:1, s:1, b:
% 0.90/1.32 0),
% 0.90/1.32 'class_OrderedGroup_Ogroup__add' [82, 1] (w:1, o:81, a:1, s:1, b:0),
% 0.90/1.32
% 0.90/1.32 'class_Ring__and__Field_Oring' [84, 1] (w:1, o:82, a:1, s:1, b:0),
% 0.90/1.32 'class_OrderedGroup_Opordered__ab__group__add' [85, 1] (w:1, o:83, a:
% 0.90/1.32 1, s:1, b:0),
% 0.90/1.32 'class_OrderedGroup_Ocomm__monoid__mult' [86, 1] (w:1, o:84, a:1, s:1
% 0.90/1.32 , b:0),
% 0.90/1.32 'class_OrderedGroup_Omonoid__mult' [87, 1] (w:1, o:86, a:1, s:1, b:0)
% 0.90/1.32 ,
% 0.90/1.32 'class_OrderedGroup_Olordered__ab__group__add' [88, 1] (w:1, o:85, a:
% 0.90/1.32 1, s:1, b:0),
% 0.90/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add' [89, 1] (w:1, o:87
% 0.90/1.32 , a:1, s:1, b:0),
% 0.90/1.32 'class_OrderedGroup_Opordered__comm__monoid__add' [90, 1] (w:1, o:88
% 0.90/1.32 , a:1, s:1, b:0),
% 0.90/1.32 'class_Orderings_Opreorder' [91, 1] (w:1, o:90, a:1, s:1, b:0),
% 0.90/1.32 'class_Orderings_Oorder' [92, 1] (w:1, o:89, a:1, s:1, b:0),
% 0.90/1.32 'class_OrderedGroup_Oab__semigroup__add' [93, 1] (w:1, o:91, a:1, s:1
% 0.90/1.32 , b:0),
% 0.90/1.32 'class_Divides_Oring__div' [94, 1] (w:1, o:75, a:1, s:1, b:0),
% 0.90/1.32 'c_Lambda_OdB_OVar' [95, 1] (w:1, o:92, a:1, s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Oring__no__zero__divisors' [96, 1] (w:1, o:93
% 0.90/1.32 , a:1, s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Ono__zero__divisors' [97, 1] (w:1, o:67, a:1
% 0.90/1.32 , s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Oordered__idom' [100, 1] (w:1, o:71, a:1, s:1
% 0.90/1.32 , b:0),
% 0.90/1.32 'class_Ring__and__Field_Oordered__semidom' [101, 1] (w:1, o:72, a:1
% 0.90/1.32 , s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Ozero__neq__one' [102, 1] (w:1, o:94, a:1, s:
% 0.90/1.32 1, b:0),
% 0.90/1.32 'c_Lambda_OdB_OAbs' [104, 1] (w:1, o:95, a:1, s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Omult__zero' [111, 1] (w:1, o:64, a:1, s:1
% 0.90/1.32 , b:0),
% 0.90/1.32 'class_Ring__and__Field_Osemiring' [115, 1] (w:1, o:96, a:1, s:1, b:0
% 0.90/1.32 ),
% 0.90/1.32 'c_Lambda_Osubst' [116, 3] (w:1, o:143, a:1, s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Opordered__cancel__semiring' [117, 1] (w:1
% 0.90/1.32 , o:97, a:1, s:1, b:0),
% 0.90/1.32 'class_OrderedGroup_Ocancel__ab__semigroup__add' [118, 1] (w:1, o:98
% 0.90/1.32 , a:1, s:1, b:0),
% 0.90/1.32 'c_Lambda_Obeta' [119, 2] (w:1, o:134, a:1, s:1, b:0),
% 0.90/1.32 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [124, 1]
% 0.90/1.32 (w:1, o:99, a:1, s:1, b:0),
% 0.90/1.32 'class_OrderedGroup_Oab__semigroup__idem__mult' [125, 1] (w:1, o:100
% 0.90/1.32 , a:1, s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Omult__mono' [129, 1] (w:1, o:65, a:1, s:1
% 0.90/1.32 , b:0),
% 0.90/1.32 'class_Ring__and__Field_Omult__mono1' [130, 1] (w:1, o:66, a:1, s:1
% 0.90/1.32 , b:0),
% 0.90/1.32 'class_OrderedGroup_Ocancel__semigroup__add' [131, 1] (w:1, o:101, a:
% 0.90/1.32 1, s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Oordered__comm__semiring__strict' [133, 1]
% 0.90/1.32 (w:1, o:73, a:1, s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Opordered__semiring' [134, 1] (w:1, o:102, a:
% 0.90/1.32 1, s:1, b:0),
% 0.90/1.32 'class_OrderedGroup_Omonoid__add' [135, 1] (w:1, o:103, a:1, s:1, b:0
% 0.90/1.32 ),
% 0.90/1.32 'class_OrderedGroup_Oab__semigroup__mult' [136, 1] (w:1, o:104, a:1
% 0.90/1.32 , s:1, b:0),
% 0.90/1.32 'class_Ring__and__Field_Ocomm__semiring' [137, 1] (w:1, o:105, a:1
% 0.90/1.32 , s:1, b:0),
% 0.90/1.32 'c_InductTermi_OIT' [140, 1] (w:1, o:106, a:1, s:1, b:0),
% 0.90/1.32 'v_ra' [141, 0] (w:1, o:50, a:1, s:1, b:0),
% 0.90/1.32 'v_ia' [142, 0] (w:1, o:51, a:1, s:1, b:0),
% 0.90/1.32 'v_ja' [143, 0] (w:1, o:52, a:1, s:1, b:0).
% 0.90/1.32
% 0.90/1.32
% 0.90/1.32 Starting Search:
% 0.90/1.32
% 0.90/1.32
% 0.90/1.32 Bliksems!, er is een bewijs:
% 0.90/1.32 % SZS status Unsatisfiable
% 0.90/1.32 % SZS output start Refutation
% 0.90/1.32
% 0.90/1.32 clause( 582, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra',
% 0.90/1.32 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 0.90/1.32 .
% 0.90/1.32 clause( 583, [] )
% 0.90/1.32 .
% 0.90/1.32
% 0.90/1.32
% 0.90/1.32 % SZS output end Refutation
% 0.90/1.32 found a proof!
