TSTP Solution File: LCL755-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL755-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n013.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 07:57:34 EDT 2022
% Result : Unsatisfiable 2.88s 3.28s
% Output : Refutation 2.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL755-1 : TPTP v8.1.0. Released v4.1.0.
% 0.13/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Mon Jul 4 18:27:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.98/1.33 *** allocated 10000 integers for termspace/termends
% 0.98/1.33 *** allocated 10000 integers for clauses
% 0.98/1.33 *** allocated 10000 integers for justifications
% 0.98/1.33 *** allocated 15000 integers for termspace/termends
% 0.98/1.33 Bliksem 1.12
% 0.98/1.33
% 0.98/1.33
% 0.98/1.33 Automatic Strategy Selection
% 0.98/1.33
% 0.98/1.33 Clauses:
% 0.98/1.33 [
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.98/1.33 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.98/1.33 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.98/1.33 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.98/1.33 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.98/1.33 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 0.98/1.33 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.98/1.33 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.98/1.33 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.98/1.33 ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.98/1.33 ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.98/1.33 Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.98/1.33 ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.98/1.33 ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.98/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.98/1.33 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.98/1.33 , X ), W, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 0.98/1.33 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.98/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.98/1.33 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.98/1.33 , X ), T, X ), W, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 0.98/1.33 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 X, Y, 'tc_nat' ) ), X, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.98/1.33 , X, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.98/1.33 ), 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OApp'( X, Y ), Z ),
% 0.98/1.33 'c_Lambda_OdB_OApp'( 'c_Lambda_Olift'( X, Z ), 'c_Lambda_Olift'( Y, Z ) )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 X, T, 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 0.98/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.33 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.98/1.33 , T, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.33 , Z, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.98/1.33 , T, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.33 , Z, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.33 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.98/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.98/1.33 , T, X ), X ), T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.98/1.33 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.98/1.33 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.98/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.98/1.33 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z,
% 0.98/1.33 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.98/1.33 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.98/1.33 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.98/1.33 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.98/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.98/1.33 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.98/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.98/1.33 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.98/1.33 , X ), W, X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.98/1.33 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.98/1.33 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 0.98/1.33 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.98/1.33 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.98/1.33 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 0.98/1.33 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 0.98/1.33 , X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.98/1.33 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.98/1.33 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.98/1.33 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.98/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 0.98/1.33 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ),
% 0.98/1.33 T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.98/1.33 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 T, X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 0.98/1.33 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.98/1.33 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.98/1.33 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.98/1.33 ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.98/1.33 ), 'tc_nat' ), X ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 0.98/1.33 , X, 'tc_nat' ), X ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.98/1.33 ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.98/1.33 ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.98/1.33 ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.98/1.33 ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.98/1.33 ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.98/1.33 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.98/1.33 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.98/1.33 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 0.98/1.33 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 Z, X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.98/1.33 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.98/1.33 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.33 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.98/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.33 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.98/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.98/1.33 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.98/1.33 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.98/1.33 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z,
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.98/1.33 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.98/1.33 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.98/1.33 ), Y ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.98/1.33 'tc_nat' ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.33 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.98/1.33 ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.98/1.33 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.98/1.33 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.98/1.33 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 0.98/1.33 'c_Suc'( X ), 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.98/1.33 , Y, X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.33 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.98/1.33 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.98/1.33 , Y, X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.98/1.33 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.98/1.33 , T, X ), X ), T, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.98/1.33 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.98/1.33 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.98/1.33 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.98/1.33 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.98/1.33 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.98/1.33 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.98/1.33 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.98/1.33 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.98/1.33 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 0.98/1.33 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.98/1.33 ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.98/1.33 ), 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.98/1.33 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' )
% 0.98/1.33 ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.98/1.33 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.98/1.33 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.98/1.33 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.98/1.33 T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.98/1.33 T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( 'c_Orderings_Oord__class_Omin'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.98/1.33 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.98/1.33 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.98/1.33 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.98/1.33 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.98/1.33 , X ), W, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.98/1.33 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.98/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.98/1.33 W, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.98/1.33 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.98/1.33 , X ), T, X ), W, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.98/1.33 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.98/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.98/1.33 W, X ), X ) ) ],
% 0.98/1.33 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 0.98/1.33 'c_lessequals'( T, X, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 0.98/1.33 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.98/1.33 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.98/1.33 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 0.98/1.33 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 0.98/1.33 Z, X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.33 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.98/1.33 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 0.98/1.33 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), 'c_HOL_Oord__class_Oless'( Y, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 Y, 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.98/1.33 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.98/1.33 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.98/1.33 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.98/1.33 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.98/1.33 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 0.98/1.33 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.98/1.33 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.98/1.33 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), Y,
% 0.98/1.33 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.33 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.98/1.33 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.33 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.98/1.33 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.98/1.33 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.98/1.33 , T ), =( X, Z ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.98/1.33 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.98/1.33 , T ), =( X, Z ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.98/1.33 ), X ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.98/1.33 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 0.98/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 0.98/1.33 X ), Z, X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.98/1.33 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 0.98/1.33 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.98/1.33 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 0.98/1.33 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 0.98/1.33 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.98/1.33 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ), =( X
% 0.98/1.33 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.98/1.33 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ),
% 0.98/1.33 T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.98/1.33 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.98/1.33 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.33 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.98/1.33 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.98/1.33 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.98/1.33 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.98/1.33 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.33 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.33 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.33 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 0.98/1.33 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.98/1.33 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.98/1.33 ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.98/1.33 , T, X ) ) ), =( Y, Z ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.98/1.33 , T, X ) ) ), =( Z, T ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.98/1.33 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.98/1.33 X ), X ), Y ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ) ), =( Y, Z ) ],
% 0.98/1.33 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.98/1.33 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.98/1.33 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.33 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.33 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 0.98/1.33 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.33 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 X ), T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 0.98/1.33 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.33 , Z, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.98/1.33 , T, X ), X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.98/1.33 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.33 'c_Suc'( X ), 'tc_nat' ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.33 'c_Suc'( X ), 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, T
% 0.98/1.33 , X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( T, Y
% 0.98/1.33 , X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 0.98/1.33 Z, Y, X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 0.98/1.33 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.98/1.33 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.98/1.33 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 0.98/1.33 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, T ), 'c_Lambda_Olift'( Y, T ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.98/1.33 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.98/1.33 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 0.98/1.33 ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.98/1.33 ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.33 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 ) ), =( Y, Z ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 ) ), =( Y, Z ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 X ), X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.98/1.33 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z
% 0.98/1.33 , T, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( T
% 0.98/1.33 , Z, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.98/1.33 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 0.98/1.33 ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 0.98/1.33 , 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 0.98/1.33 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 0.98/1.33 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.98/1.33 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.33 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.98/1.33 , X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.33 , Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.33 , Y, X ) ) ],
% 0.98/1.33 [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 0.98/1.33 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 0.98/1.33 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ) ],
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ) ],
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ), 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat'
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.98/1.33 ), =( Z, Y ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.33 ) ],
% 0.98/1.33 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 0.98/1.33 , Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.98/1.33 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.98/1.33 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.98/1.33 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.98/1.33 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.98/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.98/1.33 X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 , X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 0.98/1.33 'tc_nat' ), 'tc_nat' ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ],
% 0.98/1.33 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z, T ) ) ),
% 0.98/1.33 =( Y, T ) ],
% 0.98/1.33 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z, T ) ) ),
% 0.98/1.33 =( X, Z ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.98/1.33 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.98/1.33 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 , X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.98/1.33 X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.98/1.33 X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.98/1.33 ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.33 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.33 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.98/1.33 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 0.98/1.33 ), X, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.98/1.33 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.98/1.33 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.98/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.98/1.33 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.98/1.33 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.98/1.33 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.98/1.33 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.98/1.33 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 , X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.98/1.33 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 , X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 , X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 , X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.98/1.33 ) ), X, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.98/1.33 ) ), X, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 0.98/1.33 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.98/1.33 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.98/1.33 ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.98/1.33 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.98/1.33 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.98/1.33 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 0.98/1.33 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 0.98/1.33 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.33 , Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.33 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.98/1.33 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.98/1.33 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.98/1.33 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.33 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.98/1.33 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.98/1.33 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.98/1.33 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.98/1.33 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.98/1.33 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.98/1.33 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.98/1.33 ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.33 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.98/1.33 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 0.98/1.33 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.98/1.33 X ) ) ), =( Z, T ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.98/1.33 X ) ) ), =( Z, T ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.98/1.33 X ) ) ), =( Y, T ) ],
% 0.98/1.33 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 0.98/1.33 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oplus__class_Oplus'( Z,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X
% 0.98/1.33 ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y
% 0.98/1.33 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~( 'c_lessequals'( Y,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.98/1.33 , T, X ), X ), T, X ) ) ],
% 0.98/1.33 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 0.98/1.33 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y, Z ),
% 0.98/1.33 'c_Suc'( T ) ), 'c_Lambda_Osubst'( U, Y, T ), Z ), 'c_Lambda_Osubst'(
% 0.98/1.33 'c_Lambda_Osubst'( X, U, Z ), Y, T ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( T, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.98/1.33 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.98/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.98/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.98/1.33 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.98/1.33 X ), X ) ) ],
% 0.98/1.33 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( X
% 0.98/1.33 , Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ],
% 0.98/1.33 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z
% 0.98/1.33 , Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 0.98/1.33 Z, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.98/1.33 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 0.98/1.33 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.98/1.33 X ), X ), X ) ],
% 0.98/1.33 [ =( 'c_Orderings_Oord__class_Omax'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.98/1.33 [ =( 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), X, 'tc_nat' ), X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.98/1.33 X ), X ), Y ) ],
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 0.98/1.33 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.98/1.33 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.98/1.33 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.98/1.33 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.98/1.33 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.98/1.33 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 0.98/1.33 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.98/1.33 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ), 'c_Lambda_Olift'( Z, Y ) )
% 0.98/1.33 , ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 0.98/1.33 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( T,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), 'c_Lambda_Olift'( Y,
% 0.98/1.33 T ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 T, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Y ), 'c_Suc'( Z ) ),
% 0.98/1.33 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Z ), Y ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 0.98/1.33 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.98/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.98/1.33 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.98/1.33 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.98/1.33 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.33 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.33 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 X ), T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X
% 0.98/1.33 ), T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y
% 0.98/1.33 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 0.98/1.33 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.33 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.98/1.33 ],
% 0.98/1.33 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.33 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.98/1.33 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.98/1.33 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.33 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.98/1.33 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.98/1.33 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.98/1.34 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.98/1.34 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.98/1.34 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.98/1.34 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 0.98/1.34 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 0.98/1.34 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.98/1.34 ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.98/1.34 ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.98/1.34 ],
% 0.98/1.34 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.34 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.34 , X, 'tc_nat' ), X ) ],
% 0.98/1.34 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.98/1.34 ), 'tc_nat' ), X ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.34 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.98/1.34 ), X ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.98/1.34 ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.98/1.34 ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.98/1.34 ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.98/1.34 ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.98/1.34 ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.98/1.34 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.34 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.98/1.34 , X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.34 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.98/1.34 , X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.34 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.98/1.34 , X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.34 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.98/1.34 , X ) ) ],