% 0.90/1.32
% 0.90/1.32 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.90/1.32
% 0.90/1.32 initialclauses(
% 0.90/1.32 [ clause( 585, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X
% 0.90/1.32 , Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.90/1.32 )
% 0.90/1.32 , clause( 586, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.90/1.32 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 587, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.90/1.32 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 588, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.90/1.32 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 589, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ] )
% 0.90/1.32 , clause( 590, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ] )
% 0.90/1.32 , clause( 591, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.90/1.32 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.90/1.32 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 0.90/1.32 , clause( 592, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.90/1.32 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.90/1.32 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 0.90/1.32 , clause( 593, [ ~(
% 0.90/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.90/1.32 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.90/1.32 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.32 , clause( 594, [ ~(
% 0.90/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.90/1.32 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 0.90/1.32 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 0.90/1.32 , clause( 595, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 596, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 597, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 598, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 599, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 600, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 601, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.90/1.32 Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 602, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 603, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 604, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 0.90/1.32 , clause( 605, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 T, 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ), W, X ), X ) ) ] )
% 0.90/1.32 , clause( 606, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.32 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.90/1.32 , X ), W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X
% 0.90/1.32 ), X ) ) ] )
% 0.90/1.32 , clause( 607, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W, X ) ) ] )
% 0.90/1.32 , clause( 608, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 0.90/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ] )
% 0.90/1.32 , clause( 609, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), X, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 610, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat'
% 0.90/1.32 ), 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~(
% 0.90/1.32 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 611, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 612, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OApp'( X, Y ), Z ),
% 0.90/1.32 'c_Lambda_OdB_OApp'( 'c_Lambda_Olift'( X, Z ), 'c_Lambda_Olift'( Y, Z ) )
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 613, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ] )
% 0.90/1.32 , clause( 614, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 615, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 616, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 617, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 618, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 619, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 X, T, 'tc_nat' ) ] )
% 0.90/1.32 , clause( 620, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 621, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.32 , clause( 622, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.32 , clause( 623, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.90/1.32 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 624, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 0.90/1.32 , Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.90/1.32 ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 625, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.32 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 0.90/1.32 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 626, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) )
% 0.90/1.32 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 627, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) )
% 0.90/1.32 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 628, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.90/1.32 , T, X ), X ) ) ] )
% 0.90/1.32 , clause( 629, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.32 , Z, X ), X ) ) ] )
% 0.90/1.32 , clause( 630, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.90/1.32 , T, X ), X ) ) ] )
% 0.90/1.32 , clause( 631, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.32 , Z, X ), X ) ) ] )
% 0.90/1.32 , clause( 632, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 633, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 634, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 635, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 636, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.32 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 0.90/1.32 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 637, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 638, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 0.90/1.32 , clause( 639, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.90/1.32 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.90/1.32 , T, X ), X ), T, X ) ) ] )
% 0.90/1.32 , clause( 640, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 Z, X ), 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ] )
% 0.90/1.32 , clause( 641, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 0.90/1.32 ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 642, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 643, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 0.90/1.32 , clause( 644, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 0.90/1.32 , clause( 645, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ),
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 646, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ),
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 647, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.90/1.32 T, X ) ) ] )
% 0.90/1.32 , clause( 648, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.90/1.32 ), Z, 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z
% 0.90/1.32 , Y, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 649, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 0.90/1.32 , clause( 650, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 0.90/1.32 , clause( 651, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 0.90/1.32 , clause( 652, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.90/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.90/1.32 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 0.90/1.32 , clause( 653, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.90/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.90/1.32 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.90/1.32 , X ), W, X ) ) ] )
% 0.90/1.32 , clause( 654, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.90/1.32 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 655, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.90/1.32 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 0.90/1.32 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.90/1.32 )
% 0.90/1.32 , clause( 656, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.90/1.32 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.90/1.32 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 657, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.32 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 0.90/1.32 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.90/1.32 )
% 0.90/1.32 , clause( 658, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 659, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.32 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 660, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 0.90/1.32 , X ) ) ] )
% 0.90/1.32 , clause( 661, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ] )
% 0.90/1.32 , clause( 662, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ] )
% 0.90/1.32 , clause( 663, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.90/1.32 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 664, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.90/1.32 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 665, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.90/1.32 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 666, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.90/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 0.90/1.32 , clause( 667, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 668, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 0.90/1.32 'tc_nat' ) ] )
% 0.90/1.32 , clause( 669, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.32 =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X
% 0.90/1.32 ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ] )
% 0.90/1.32 , clause( 670, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T,
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 671, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( Y
% 0.90/1.32 , Z, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 672, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 673, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 0.90/1.32 , clause( 674, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'(
% 0.90/1.32 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 0.90/1.32 , clause( 675, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 676, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 677, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 678, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 679, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 680, [ ~(
% 0.90/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.90/1.32 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X
% 0.90/1.32 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 681, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 682, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 683, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.90/1.32 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 684, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 685, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 686, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 687, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ),
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 688, [ =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.90/1.32 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 689, [ =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.90/1.32 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 690, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.32 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.32 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 0.90/1.32 , clause( 691, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.32 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.32 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 0.90/1.32 , clause( 692, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 693, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 0.90/1.32 , clause( 694, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 695, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.90/1.32 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 696, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 0.90/1.32 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.90/1.32 , 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 0.90/1.32 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 0.90/1.32 X, T, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 697, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 0.90/1.32 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.90/1.32 , 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 0.90/1.32 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U, 'tc_nat' ) ), ~(
% 0.90/1.32 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 698, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.90/1.32 ), Y ) ] )
% 0.90/1.32 , clause( 699, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.90/1.32 'tc_nat' ) ] )
% 0.90/1.32 , clause( 700, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.32 'tc_nat' ) ] )
% 0.90/1.32 , clause( 701, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.90/1.32 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.32 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 702, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 0.90/1.32 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.90/1.32 ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 703, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.90/1.32 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 704, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 705, [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.90/1.32 , clause( 706, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.90/1.32 , Y, X ) ) ] )
% 0.90/1.32 , clause( 707, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 708, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.32 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.90/1.32 )
% 0.90/1.32 , clause( 709, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 710, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.32 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.90/1.32 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.90/1.32 )
% 0.90/1.32 , clause( 711, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.90/1.32 , Y, X ) ) ] )
% 0.90/1.32 , clause( 712, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 0.90/1.32 , Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.90/1.32 , clause( 713, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.32 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.90/1.32 , T, X ), X ), T, X ) ) ] )
% 0.90/1.32 , clause( 714, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.32 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 715, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.32 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 716, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 0.90/1.32 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 717, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.90/1.32 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.90/1.32 , clause( 718, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 719, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 720, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 721, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.32 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 722, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.32 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 723, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.90/1.32 ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 724, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 X, Y, 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 725, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.90/1.32 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 726, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.32 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 727, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.90/1.32 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 728, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.32 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 729, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.90/1.32 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 730, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.32 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 731, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.90/1.32 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 732, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 733, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 734, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 735, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.32 , X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 736, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 0.90/1.32 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 737, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.32 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 0.90/1.32 , clause( 738, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 739, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 740, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 741, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 742, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 743, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 744, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.90/1.32 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 0.90/1.32 , clause( 745, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.90/1.32 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 0.90/1.32 , clause( 746, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.90/1.32 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 0.90/1.32 , clause( 747, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 748, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.90/1.32 T, X ) ) ] )
% 0.90/1.32 , clause( 749, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.90/1.32 T, X ) ) ] )
% 0.90/1.32 , clause( 750, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.90/1.32 T, X ) ) ] )
% 0.90/1.32 , clause( 751, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ),
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 752, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ),
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 753, [ =( 'c_Orderings_Oord__class_Omin'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 754, [ =( 'c_Orderings_Oord__class_Omin'( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 755, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.90/1.32 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 756, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.32 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 757, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.32 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 758, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 759, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 760, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.32 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 761, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.32 , clause( 762, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.90/1.32 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.90/1.32 , X ), W, X ), X ) ) ] )
% 0.90/1.32 , clause( 763, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.90/1.32 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.90/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.90/1.32 W, X ), X ) ) ] )
% 0.90/1.32 , clause( 764, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.90/1.32 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.90/1.32 , X ), T, X ), W, X ) ) ] )
% 0.90/1.32 , clause( 765, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.90/1.32 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.90/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.90/1.32 W, X ), X ) ) ] )
% 0.90/1.32 , clause( 766, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.32 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 767, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.90/1.32 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.90/1.32 'tc_nat' ), U ) ] )
% 0.90/1.32 , clause( 768, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.90/1.32 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z,
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 769, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 Z, X ), 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ] )
% 0.90/1.32 , clause( 770, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.90/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 771, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.90/1.32 ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.32 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 772, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 0.90/1.32 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 773, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 0.90/1.32 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 774, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 775, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.90/1.32 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 0.90/1.32 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 0.90/1.32 Z, X ) ) ] )
% 0.90/1.32 , clause( 776, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 777, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 778, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 779, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 780, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 781, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.32 , clause( 782, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 783, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.90/1.32 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.90/1.32 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 0.90/1.32 , clause( 784, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.90/1.32 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.90/1.32 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 0.90/1.32 , clause( 785, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 786, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 787, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.90/1.32 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 788, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 789, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 790, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 791, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 792, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 793, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 794, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 795, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 796, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 797, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.32 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 798, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Y, T, X
% 0.90/1.32 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( T, Z
% 0.90/1.32 , X ), X ) ) ] )
% 0.90/1.32 , clause( 799, [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat'
% 0.90/1.32 ), 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 800, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat'
% 0.90/1.32 ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 801, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 802, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.90/1.32 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 0.90/1.32 , clause( 803, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.90/1.32 ), =( X, Y ) ] )
% 0.90/1.32 , clause( 804, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.90/1.32 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 805, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.32 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.90/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.90/1.32 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 806, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.90/1.32 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.90/1.32 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 807, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.90/1.32 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 0.90/1.32 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.90/1.32 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 808, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.90/1.32 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 809, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 0.90/1.32 ), Z, 'tc_nat' ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 0.90/1.32 Z ), Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 810, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.90/1.32 ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( T, Y, X
% 0.90/1.32 ), Z, X ) ) ] )
% 0.90/1.32 , clause( 811, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.32 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.32 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 0.90/1.32 =( Y, T ) ] )
% 0.90/1.32 , clause( 812, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.32 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.32 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 0.90/1.32 =( Y, T ) ] )
% 0.90/1.32 , clause( 813, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.90/1.32 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.90/1.32 , T ), =( X, Z ) ] )
% 0.90/1.32 , clause( 814, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.90/1.32 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.90/1.32 , T ), =( X, Z ) ] )