% 0.98/1.34 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.98/1.34 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 0.98/1.34 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.98/1.34 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.98/1.34 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.98/1.34 ), Y ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.98/1.34 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.98/1.34 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.34 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.98/1.34 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.98/1.34 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.98/1.34 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 Y, T, X ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.34 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 Y, T, X ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.34 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.98/1.34 X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 Z, T, X ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.34 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 Z, T, X ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.34 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.98/1.34 X ), X ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.98/1.34 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.98/1.34 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.34 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 0.98/1.34 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.34 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.34 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.98/1.34 ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.34 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.98/1.34 ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.34 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.34 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.98/1.34 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 0.98/1.34 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.98/1.34 ,
% 0.98/1.34 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.34 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.98/1.34 , X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.34 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.98/1.34 , X ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.98/1.34 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 0.98/1.34 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 0.98/1.34 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.98/1.34 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.98/1.34 , 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 0.98/1.34 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.34 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.98/1.34 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.98/1.34 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.34 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.98/1.34 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.34 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.34 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.98/1.34 ,
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.34 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.98/1.34 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.34 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.34 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.34 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.34 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.34 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.34 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.98/1.34 ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.34 , Y, X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.98/1.34 , T, X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.98/1.34 , T, X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.98/1.34 , Y, X ), X ) ) ],
% 0.98/1.34 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.34 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.34 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.98/1.34 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.98/1.34 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.98/1.34 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.98/1.34 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.98/1.34 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.98/1.34 ,
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.98/1.34 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.98/1.34 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.98/1.34 ,
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.98/1.34 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.98/1.34 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.98/1.34 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.98/1.34 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.98/1.34 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.98/1.34 ) ) ],
% 0.98/1.34 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.98/1.34 ) ) ],
% 0.98/1.34 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.98/1.34 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 0.98/1.34 ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.98/1.34 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.34 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.98/1.34 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.98/1.34 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.98/1.34 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.98/1.34 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.34 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.34 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.98/1.34 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.34 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.98/1.34 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.98/1.34 ,
% 0.98/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.34 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.34 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.34 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.98/1.34 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.98/1.34 ,
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.98/1.34 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.98/1.34 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.98/1.34 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.98/1.34 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.98/1.34 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.34 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 0.98/1.34 , X ) ) ],
% 0.98/1.34 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 0.98/1.34 , X ) ) ],
% 0.98/1.34 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 0.98/1.34 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.98/1.34 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 0.98/1.34 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.98/1.34 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.98/1.34 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.98/1.34 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.98/1.34 T, X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.98/1.34 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.98/1.34 X ), Z, X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.98/1.34 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.98/1.34 T, X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.98/1.34 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.98/1.34 X ), T, X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.98/1.34 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.98/1.34 T, X ), X ) ) ],
% 0.98/1.34 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.98/1.34 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.98/1.34 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.98/1.34 X ), T, X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.98/1.34 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.98/1.34 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.98/1.34 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.98/1.34 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.34 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.98/1.34 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.98/1.34 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.34 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.34 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.98/1.34 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 0.98/1.34 ,
% 0.98/1.34 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.98/1.34 'c_lessequals'( Z, Y, X ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.34 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.98/1.34 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.34 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.98/1.34 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.98/1.34 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 0.98/1.34 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.98/1.34 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 0.98/1.34 ],
% 0.98/1.34 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T ),
% 0.98/1.34 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubst'( X, Z, T ), 'c_Lambda_Osubst'( Y,
% 0.98/1.34 Z, T ) ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.98/1.34 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OAbs'( Z ) ) ) ],
% 0.98/1.34 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.98/1.34 ) ],
% 0.98/1.34 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OApp'( Y, Z ) ) ) ],
% 0.98/1.34 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.98/1.34 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 0.98/1.34 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.98/1.34 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.98/1.34 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.98/1.34 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.98/1.34 ) ) ],
% 0.98/1.34 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 0.98/1.34 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 0.98/1.34 'tc_nat' ) ) ],
% 0.98/1.34 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.98/1.34 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.98/1.34 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 0.98/1.34 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.98/1.34 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.98/1.34 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.98/1.34 [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ],
% 0.98/1.34 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.34 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.34 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.98/1.34 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.98/1.34 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.98/1.34 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.98/1.34 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OApp'( Y, Z ) ) ) ],
% 0.98/1.34 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.98/1.34 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.98/1.34 ) ],
% 0.98/1.34 [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 0.98/1.34 'c_InductTermi_OIT'( X ) ) ],
% 0.98/1.34 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.98/1.34 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.98/1.34 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.98/1.34 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.98/1.34 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.98/1.34 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.98/1.34 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.98/1.34 [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ), 'c_Lambda_Osubst'( T,
% 0.98/1.34 Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ],
% 0.98/1.34 [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.98/1.34 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) )
% 0.98/1.34 ],
% 0.98/1.34 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.98/1.34 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.98/1.34 'tc_nat' ) ],
% 0.98/1.34 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 0.98/1.34 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubst'(
% 0.98/1.34 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.98/1.34 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.98/1.34 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 0.98/1.34 , X, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 0.98/1.34 'tc_nat' ) ],
% 0.98/1.34 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.98/1.34 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.98/1.34 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.98/1.34 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 0.98/1.34 'c_InductTermi_OIT'( X ) ) ],
% 0.98/1.34 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.98/1.34 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X ) ],
% 0.98/1.34 [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.98/1.34 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat' ) ) )
% 0.98/1.34 ],
% 0.98/1.34 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.98/1.34 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.98/1.34 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.98/1.34 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.98/1.34 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 0.98/1.34 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OVar'( Z ) ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.98/1.34 ,
% 0.98/1.34 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.98/1.34 [ 'c_InductTermi_OIT'( 'v_ra' ) ],
% 0.98/1.34 [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra', 'c_Lambda_OdB_OVar'( X
% 0.98/1.34 ), Y ) ) ],
% 0.98/1.34 [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'( 'v_ra'
% 0.98/1.34 , 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' ) ), 'c_Suc'( 'v_ja' ) ) ) ) ) ]
% 0.98/1.34 ,
% 0.98/1.34 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.98/1.34 ],
% 0.98/1.34 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.98/1.34 ) ],
% 0.98/1.34 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.98/1.34 ],
% 0.98/1.34 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 0.98/1.34 ,
% 0.98/1.34 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.98/1.34 [ 'class_Orderings_Oorder'( 'tc_nat' ) ]
% 0.98/1.34 ] .