% 0.90/1.32 , clause( 815, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.32 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 816, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.32 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 817, [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) )
% 0.90/1.32 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 818, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), X
% 0.90/1.32 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 0.90/1.32 , clause( 819, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.90/1.32 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 0.90/1.32 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 0.90/1.32 X ), Z, X ) ) ] )
% 0.90/1.32 , clause( 820, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 821, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat'
% 0.90/1.32 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 822, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.32 , clause( 823, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 0.90/1.32 , clause( 824, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 0.90/1.32 , clause( 825, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 0.90/1.32 , clause( 826, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'(
% 0.90/1.32 X ), X ) ] )
% 0.90/1.32 , clause( 827, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 828, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 829, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.90/1.32 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 830, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.90/1.32 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y,
% 0.90/1.32 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 831, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 832, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 833, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 834, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 835, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 836, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 0.90/1.32 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ] )
% 0.90/1.32 , clause( 837, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 0.90/1.32 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 838, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.90/1.32 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 839, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 840, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ), =( X
% 0.90/1.32 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 841, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 0.90/1.32 , Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 842, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 843, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ),
% 0.90/1.32 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 844, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.32 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 845, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 0.90/1.32 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 846, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 847, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 848, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 849, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 0.90/1.32 X ) ) ] )
% 0.90/1.32 , clause( 850, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.32 =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X
% 0.90/1.32 ), T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ] )
% 0.90/1.32 , clause( 851, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X
% 0.90/1.32 , Y, 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 852, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 0.90/1.32 , clause( 853, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 0.90/1.32 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.90/1.32 , clause( 854, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 0.90/1.32 , clause( 855, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.90/1.32 )
% 0.90/1.32 , clause( 856, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 0.90/1.32 , clause( 857, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 0.90/1.32 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 0.90/1.32 , clause( 858, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 0.90/1.32 , clause( 859, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 0.90/1.32 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 0.90/1.32 , clause( 860, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.32 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 0.90/1.32 , clause( 861, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.32 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 0.90/1.32 , clause( 862, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.90/1.32 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 0.90/1.32 , clause( 863, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.90/1.32 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 0.90/1.32 , clause( 864, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 865, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 866, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 867, [ ~(
% 0.90/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.90/1.32 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.32 , clause( 868, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 869, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 870, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat'
% 0.90/1.32 ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 871, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.90/1.32 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 872, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 873, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 874, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.90/1.32 , T, X ) ) ), =( Y, Z ) ] )
% 0.90/1.32 , clause( 875, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.90/1.32 , T, X ) ) ), =( Z, T ) ] )
% 0.90/1.32 , clause( 876, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.90/1.32 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ] )
% 0.90/1.32 , clause( 877, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ] )
% 0.90/1.32 , clause( 878, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.90/1.32 X ), X ), Y ) ] )
% 0.90/1.32 , clause( 879, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.32 'tc_nat' ) ), =( Y, Z ) ] )
% 0.90/1.32 , clause( 880, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 881, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.32 , clause( 882, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 883, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 884, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.90/1.32 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 885, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.90/1.32 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 886, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 887, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 888, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.32 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 889, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 0.90/1.32 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 890, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.32 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 X ), T, X ) ) ] )
% 0.90/1.32 , clause( 891, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 0.90/1.32 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 892, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.32 , Z, X ), X ) ) ] )
% 0.90/1.32 , clause( 893, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.90/1.32 , T, X ), X ) ) ] )
% 0.90/1.32 , clause( 894, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 0.90/1.32 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.32 ) ), Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 895, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 896, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 Z, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 897, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 X, Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 898, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.90/1.32 , clause( 899, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.90/1.32 , clause( 900, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 901, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 902, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 903, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 904, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ] )
% 0.90/1.32 , clause( 905, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ] )
% 0.90/1.32 , clause( 906, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 0.90/1.32 Z, Y, X ) ) ] )
% 0.90/1.32 , clause( 907, [ =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 0.90/1.32 ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.90/1.32 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 908, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.90/1.32 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 0.90/1.32 , clause( 909, [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 0.90/1.32 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, T ), 'c_Lambda_Olift'( Y, T ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.32 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 910, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.32 'tc_nat' ), X, 'tc_nat' ) ] )
% 0.90/1.32 , clause( 911, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.90/1.32 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 912, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.90/1.32 Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 913, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.32 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 914, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.32 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.90/1.32 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 0.90/1.32 , clause( 915, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.32 ) ), =( Y, Z ) ] )
% 0.90/1.32 , clause( 916, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.32 ) ), =( Y, Z ) ] )
% 0.90/1.32 , clause( 917, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 X ), X ) ) ] )
% 0.90/1.32 , clause( 918, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 X ), X ) ) ] )
% 0.90/1.32 , clause( 919, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 920, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 921, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 922, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.90/1.32 , clause( 923, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 0.90/1.32 , clause( 924, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ] )
% 0.90/1.32 , clause( 925, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 926, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.90/1.32 , clause( 927, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.90/1.32 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 928, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 0.90/1.32 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 929, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.90/1.32 , 'tc_nat' ) ] )
% 0.90/1.32 , clause( 930, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.32 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 931, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.32 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 932, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 0.90/1.32 , Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat'
% 0.90/1.32 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 X, Z, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 933, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 934, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 935, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 0.90/1.32 ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 936, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 0.90/1.32 ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 937, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 0.90/1.32 ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 938, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 0.90/1.32 ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 939, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 0.90/1.32 ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.32 , clause( 940, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 941, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_Suc'( X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 0.90/1.32 Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 942, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.90/1.32 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 943, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 0.90/1.32 , clause( 944, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 0.90/1.32 , clause( 945, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 0.90/1.32 , clause( 946, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.32 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 0.90/1.32 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 0.90/1.32 , clause( 947, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) )
% 0.90/1.32 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 Y, T, X ) ) ), =( Z, T ) ] )
% 0.90/1.32 , clause( 948, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.90/1.32 , clause( 949, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.90/1.32 , clause( 950, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.90/1.32 , clause( 951, [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 0.90/1.32 , clause( 952, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ] )
% 0.90/1.32 , clause( 953, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.90/1.32 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 0.90/1.32 )
% 0.90/1.32 , clause( 954, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OAbs'(
% 0.90/1.32 X ), Y ), 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 955, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.32 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 956, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ] )
% 0.90/1.32 , clause( 957, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ] )
% 0.90/1.32 , clause( 958, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ] )
% 0.90/1.32 , clause( 959, [ =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ),
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 960, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.90/1.32 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 X ), X ) ) ] )
% 0.90/1.32 , clause( 961, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.32 ), =( Z, Y ) ] )
% 0.90/1.32 , clause( 962, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 963, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 0.90/1.32 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 964, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 0.90/1.32 , clause( 965, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 0.90/1.32 , clause( 966, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 0.90/1.32 , clause( 967, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 0.90/1.32 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 968, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.32 ), =( Z, Y ) ] )
% 0.90/1.32 , clause( 969, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 0.90/1.32 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 970, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 0.90/1.32 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 0.90/1.32 , clause( 971, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 0.90/1.32 , clause( 972, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 973, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.90/1.32 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.90/1.32 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.90/1.32 X ), Z, X ) ) ] )
% 0.90/1.32 , clause( 974, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.32 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.32 , X ) ) ] )
% 0.90/1.32 , clause( 975, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 976, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), X ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 977, [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 978, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ] )
% 0.90/1.32 , clause( 979, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z
% 0.90/1.32 , T ) ) ), =( Y, T ) ] )
% 0.90/1.32 , clause( 980, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z
% 0.90/1.32 , T ) ) ), =( X, Z ) ] )
% 0.90/1.32 , clause( 981, [ ~(
% 0.90/1.32 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 982, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.32 Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 983, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 984, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 985, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z,
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 986, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.32 Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 987, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.90/1.32 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.90/1.32 )
% 0.90/1.32 , clause( 988, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.32 , X ) ) ] )
% 0.90/1.32 , clause( 989, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.32 , X ) ) ] )
% 0.90/1.32 , clause( 990, [ ~(
% 0.90/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 991, [ ~(
% 0.90/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.32 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 0.90/1.32 , clause( 992, [ ~(
% 0.90/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 993, [ ~(
% 0.90/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.32 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ) ) ] )
% 0.90/1.32 , clause( 994, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 0.90/1.32 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 995, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 0.90/1.32 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.90/1.32 ) ] )
% 0.90/1.32 , clause( 996, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.90/1.32 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.32 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 997, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 998, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.90/1.32 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.32 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 999, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 0.90/1.32 , clause( 1000, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 0.90/1.32 ), X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1001, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 0.90/1.32 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1002, [ =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ), ~(
% 0.90/1.32 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1003, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.90/1.32 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1004, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.90/1.32 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1005, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 0.90/1.32 , clause( 1006, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.90/1.32 ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1007, [ =( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.90/1.32 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1008, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 0.90/1.32 , =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.90/1.32 , X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 1009, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( T, 'c_HOL_Otimes__class_Otimes'( Y, U,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ) ), =( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.90/1.32 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1010, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.32 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.32 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.90/1.32 )
% 0.90/1.32 , clause( 1011, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.32 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.32 , clause( 1012, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 1013, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1014, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.90/1.32 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 0.90/1.32 , clause( 1015, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.90/1.32 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 0.90/1.32 , clause( 1016, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.90/1.32 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.32 , X ) ) ] )
% 0.90/1.32 , clause( 1017, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.32 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.32 , X ) ) ] )
% 0.90/1.32 , clause( 1018, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.32 , X ) ) ] )
% 0.90/1.32 , clause( 1019, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.32 , X ) ) ] )
% 0.90/1.32 , clause( 1020, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.32 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.32 , clause( 1021, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.32 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 1022, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.32 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.32 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 1023, [ 'c_HOL_Oord__class_Oless'( X,
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.32 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1024, [ 'c_HOL_Oord__class_Oless'( X,
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.32 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1025, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 0.90/1.32 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.90/1.32 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 1026, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 0.90/1.32 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.90/1.32 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 1027, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.90/1.32 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.32 , clause( 1028, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 0.90/1.32 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 1029, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 0.90/1.32 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 1030, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1031, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1032, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1033, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1034, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 0.90/1.32 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 0.90/1.32 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.90/1.32 , Z, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1035, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 0.90/1.32 )
% 0.90/1.32 , clause( 1036, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 0.90/1.32 )
% 0.90/1.32 , clause( 1037, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 1038, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 1039, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 1040, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.90/1.32 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 1041, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.32 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 1042, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1043, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X
% 0.90/1.32 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 1044, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X
% 0.90/1.32 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 1045, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 0.90/1.32 , clause( 1046, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 0.90/1.32 , Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1047, [ 'c_HOL_Oord__class_Oless'( X,
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.90/1.32 Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1048, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.90/1.32 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 Y, T, X ) ) ), =( Z, T ) ] )
% 0.90/1.32 , clause( 1049, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.90/1.32 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 T, Z, X ) ) ), =( Y, T ) ] )
% 0.90/1.32 , clause( 1050, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 0.90/1.32 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oplus__class_Oplus'( Z,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ] )
% 0.90/1.32 , clause( 1051, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.90/1.32 'tc_nat' ), X, 'tc_nat' ) ] )
% 0.90/1.32 , clause( 1052, [ ~(
% 0.90/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T
% 0.90/1.32 , X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.90/1.32 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 0.90/1.32 , clause( 1053, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1054, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~(