% 0.98/1.34
% 0.98/1.34
% 0.98/1.34 percentage equality = 0.256875, percentage horn = 0.896499
% 0.98/1.34 This is a problem with some equality
% 0.98/1.34
% 0.98/1.34
% 0.98/1.34
% 0.98/1.34 Options Used:
% 0.98/1.34
% 0.98/1.34 useres = 1
% 0.98/1.34 useparamod = 1
% 0.98/1.34 useeqrefl = 1
% 0.98/1.34 useeqfact = 1
% 0.98/1.34 usefactor = 1
% 0.98/1.34 usesimpsplitting = 0
% 0.98/1.34 usesimpdemod = 5
% 0.98/1.34 usesimpres = 3
% 0.98/1.34
% 0.98/1.34 resimpinuse = 1000
% 0.98/1.34 resimpclauses = 20000
% 0.98/1.34 substype = eqrewr
% 0.98/1.34 backwardsubs = 1
% 0.98/1.34 selectoldest = 5
% 0.98/1.34
% 0.98/1.34 litorderings [0] = split
% 0.98/1.34 litorderings [1] = extend the termordering, first sorting on arguments
% 0.98/1.34
% 0.98/1.34 termordering = kbo
% 0.98/1.34
% 0.98/1.34 litapriori = 0
% 0.98/1.34 termapriori = 1
% 0.98/1.34 litaposteriori = 0
% 0.98/1.34 termaposteriori = 0
% 2.88/3.28 demodaposteriori = 0
% 2.88/3.28 ordereqreflfact = 0
% 2.88/3.28
% 2.88/3.28 litselect = negord
% 2.88/3.28
% 2.88/3.28 maxweight = 15
% 2.88/3.28 maxdepth = 30000
% 2.88/3.28 maxlength = 115
% 2.88/3.28 maxnrvars = 195
% 2.88/3.28 excuselevel = 1
% 2.88/3.28 increasemaxweight = 1
% 2.88/3.28
% 2.88/3.28 maxselected = 10000000
% 2.88/3.28 maxnrclauses = 10000000
% 2.88/3.28
% 2.88/3.28 showgenerated = 0
% 2.88/3.28 showkept = 0
% 2.88/3.28 showselected = 0
% 2.88/3.28 showdeleted = 0
% 2.88/3.28 showresimp = 1
% 2.88/3.28 showstatus = 2000
% 2.88/3.28
% 2.88/3.28 prologoutput = 1
% 2.88/3.28 nrgoals = 5000000
% 2.88/3.28 totalproof = 1
% 2.88/3.28
% 2.88/3.28 Symbols occurring in the translation:
% 2.88/3.28
% 2.88/3.28 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.88/3.28 . [1, 2] (w:1, o:107, a:1, s:1, b:0),
% 2.88/3.28 ! [4, 1] (w:0, o:53, a:1, s:1, b:0),
% 2.88/3.28 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.88/3.28 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.88/3.28 'class_Orderings_Olinorder' [40, 1] (w:1, o:58, a:1, s:1, b:0),
% 2.88/3.28 'c_Orderings_Oord__class_Omax' [43, 3] (w:1, o:135, a:1, s:1, b:0),
% 2.88/3.28 'c_lessequals' [45, 3] (w:1, o:136, a:1, s:1, b:0),
% 2.88/3.28 'c_Orderings_Oord__class_Omin' [48, 3] (w:1, o:137, a:1, s:1, b:0),
% 2.88/3.28 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [49, 1]
% 2.88/3.28 (w:1, o:59, a:1, s:1, b:0),
% 2.88/3.28 'class_OrderedGroup_Ocomm__monoid__add' [50, 1] (w:1, o:60, a:1, s:1
% 2.88/3.28 , b:0),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus' [52, 3] (w:1, o:139, a:1, s:1, b:0),
% 2.88/3.28 'c_HOL_Ozero__class_Ozero' [53, 1] (w:1, o:61, a:1, s:1, b:0),
% 2.88/3.28 'c_Suc' [55, 1] (w:1, o:62, a:1, s:1, b:0),
% 2.88/3.28 'tc_nat' [57, 0] (w:1, o:29, a:1, s:1, b:0),
% 2.88/3.28 'c_HOL_Oord__class_Oless' [58, 3] (w:1, o:138, a:1, s:1, b:0),
% 2.88/3.28 'c_HOL_Oone__class_Oone' [62, 1] (w:1, o:63, a:1, s:1, b:0),
% 2.88/3.28 'c_HOL_Ominus__class_Ominus' [63, 3] (w:1, o:140, a:1, s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Opordered__ring' [64, 1] (w:1, o:74, a:1, s:1
% 2.88/3.28 , b:0),
% 2.88/3.28 'c_HOL_Otimes__class_Otimes' [66, 3] (w:1, o:141, a:1, s:1, b:0),
% 2.88/3.28 'c_Divides_Odiv__class_Omod' [68, 3] (w:1, o:142, a:1, s:1, b:0),
% 2.88/3.28 'c_Lambda_OdB_OApp' [71, 2] (w:1, o:132, a:1, s:1, b:0),
% 2.88/3.28 'c_Lambda_Olift' [72, 2] (w:1, o:133, a:1, s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Oordered__ring__strict' [73, 1] (w:1, o:68
% 2.88/3.28 , a:1, s:1, b:0),
% 2.88/3.28 'class_Divides_Osemiring__div' [74, 1] (w:1, o:76, a:1, s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Ocomm__semiring__1' [75, 1] (w:1, o:77, a:1
% 2.88/3.28 , s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Oidom' [77, 1] (w:1, o:78, a:1, s:1, b:0),
% 2.88/3.28 'class_Int_Onumber__ring' [78, 1] (w:1, o:79, a:1, s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Oordered__semiring__strict' [79, 1] (w:1, o:
% 2.88/3.28 69, a:1, s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Oordered__semiring' [80, 1] (w:1, o:70, a:1
% 2.88/3.28 , s:1, b:0),
% 2.88/3.28 'class_OrderedGroup_Oab__group__add' [81, 1] (w:1, o:80, a:1, s:1, b:
% 2.88/3.28 0),
% 2.88/3.28 'class_OrderedGroup_Ogroup__add' [82, 1] (w:1, o:81, a:1, s:1, b:0),
% 2.88/3.28
% 2.88/3.28 'class_Ring__and__Field_Oring' [84, 1] (w:1, o:82, a:1, s:1, b:0),
% 2.88/3.28 'class_OrderedGroup_Opordered__ab__group__add' [85, 1] (w:1, o:83, a:
% 2.88/3.28 1, s:1, b:0),
% 2.88/3.28 'class_OrderedGroup_Ocomm__monoid__mult' [86, 1] (w:1, o:84, a:1, s:1
% 2.88/3.28 , b:0),
% 2.88/3.28 'class_OrderedGroup_Omonoid__mult' [87, 1] (w:1, o:86, a:1, s:1, b:0)
% 2.88/3.28 ,
% 2.88/3.28 'class_OrderedGroup_Olordered__ab__group__add' [88, 1] (w:1, o:85, a:
% 2.88/3.28 1, s:1, b:0),
% 2.88/3.28 'class_OrderedGroup_Opordered__ab__semigroup__add' [89, 1] (w:1, o:87
% 2.88/3.28 , a:1, s:1, b:0),
% 2.88/3.28 'class_OrderedGroup_Opordered__comm__monoid__add' [90, 1] (w:1, o:88
% 2.88/3.28 , a:1, s:1, b:0),
% 2.88/3.28 'class_Orderings_Opreorder' [91, 1] (w:1, o:90, a:1, s:1, b:0),