% 0.90/1.32 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.90/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 1055, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.32 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~(
% 0.90/1.32 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.90/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.32 , clause( 1056, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.90/1.32 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.90/1.32 , T, X ), X ), T, X ) ) ] )
% 0.90/1.32 , clause( 1057, [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.90/1.32 'tc_nat' ) ), Y ) ), =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1058, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X,
% 0.90/1.32 'c_Lambda_Olift'( Y, Z ), 'c_Suc'( T ) ), 'c_Lambda_Osubst'( U, Y, T ), Z
% 0.90/1.32 ), 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X, U, Z ), Y, T ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oplus__class_Oplus'( T,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1059, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.90/1.32 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 0.90/1.32 , clause( 1060, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.90/1.32 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 0.90/1.32 , clause( 1061, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1062, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.32 , clause( 1063, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ),
% 0.90/1.32 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 0.90/1.32 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1064, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X
% 0.90/1.32 ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1065, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 0.90/1.32 )
% 0.90/1.32 , clause( 1066, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 1067, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.32 , clause( 1068, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.90/1.32 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.90/1.32 X ), X ) ) ] )
% 0.90/1.32 , clause( 1069, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ),
% 0.90/1.32 'c_Lambda_OdB_OApp'( X, Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ] )
% 0.90/1.32 , clause( 1070, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ),
% 0.90/1.32 'c_Lambda_OdB_OApp'( Z, Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ] )
% 0.90/1.32 , clause( 1071, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 0.90/1.32 Z, Y, X ) ) ] )
% 0.90/1.32 , clause( 1072, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.90/1.32 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 0.90/1.32 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.90/1.32 X ), X ), X ) ] )
% 0.90/1.32 , clause( 1073, [ =( 'c_Orderings_Oord__class_Omax'( X,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 0.90/1.32 , clause( 1074, [ =( 'c_Orderings_Oord__class_Omax'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 0.90/1.32 , clause( 1075, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.32 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.90/1.32 X ), X ), Y ) ] )
% 0.90/1.32 , clause( 1076, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X,
% 0.90/1.32 'tc_nat' ), 'tc_nat' ) ] )
% 0.90/1.32 , clause( 1077, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 0.90/1.32 , clause( 1078, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y,
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 0.90/1.32 ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 0.90/1.32 , clause( 1079, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 0.90/1.32 , clause( 1080, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y,
% 0.90/1.32 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 0.90/1.32 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 0.90/1.32 , clause( 1081, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 0.90/1.32 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1082, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'(
% 0.90/1.32 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1083, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.90/1.32 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 1084, [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ),
% 0.90/1.32 'c_Lambda_Olift'( Z, Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ] )
% 0.90/1.32 , clause( 1085, [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 0.90/1.32 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( T,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), 'c_Lambda_Olift'( Y,
% 0.90/1.32 T ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.32 T, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1086, [ =( 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Y ), 'c_Suc'( Z
% 0.90/1.32 ) ), 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Z ), Y ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.90/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1087, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 1088, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 0.90/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 0.90/1.32 ] )
% 0.90/1.32 , clause( 1089, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 0.90/1.32 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1090, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.90/1.32 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1091, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.90/1.32 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 1092, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 0.90/1.32 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.90/1.32 ) ) ] )
% 0.90/1.32 , clause( 1093, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.90/1.32 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1094, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.32 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.90/1.32 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.32 'tc_nat' ) ) ] )
% 0.90/1.32 , clause( 1095, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.32 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 1096, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.32 , clause( 1097, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.32 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.32 X ), T, X ) ) ] )
% 0.90/1.32 , clause( 1098, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.32 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.32 , clause( 1099, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.90/1.33 , clause( 1100, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.33 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.33 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.90/1.33 , clause( 1101, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.33 , clause( 1102, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.33 , clause( 1103, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 0.90/1.33 , clause( 1104, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.33 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.33 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.33 , clause( 1105, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.33 , clause( 1106, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.33 , clause( 1107, [ ~(
% 0.90/1.33 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.90/1.33 , clause( 1108, [ ~(
% 0.90/1.33 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T
% 0.90/1.33 , X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.90/1.33 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1109, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.33 ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat'
% 0.90/1.33 ) ) ] )
% 0.90/1.33 , clause( 1110, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 0.90/1.33 )
% 0.90/1.33 , clause( 1111, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 0.90/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 0.90/1.33 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.33 , clause( 1112, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 0.90/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 0.90/1.33 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.33 , clause( 1113, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.33 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.90/1.33 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 0.90/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1114, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.90/1.33 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 0.90/1.33 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1115, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.90/1.33 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 0.90/1.33 , clause( 1116, [ =( 'c_Divides_Odiv__class_Omod'(
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 0.90/1.33 ), Z, 'tc_nat' ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y,
% 0.90/1.33 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1117, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ] )
% 0.90/1.33 , clause( 1118, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 0.90/1.33 , clause( 1119, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.90/1.33 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.90/1.33 ) ) ] )
% 0.90/1.33 , clause( 1120, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.90/1.33 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 0.90/1.33 ) ] )
% 0.90/1.33 , clause( 1121, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.90/1.33 ] )
% 0.90/1.33 , clause( 1122, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1123, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.33 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 0.90/1.33 , clause( 1124, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 0.90/1.33 , clause( 1125, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.33 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.33 , clause( 1126, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.90/1.33 ] )
% 0.90/1.33 , clause( 1127, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.90/1.33 ] )
% 0.90/1.33 , clause( 1128, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.90/1.33 ] )
% 0.90/1.33 , clause( 1129, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.90/1.33 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.90/1.33 ) ] )
% 0.90/1.33 , clause( 1130, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.90/1.33 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 0.90/1.33 ) ] )
% 0.90/1.33 , clause( 1131, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 0.90/1.33 , clause( 1132, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ),
% 0.90/1.33 'c_Lambda_OdB_OAbs'( Y ) ), ~( 'c_Lambda_Obeta'( X, Y ) ) ] )
% 0.90/1.33 , clause( 1133, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.90/1.33 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ] )
% 0.90/1.33 , clause( 1134, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.33 , X ) ) ] )
% 0.90/1.33 , clause( 1135, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.90/1.33 , X ) ) ] )
% 0.90/1.33 , clause( 1136, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.33 , X ) ) ] )
% 0.90/1.33 , clause( 1137, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.90/1.33 , X ) ) ] )
% 0.90/1.33 , clause( 1138, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ) ] )
% 0.90/1.33 , clause( 1139, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 0.90/1.33 , clause( 1140, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.33 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.90/1.33 ), Y ) ] )
% 0.90/1.33 , clause( 1141, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 0.90/1.33 , clause( 1142, [ ~(
% 0.90/1.33 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.33 , clause( 1143, [ ~(
% 0.90/1.33 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.90/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.33 , clause( 1144, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.33 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.90/1.33 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1145, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.33 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.33 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1146, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 0.90/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 0.90/1.33 , clause( 1147, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 0.90/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.33 , clause( 1148, [ ~(
% 0.90/1.33 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 Y, T, X ) ) ] )
% 0.90/1.33 , clause( 1149, [ ~(
% 0.90/1.33 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 Y, T, X ) ) ] )