% 2.88/3.28 'class_Orderings_Oorder' [92, 1] (w:1, o:89, a:1, s:1, b:0),
% 2.88/3.28 'class_OrderedGroup_Oab__semigroup__add' [93, 1] (w:1, o:91, a:1, s:1
% 2.88/3.28 , b:0),
% 2.88/3.28 'class_Divides_Oring__div' [94, 1] (w:1, o:75, a:1, s:1, b:0),
% 2.88/3.28 'c_Lambda_OdB_OVar' [95, 1] (w:1, o:92, a:1, s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Oring__no__zero__divisors' [96, 1] (w:1, o:93
% 2.88/3.28 , a:1, s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Ono__zero__divisors' [97, 1] (w:1, o:67, a:1
% 2.88/3.28 , s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Oordered__idom' [100, 1] (w:1, o:71, a:1, s:1
% 2.88/3.28 , b:0),
% 2.88/3.28 'class_Ring__and__Field_Oordered__semidom' [101, 1] (w:1, o:72, a:1
% 2.88/3.28 , s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Ozero__neq__one' [102, 1] (w:1, o:94, a:1, s:
% 2.88/3.28 1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Omult__zero' [108, 1] (w:1, o:64, a:1, s:1
% 2.88/3.28 , b:0),
% 2.88/3.28 'class_Ring__and__Field_Osemiring' [112, 1] (w:1, o:95, a:1, s:1, b:0
% 2.88/3.28 ),
% 2.88/3.28 'c_Lambda_Osubst' [113, 3] (w:1, o:143, a:1, s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Opordered__cancel__semiring' [114, 1] (w:1
% 2.88/3.28 , o:96, a:1, s:1, b:0),
% 2.88/3.28 'c_Lambda_OdB_OAbs' [115, 1] (w:1, o:97, a:1, s:1, b:0),
% 2.88/3.28 'c_Lambda_Obeta' [116, 2] (w:1, o:134, a:1, s:1, b:0),
% 2.88/3.28 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [121, 1]
% 2.88/3.28 (w:1, o:98, a:1, s:1, b:0),
% 2.88/3.28 'class_OrderedGroup_Oab__semigroup__idem__mult' [122, 1] (w:1, o:99
% 2.88/3.28 , a:1, s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Omult__mono' [126, 1] (w:1, o:65, a:1, s:1
% 2.88/3.28 , b:0),
% 2.88/3.28 'class_Ring__and__Field_Omult__mono1' [127, 1] (w:1, o:66, a:1, s:1
% 2.88/3.28 , b:0),
% 2.88/3.28 'class_OrderedGroup_Ocancel__ab__semigroup__add' [128, 1] (w:1, o:100
% 2.88/3.28 , a:1, s:1, b:0),
% 2.88/3.28 'class_OrderedGroup_Ocancel__semigroup__add' [129, 1] (w:1, o:101, a:
% 2.88/3.28 1, s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Oordered__comm__semiring__strict' [131, 1]
% 2.88/3.28 (w:1, o:73, a:1, s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Opordered__semiring' [132, 1] (w:1, o:102, a:
% 2.88/3.28 1, s:1, b:0),
% 2.88/3.28 'class_OrderedGroup_Omonoid__add' [133, 1] (w:1, o:103, a:1, s:1, b:0
% 2.88/3.28 ),
% 2.88/3.28 'class_OrderedGroup_Oab__semigroup__mult' [134, 1] (w:1, o:104, a:1
% 2.88/3.28 , s:1, b:0),
% 2.88/3.28 'class_Ring__and__Field_Ocomm__semiring' [135, 1] (w:1, o:105, a:1
% 2.88/3.28 , s:1, b:0),
% 2.88/3.28 'c_InductTermi_OIT' [140, 1] (w:1, o:106, a:1, s:1, b:0),
% 2.88/3.28 'v_ra' [141, 0] (w:1, o:50, a:1, s:1, b:0),
% 2.88/3.28 'v_ia' [142, 0] (w:1, o:51, a:1, s:1, b:0),
% 2.88/3.28 'v_ja' [143, 0] (w:1, o:52, a:1, s:1, b:0).
% 2.88/3.28
% 2.88/3.28
% 2.88/3.28 Starting Search:
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28
% 2.88/3.28 Intermediate Status:
% 2.88/3.28 Generated: 4595
% 2.88/3.28 Kept: 2006
% 2.88/3.28 Inuse: 179
% 2.88/3.28 Deleted: 3
% 2.88/3.28 Deletedinuse: 0
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28
% 2.88/3.28 Intermediate Status:
% 2.88/3.28 Generated: 15821
% 2.88/3.28 Kept: 4077
% 2.88/3.28 Inuse: 266
% 2.88/3.28 Deleted: 6
% 2.88/3.28 Deletedinuse: 1
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28
% 2.88/3.28 Intermediate Status:
% 2.88/3.28 Generated: 25438
% 2.88/3.28 Kept: 6084
% 2.88/3.28 Inuse: 353
% 2.88/3.28 Deleted: 7
% 2.88/3.28 Deletedinuse: 1
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28
% 2.88/3.28 Intermediate Status:
% 2.88/3.28 Generated: 37539
% 2.88/3.28 Kept: 9024
% 2.88/3.28 Inuse: 404
% 2.88/3.28 Deleted: 9
% 2.88/3.28 Deletedinuse: 1
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28
% 2.88/3.28 Intermediate Status:
% 2.88/3.28 Generated: 47004
% 2.88/3.28 Kept: 11034
% 2.88/3.28 Inuse: 492
% 2.88/3.28 Deleted: 20
% 2.88/3.28 Deletedinuse: 2
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28
% 2.88/3.28 Intermediate Status:
% 2.88/3.28 Generated: 60091
% 2.88/3.28 Kept: 13432
% 2.88/3.28 Inuse: 578
% 2.88/3.28 Deleted: 34
% 2.88/3.28 Deletedinuse: 11
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28
% 2.88/3.28 Intermediate Status:
% 2.88/3.28 Generated: 70989
% 2.88/3.28 Kept: 15830
% 2.88/3.28 Inuse: 639
% 2.88/3.28 Deleted: 40
% 2.88/3.28 Deletedinuse: 13
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28
% 2.88/3.28 Intermediate Status:
% 2.88/3.28 Generated: 80930
% 2.88/3.28 Kept: 18559
% 2.88/3.28 Inuse: 654
% 2.88/3.28 Deleted: 40
% 2.88/3.28 Deletedinuse: 13
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28 Resimplifying inuse:
% 2.88/3.28 Done
% 2.88/3.28
% 2.88/3.28 Resimplifying clauses:
% 2.88/3.28
% 2.88/3.28 Bliksems!, er is een bewijs:
% 2.88/3.28 % SZS status Unsatisfiable
% 2.88/3.28 % SZS output start Refutation
% 2.88/3.28
% 2.88/3.28 clause( 571, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 2.88/3.28 'c_InductTermi_OIT'( X ) ) ] )
% 2.88/3.28 .