% 0.90/1.33 , clause( 1150, [ ~(
% 0.90/1.33 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.90/1.33 X ), X ) ) ] )
% 0.90/1.33 , clause( 1151, [ ~(
% 0.90/1.33 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 Z, T, X ) ) ] )
% 0.90/1.33 , clause( 1152, [ ~(
% 0.90/1.33 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 Z, T, X ) ) ] )
% 0.90/1.33 , clause( 1153, [ ~(
% 0.90/1.33 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.90/1.33 X ), X ) ) ] )
% 0.90/1.33 , clause( 1154, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 0.90/1.33 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.90/1.33 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1155, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1156, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 0.90/1.33 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 0.90/1.33 , ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1157, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.33 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.90/1.33 , ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y
% 0.90/1.33 , 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.33 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1158, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 0.90/1.33 , X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 0.90/1.33 )
% 0.90/1.33 , clause( 1159, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.90/1.33 , clause( 1160, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.90/1.33 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 0.90/1.33 , clause( 1161, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.33 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.33 , clause( 1162, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 0.90/1.33 , Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 0.90/1.33 ] )
% 0.90/1.33 , clause( 1163, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 0.90/1.33 , clause( 1164, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y
% 0.90/1.33 , 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1165, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 0.90/1.33 , clause( 1166, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y
% 0.90/1.33 , X ) ] )
% 0.90/1.33 , clause( 1167, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 0.90/1.33 , Y, X ) ] )
% 0.90/1.33 , clause( 1168, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 0.90/1.33 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.33 , clause( 1169, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.33 , clause( 1170, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 0.90/1.33 , 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 0.90/1.33 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ] )
% 0.90/1.33 , clause( 1171, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OApp'( Y, Z
% 0.90/1.33 ) ) ) ] )
% 0.90/1.33 , clause( 1172, [ =( 'c_Orderings_Oord__class_Omin'(
% 0.90/1.33 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.90/1.33 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.33 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 0.90/1.33 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1173, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.33 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 0.90/1.33 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.33 , clause( 1174, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 0.90/1.33 , =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 0.90/1.33 , clause( 1175, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.90/1.33 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.33 , clause( 1176, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.90/1.33 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.33 , clause( 1177, [ =( 'c_Divides_Odiv__class_Omod'(
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), X, 'tc_nat' ),
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1178, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.33 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.33 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.33 , clause( 1179, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 0.90/1.33 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1180, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OAbs'( Z
% 0.90/1.33 ) ) ) ] )
% 0.90/1.33 , clause( 1181, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.33 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1182, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.33 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1183, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.33 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1184, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.90/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.33 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1185, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.90/1.33 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1186, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.33 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.33 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1187, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.33 ) ) ] )
% 0.90/1.33 , clause( 1188, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.33 , Y, X ), X ) ) ] )
% 0.90/1.33 , clause( 1189, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.33 , T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1190, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.33 , T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1191, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.90/1.33 , Y, X ), X ) ) ] )
% 0.90/1.33 , clause( 1192, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.90/1.33 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1193, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.33 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.90/1.33 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1194, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.90/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.90/1.33 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.90/1.33 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ] )
% 0.90/1.33 , clause( 1195, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 0.90/1.33 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 0.90/1.33 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 0.90/1.33 , clause( 1196, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 0.90/1.33 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 0.90/1.33 ~( 'c_lessequals'( U, T, X ) ) ] )
% 0.90/1.33 , clause( 1197, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 0.90/1.33 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 0.90/1.33 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.90/1.33 , clause( 1198, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 0.90/1.33 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.33 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 0.90/1.33 , clause( 1199, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.90/1.33 ) ) ] )
% 0.90/1.33 , clause( 1200, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.33 ) ) ] )
% 0.90/1.33 , clause( 1201, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 0.90/1.33 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 0.90/1.33 , clause( 1202, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.33 X, 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1203, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.33 , clause( 1204, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.90/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1205, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.33 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.90/1.33 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.90/1.33 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1206, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.90/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.90/1.33 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.90/1.33 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1207, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 0.90/1.33 , X ) ) ] )
% 0.90/1.33 , clause( 1208, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 0.90/1.33 Z, Y ) ] )
% 0.90/1.33 , clause( 1209, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 0.90/1.33 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1210, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.90/1.33 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1211, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 0.90/1.33 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1212, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.33 , clause( 1213, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.90/1.33 , X ) ) ] )
% 0.90/1.33 , clause( 1214, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.90/1.33 , X ) ) ] )
% 0.90/1.33 , clause( 1215, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 0.90/1.33 Y, Z ) ] )
% 0.90/1.33 , clause( 1216, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 0.90/1.33 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 0.90/1.33 , clause( 1217, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.33 , clause( 1218, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.90/1.33 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.33 , clause( 1219, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.33 , clause( 1220, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.33 , clause( 1221, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.33 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ] )
% 0.90/1.33 , clause( 1222, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.33 , clause( 1223, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.33 , clause( 1224, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.33 , clause( 1225, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 0.90/1.33 , X ) ) ] )
% 0.90/1.33 , clause( 1226, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 0.90/1.33 , X ) ) ] )
% 0.90/1.33 , clause( 1227, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 0.90/1.33 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.90/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ] )
% 0.90/1.33 , clause( 1228, [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.90/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1229, [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.90/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1230, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.90/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.90/1.33 T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1231, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.90/1.33 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.33 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.90/1.33 T, X ), Z, X ) ) ] )
% 0.90/1.33 , clause( 1232, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.90/1.33 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.90/1.33 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.33 Z, T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1233, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.90/1.33 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 0.90/1.33 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.90/1.33 , X ), T, X ) ) ] )
% 0.90/1.33 , clause( 1234, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.90/1.33 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 0.90/1.33 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 0.90/1.33 , T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1235, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.90/1.33 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1236, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.90/1.33 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 0.90/1.33 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.90/1.33 , X ), T, X ) ) ] )
% 0.90/1.33 , clause( 1237, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.90/1.33 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 0.90/1.33 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 0.90/1.33 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1238, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.90/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.90/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1239, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.90/1.33 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1240, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.90/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 0.90/1.33 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1241, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.90/1.33 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 0.90/1.33 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 0.90/1.33 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 0.90/1.33 , clause( 1242, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.33 Y, X ) ) ] )