% 2.88/3.28 clause( 581, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra',
% 2.88/3.28 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 2.88/3.28 .
% 2.88/3.28 clause( 582, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'(
% 2.88/3.28 'c_Lambda_Osubst'( 'v_ra', 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' ) ),
% 2.88/3.28 'c_Suc'( 'v_ja' ) ) ) ) ) ] )
% 2.88/3.28 .
% 2.88/3.28 clause( 1053, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'(
% 2.88/3.28 'v_ra', 'c_Lambda_OdB_OVar'( X ), Y ) ) ) ] )
% 2.88/3.28 .
% 2.88/3.28 clause( 20261, [] )
% 2.88/3.28 .
% 2.88/3.28
% 2.88/3.28
% 2.88/3.28 % SZS output end Refutation
% 2.88/3.28 found a proof!
% 2.88/3.28
% 2.88/3.28 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.88/3.28
% 2.88/3.28 initialclauses(
% 2.88/3.28 [ clause( 20263, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.88/3.28 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 2.88/3.28 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.88/3.28 , clause( 20264, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.88/3.28 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 2.88/3.28 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.88/3.28 , clause( 20265, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.88/3.28 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 2.88/3.28 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.88/3.28 , clause( 20266, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.28 , 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ] )
% 2.88/3.28 , clause( 20267, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.28 , 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ] )
% 2.88/3.28 , clause( 20268, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.28 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 2.88/3.28 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 2.88/3.28 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 2.88/3.28 , clause( 20269, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.28 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 2.88/3.28 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 2.88/3.28 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 2.88/3.28 , clause( 20270, [ ~(
% 2.88/3.28 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 2.88/3.28 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 2.88/3.28 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.88/3.28 , clause( 20271, [ ~(
% 2.88/3.28 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 2.88/3.28 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 2.88/3.28 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 2.88/3.28 , clause( 20272, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 2.88/3.28 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20273, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.88/3.28 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20274, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 2.88/3.28 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20275, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.88/3.28 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20276, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 2.88/3.28 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20277, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 2.88/3.28 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20278, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.88/3.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 2.88/3.28 Y, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20279, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 2.88/3.28 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20280, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 2.88/3.28 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20281, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 2.88/3.28 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 2.88/3.28 , clause( 20282, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 2.88/3.28 T, 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ), W, X ), X ) ) ] )
% 2.88/3.28 , clause( 20283, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.28 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 2.88/3.28 , X ), W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X ),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X
% 2.88/3.28 ), X ) ) ] )
% 2.88/3.28 , clause( 20284, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W, X ) ) ] )
% 2.88/3.28 , clause( 20285, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 2.88/3.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ] )
% 2.88/3.28 , clause( 20286, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), X, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.28 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20287, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y,
% 2.88/3.28 'tc_nat' ), 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ),
% 2.88/3.28 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20288, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.88/3.28 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20289, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OApp'( X, Y ), Z ),
% 2.88/3.28 'c_Lambda_OdB_OApp'( 'c_Lambda_Olift'( X, Z ), 'c_Lambda_Olift'( Y, Z ) )
% 2.88/3.28 ) ] )
% 2.88/3.28 , clause( 20290, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.28 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ] )
% 2.88/3.28 , clause( 20291, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.28 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 2.88/3.28 ) ] )
% 2.88/3.28 , clause( 20292, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.28 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.88/3.28 ) ] )
% 2.88/3.28 , clause( 20293, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.28 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 2.88/3.28 Y, X ) ) ] )
% 2.88/3.28 , clause( 20294, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 2.88/3.28 X ) ) ] )
% 2.88/3.28 , clause( 20295, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20296, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 2.88/3.28 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 2.88/3.28 X, T, 'tc_nat' ) ] )
% 2.88/3.28 , clause( 20297, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.28 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 2.88/3.28 Y, X ) ) ] )
% 2.88/3.28 , clause( 20298, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.28 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.88/3.28 , clause( 20299, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.28 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.88/3.28 , clause( 20300, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 2.88/3.28 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20301, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.28 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 2.88/3.28 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 2.88/3.28 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20302, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.88/3.28 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 2.88/3.28 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.28 , clause( 20303, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X )
% 2.88/3.28 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20304, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) )
% 2.88/3.28 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20305, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.28 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.88/3.28 , T, X ), X ) ) ] )
% 2.88/3.28 , clause( 20306, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.28 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.88/3.28 , Z, X ), X ) ) ] )
% 2.88/3.28 , clause( 20307, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 2.88/3.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.88/3.28 , T, X ), X ) ) ] )
% 2.88/3.28 , clause( 20308, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 2.88/3.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.88/3.28 , Z, X ), X ) ) ] )
% 2.88/3.28 , clause( 20309, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.88/3.28 ) ] )
% 2.88/3.28 , clause( 20310, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.88/3.28 ) ] )
% 2.88/3.28 , clause( 20311, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 2.88/3.28 ) ] )
% 2.88/3.28 , clause( 20312, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.88/3.28 ) ] )
% 2.88/3.28 , clause( 20313, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.88/3.28 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 2.88/3.28 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.28 , clause( 20314, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20315, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 2.88/3.28 , clause( 20316, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 2.88/3.28 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 2.88/3.28 , T, X ), X ), T, X ) ) ] )
% 2.88/3.28 , clause( 20317, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.28 , Z, X ), 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 2.88/3.28 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ] )
% 2.88/3.28 , clause( 20318, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 2.88/3.28 ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 2.88/3.28 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20319, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20320, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 2.88/3.28 , clause( 20321, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 2.88/3.28 , clause( 20322, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 2.88/3.28 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X
% 2.88/3.28 , Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 2.88/3.28 )
% 2.88/3.28 , clause( 20323, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.88/3.28 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 2.88/3.28 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20324, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 2.88/3.28 , clause( 20325, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 2.88/3.28 , clause( 20326, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 2.88/3.28 , clause( 20327, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 2.88/3.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 2.88/3.28 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 2.88/3.28 , clause( 20328, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 2.88/3.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 2.88/3.28 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 2.88/3.28 , X ), W, X ) ) ] )
% 2.88/3.28 , clause( 20329, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 2.88/3.28 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 2.88/3.28 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20330, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 2.88/3.28 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 2.88/3.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 2.88/3.28 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 2.88/3.28 )
% 2.88/3.28 , clause( 20331, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 2.88/3.28 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 2.88/3.28 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20332, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.88/3.28 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 2.88/3.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 2.88/3.28 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 2.88/3.28 )
% 2.88/3.28 , clause( 20333, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 2.88/3.28 ) ) ] )
% 2.88/3.28 , clause( 20334, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.28 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.28 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.28 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.88/3.28 , clause( 20335, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 2.88/3.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 2.88/3.28 , X ) ) ] )
% 2.88/3.28 , clause( 20336, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.88/3.28 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ] )
% 2.88/3.28 , clause( 20337, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.88/3.28 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ] )
% 2.88/3.28 , clause( 20338, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.28 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 2.88/3.28 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.88/3.28 , clause( 20339, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.28 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 2.88/3.28 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.88/3.28 , clause( 20340, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.28 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 2.88/3.28 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.88/3.28 , clause( 20341, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 2.88/3.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 2.88/3.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 2.88/3.28 , clause( 20342, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 2.88/3.28 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20343, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 2.88/3.28 'tc_nat' ) ] )
% 2.88/3.28 , clause( 20344, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.88/3.28 , =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z,
% 2.88/3.28 X ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.28 Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ] )
% 2.88/3.28 , clause( 20345, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.28 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T,
% 2.88/3.28 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~(
% 2.88/3.28 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.88/3.28 , clause( 20346, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 2.88/3.28 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( Y
% 2.88/3.28 , Z, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.28 , clause( 20347, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.28 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 2.88/3.28 ) ] )
% 2.88/3.28 , clause( 20348, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 2.88/3.28 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 2.88/3.28 , clause( 20349, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.28 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 2.88/3.28 , clause( 20350, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 2.88/3.28 ] )
% 2.88/3.28 , clause( 20351, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 2.88/3.28 ] )
% 2.88/3.28 , clause( 20352, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.88/3.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 2.88/3.28 ] )
% 2.88/3.28 , clause( 20353, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.28 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 2.88/3.28 ) ] )
% 2.88/3.28 , clause( 20354, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.28 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 2.88/3.28 ) ] )
% 2.88/3.28 , clause( 20355, [ ~(
% 2.88/3.28 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 2.88/3.28 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 2.88/3.28 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X
% 2.88/3.29 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20356, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20357, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20358, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 2.88/3.29 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20359, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20360, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20361, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20362, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ),
% 2.88/3.29 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20363, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 2.88/3.29 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20364, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 2.88/3.29 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20365, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.88/3.29 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.88/3.29 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.88/3.29 , clause( 20366, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.88/3.29 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.88/3.29 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.88/3.29 , clause( 20367, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20368, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 2.88/3.29 , clause( 20369, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20370, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 2.88/3.29 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20371, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 2.88/3.29 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 2.88/3.29 , 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 2.88/3.29 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 2.88/3.29 X, T, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20372, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 2.88/3.29 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 2.88/3.29 , 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 2.88/3.29 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20373, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 2.88/3.29 ), Y ) ] )
% 2.88/3.29 , clause( 20374, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.88/3.29 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20375, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.88/3.29 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20376, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 2.88/3.29 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20377, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 2.88/3.29 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 2.88/3.29 ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20378, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20379, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20380, [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20381, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 Z, Y, X ) ) ] )
% 2.88/3.29 , clause( 20382, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20383, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.88/3.29 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20384, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20385, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.88/3.29 ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20386, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 Z, Y, X ) ) ] )
% 2.88/3.29 , clause( 20387, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 X, Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20388, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.88/3.29 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 2.88/3.29 , T, X ), X ), T, X ) ) ] )
% 2.88/3.29 , clause( 20389, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.88/3.29 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20390, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.88/3.29 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20391, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 2.88/3.29 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20392, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 2.88/3.29 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.88/3.29 , clause( 20393, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 2.88/3.29 X ) ) ] )
% 2.88/3.29 , clause( 20394, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20395, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 2.88/3.29 X ) ) ] )
% 2.88/3.29 , clause( 20396, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 2.88/3.29 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20397, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.88/3.29 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20398, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 2.88/3.29 ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20399, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat'
% 2.88/3.29 ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20400, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 2.88/3.29 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20401, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.88/3.29 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20402, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 2.88/3.29 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20403, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 2.88/3.29 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20404, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 2.88/3.29 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20405, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 2.88/3.29 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20406, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 2.88/3.29 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20407, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20408, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20409, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20410, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.88/3.29 , X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20411, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 2.88/3.29 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20412, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.88/3.29 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 2.88/3.29 , clause( 20413, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20414, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20415, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20416, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20417, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20418, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20419, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 2.88/3.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 2.88/3.29 , clause( 20420, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 2.88/3.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 2.88/3.29 , clause( 20421, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 2.88/3.29 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( X,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20422, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X )
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20423, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X )
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20424, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 2.88/3.29 T, X ) ) ] )
% 2.88/3.29 , clause( 20425, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 2.88/3.29 T, X ) ) ] )
% 2.88/3.29 , clause( 20426, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 2.88/3.29 T, X ) ) ] )
% 2.88/3.29 , clause( 20427, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 2.88/3.29 T, X ) ) ] )
% 2.88/3.29 , clause( 20428, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X )
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20429, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X )
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20430, [ =( 'c_Orderings_Oord__class_Omin'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20431, [ =( 'c_Orderings_Oord__class_Omin'( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20432, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 2.88/3.29 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20433, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.88/3.29 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20434, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.88/3.29 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20435, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20436, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20437, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.88/3.29 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20438, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.88/3.29 , clause( 20439, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 2.88/3.29 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 2.88/3.29 , X ), W, X ), X ) ) ] )
% 2.88/3.29 , clause( 20440, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 2.88/3.29 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 2.88/3.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 2.88/3.29 W, X ), X ) ) ] )
% 2.88/3.29 , clause( 20441, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 2.88/3.29 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 2.88/3.29 , X ), T, X ), W, X ) ) ] )