% 0.90/1.33 , clause( 1243, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.33 Y, X ) ) ] )
% 0.90/1.33 , clause( 1244, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 0.90/1.33 'tc_nat' ) ] )
% 0.90/1.33 , clause( 1245, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 0.90/1.33 , Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 0.90/1.33 , clause( 1246, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.33 Y, X ) ) ] )
% 0.90/1.33 , clause( 1247, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.33 Y, X ) ) ] )
% 0.90/1.33 , clause( 1248, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ),
% 0.90/1.33 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1249, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.33 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1250, [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 0.90/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) )
% 0.90/1.33 , =( Y, Z ) ] )
% 0.90/1.33 , clause( 1251, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T )
% 0.90/1.33 , 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubst'( X, Z, T ), 'c_Lambda_Osubst'( Y
% 0.90/1.33 , Z, T ) ) ) ] )
% 0.90/1.33 , clause( 1252, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.90/1.33 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1253, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1254, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y )
% 0.90/1.33 ) ) ] )
% 0.90/1.33 , clause( 1255, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y )
% 0.90/1.33 ) ), =( X, Y ) ] )
% 0.90/1.33 , clause( 1256, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y
% 0.90/1.33 ) ] )
% 0.90/1.33 , clause( 1257, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 0.90/1.33 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 0.90/1.33 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1258, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 0.90/1.33 , clause( 1259, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 0.90/1.33 , clause( 1260, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.90/1.33 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.90/1.33 ) ) ] )
% 0.90/1.33 , clause( 1261, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1262, [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.90/1.33 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1263, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.90/1.33 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1264, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.90/1.33 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1265, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.90/1.33 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.90/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1266, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.90/1.33 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.90/1.33 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1267, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 0.90/1.33 )
% 0.90/1.33 , clause( 1268, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 0.90/1.33 )
% 0.90/1.33 , clause( 1269, [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 0.90/1.33 , clause( 1270, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.33 ) ) ) ] )
% 0.90/1.33 , clause( 1271, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.90/1.33 ) ) ) ] )
% 0.90/1.33 , clause( 1272, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 0.90/1.33 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 0.90/1.33 , clause( 1273, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X )
% 0.90/1.33 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 0.90/1.33 , clause( 1274, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.90/1.33 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1275, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OApp'( Y, Z
% 0.90/1.33 ) ) ) ] )
% 0.90/1.33 , clause( 1276, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y
% 0.90/1.33 ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1277, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 0.90/1.33 'c_InductTermi_OIT'( X ) ) ] )
% 0.90/1.33 , clause( 1278, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 0.90/1.33 ) ) ] )
% 0.90/1.33 , clause( 1279, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 0.90/1.33 , clause( 1280, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 0.90/1.33 , clause( 1281, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 0.90/1.33 ) ) ) ] )
% 0.90/1.33 , clause( 1282, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 0.90/1.33 ) ) ) ] )
% 0.90/1.33 , clause( 1283, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 0.90/1.33 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 0.90/1.33 , clause( 1284, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat'
% 0.90/1.33 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 0.90/1.33 , clause( 1285, [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ),
% 0.90/1.33 'c_Lambda_Osubst'( T, Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ] )
% 0.90/1.33 , clause( 1286, [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'(
% 0.90/1.33 Y ), 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat'
% 0.90/1.33 ) ) ) ] )
% 0.90/1.33 , clause( 1287, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.90/1.33 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.90/1.33 'tc_nat' ) ] )
% 0.90/1.33 , clause( 1288, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 0.90/1.33 'tc_nat' ), 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ),
% 0.90/1.33 =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ] )
% 0.90/1.33 , clause( 1289, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 0.90/1.33 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ] )
% 0.90/1.33 , clause( 1290, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 0.90/1.33 ), 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1291, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.90/1.33 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 0.90/1.33 )
% 0.90/1.33 , clause( 1292, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 0.90/1.33 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1293, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.90/1.33 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 0.90/1.33 , clause( 1294, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.90/1.33 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 0.90/1.33 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 0.90/1.33 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 0.90/1.33 , clause( 1295, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 0.90/1.33 'c_InductTermi_OIT'( X ) ) ] )
% 0.90/1.33 , clause( 1296, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ]
% 0.90/1.33 )
% 0.90/1.33 , clause( 1297, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X
% 0.90/1.33 ) ] )
% 0.90/1.33 , clause( 1298, [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'(
% 0.90/1.33 Y ), 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat'
% 0.90/1.33 ) ) ) ] )
% 0.90/1.33 , clause( 1299, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ),
% 0.90/1.33 ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.95/1.34 , clause( 1300, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 0.95/1.34 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1301, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.95/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 0.95/1.34 , clause( 1302, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.95/1.34 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1303, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OVar'( Z
% 0.95/1.34 ) ) ) ] )
% 0.95/1.34 , clause( 1304, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.95/1.34 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.95/1.34 , clause( 1305, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.95/1.34 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.95/1.34 , clause( 1306, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.95/1.34 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.95/1.34 , clause( 1307, [ 'c_InductTermi_OIT'( 'v_ra' ) ] )
% 0.95/1.34 , clause( 1308, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra',
% 0.95/1.34 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 0.95/1.34 , clause( 1309, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra',
% 0.95/1.34 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' ) ), 'c_Suc'( 'v_ja' ) ) ) ) ] )
% 0.95/1.34 , clause( 1310, [
% 0.95/1.34 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 0.95/1.34 )
% 0.95/1.34 , clause( 1311, [
% 0.95/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 0.95/1.34 )
% 0.95/1.34 , clause( 1312, [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.95/1.34 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1313, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.95/1.34 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1314, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.95/1.34 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1315, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 0.95/1.34 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1316, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.95/1.34 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1317, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.95/1.34 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1318, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 0.95/1.34 ] )
% 0.95/1.34 , clause( 1319, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' )
% 0.95/1.34 ] )
% 0.95/1.34 , clause( 1320, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ]
% 0.95/1.34 )
% 0.95/1.34 , clause( 1321, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 0.95/1.34 ] )
% 0.95/1.34 , clause( 1322, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 0.95/1.34 )
% 0.95/1.34 , clause( 1323, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ]
% 0.95/1.34 )
% 0.95/1.34 , clause( 1324, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 0.95/1.34 )
% 0.95/1.34 , clause( 1325, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1326, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1327, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1328, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1329, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1330, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1331, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1332, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1333, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1334, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1335, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1336, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1337, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1338, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1339, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 0.95/1.34 ] ).
% 0.95/1.34
% 0.95/1.34
% 0.95/1.34
% 0.95/1.34 subsumption(
% 0.95/1.34 clause( 582, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra',
% 0.95/1.34 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 0.95/1.34 , clause( 1308, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra',
% 0.95/1.34 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 0.95/1.34 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.95/1.34 )] ) ).
% 0.95/1.34
% 0.95/1.34
% 0.95/1.34 resolution(
% 0.95/1.34 clause( 2828, [] )
% 0.95/1.34 , clause( 1309, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra',
% 0.95/1.34 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' ) ), 'c_Suc'( 'v_ja' ) ) ) ) ] )
% 0.95/1.34 , 0, clause( 582, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra',
% 0.95/1.34 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 0.95/1.34 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_Suc'( 'v_ia' ) ),
% 0.95/1.34 :=( Y, 'c_Suc'( 'v_ja' ) )] )).
% 0.95/1.34
% 0.95/1.34
% 0.95/1.34 subsumption(
% 0.95/1.34 clause( 583, [] )
% 0.95/1.34 , clause( 2828, [] )
% 0.95/1.34 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.95/1.34
% 0.95/1.34
% 0.95/1.34 end.
% 0.95/1.34
% 0.95/1.34 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.95/1.34
% 0.95/1.34 Memory use:
% 0.95/1.34
% 0.95/1.34 space for terms: 39197
% 0.95/1.34 space for clauses: 49614
% 0.95/1.34
% 0.95/1.34
% 0.95/1.34 clauses generated: 725
% 0.95/1.34 clauses kept: 584
% 0.95/1.34 clauses selected: 0
% 0.95/1.34 clauses deleted: 0
% 0.95/1.34 clauses inuse deleted: 0
% 0.95/1.34
% 0.95/1.34 subsentry: 10468
% 0.95/1.34 literals s-matched: 4860
% 0.95/1.34 literals matched: 4703
% 0.95/1.34 full subsumption: 1261
% 0.95/1.34
% 0.95/1.34 checksum: -1522590109
% 0.95/1.34
% 0.95/1.34
% 0.95/1.34 Bliksem ended
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