% 2.88/3.29 , clause( 20442, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 2.88/3.29 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 2.88/3.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 2.88/3.29 W, X ), X ) ) ] )
% 2.88/3.29 , clause( 20443, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.88/3.29 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20444, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 2.88/3.29 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 2.88/3.29 'tc_nat' ), U ) ] )
% 2.88/3.29 , clause( 20445, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 2.88/3.29 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z,
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20446, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20447, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 2.88/3.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20448, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 2.88/3.29 ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 2.88/3.29 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20449, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 2.88/3.29 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20450, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 2.88/3.29 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20451, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20452, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 2.88/3.29 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 2.88/3.29 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 2.88/3.29 Z, X ) ) ] )
% 2.88/3.29 , clause( 20453, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20454, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20455, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20456, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20457, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20458, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.88/3.29 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.88/3.29 , clause( 20459, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.88/3.29 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20460, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.88/3.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 2.88/3.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.88/3.29 , clause( 20461, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.88/3.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 2.88/3.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 2.88/3.29 , clause( 20462, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20463, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20464, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.88/3.29 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20465, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20466, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20467, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20468, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20469, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20470, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20471, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20472, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20473, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20474, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.88/3.29 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20475, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Y, T, X
% 2.88/3.29 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( T, Z
% 2.88/3.29 , X ), X ) ) ] )
% 2.88/3.29 , clause( 20476, [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ),
% 2.88/3.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20477, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20478, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.88/3.29 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20479, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.88/3.29 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20480, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.88/3.29 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20481, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.88/3.29 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 2.88/3.29 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20482, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 2.88/3.29 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 2.88/3.29 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20483, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 2.88/3.29 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 2.88/3.29 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 2.88/3.29 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20484, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 2.88/3.29 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20485, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 2.88/3.29 ), Z, 'tc_nat' ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 2.88/3.29 Z ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20486, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( T, Z, X
% 2.88/3.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( T, Y, X
% 2.88/3.29 ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20487, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.88/3.29 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.88/3.29 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 2.88/3.29 =( Y, T ) ] )
% 2.88/3.29 , clause( 20488, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.88/3.29 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.88/3.29 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 2.88/3.29 =( Y, T ) ] )
% 2.88/3.29 , clause( 20489, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 2.88/3.29 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 2.88/3.29 , T ), =( X, Z ) ] )
% 2.88/3.29 , clause( 20490, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 2.88/3.29 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 2.88/3.29 , T ), =( X, Z ) ] )
% 2.88/3.29 , clause( 20491, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.88/3.29 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20492, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.88/3.29 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20493, [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' )
% 2.88/3.29 ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20494, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), X
% 2.88/3.29 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 2.88/3.29 , clause( 20495, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 2.88/3.29 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 2.88/3.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 2.88/3.29 X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20496, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20497, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat'
% 2.88/3.29 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20498, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.88/3.29 , clause( 20499, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 2.88/3.29 , clause( 20500, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 2.88/3.29 , clause( 20501, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 2.88/3.29 , clause( 20502, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'(
% 2.88/3.29 X ), X ) ] )
% 2.88/3.29 , clause( 20503, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.88/3.29 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20504, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.88/3.29 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20505, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 2.88/3.29 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.88/3.29 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20506, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 2.88/3.29 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 2.88/3.29 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20507, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20508, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20509, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20510, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20511, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.88/3.29 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20512, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 2.88/3.29 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20513, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 2.88/3.29 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20514, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 2.88/3.29 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20515, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20516, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ), =( X
% 2.88/3.29 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20517, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20518, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20519, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ),
% 2.88/3.29 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20520, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.88/3.29 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20521, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 2.88/3.29 'c_lessequals'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20522, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 2.88/3.29 X ) ) ] )
% 2.88/3.29 , clause( 20523, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20524, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 2.88/3.29 X ) ) ] )
% 2.88/3.29 , clause( 20525, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.88/3.29 , =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z,
% 2.88/3.29 X ), T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20526, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'(
% 2.88/3.29 X, Y, 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20527, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 2.88/3.29 , clause( 20528, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 2.88/3.29 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.88/3.29 , clause( 20529, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 2.88/3.29 , clause( 20530, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20531, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 2.88/3.29 , clause( 20532, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 2.88/3.29 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 2.88/3.29 , clause( 20533, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 2.88/3.29 , clause( 20534, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 2.88/3.29 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 2.88/3.29 , clause( 20535, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.88/3.29 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 2.88/3.29 , clause( 20536, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.88/3.29 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 2.88/3.29 , clause( 20537, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 2.88/3.29 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20538, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 2.88/3.29 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20539, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20540, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20541, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.88/3.29 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20542, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 2.88/3.29 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20543, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20544, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20545, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat'
% 2.88/3.29 ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20546, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 2.88/3.29 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20547, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20548, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20549, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 2.88/3.29 , T, X ) ) ), =( Y, Z ) ] )
% 2.88/3.29 , clause( 20550, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 2.88/3.29 , T, X ) ) ), =( Z, T ) ] )
% 2.88/3.29 , clause( 20551, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 2.88/3.29 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ] )
% 2.88/3.29 , clause( 20552, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.88/3.29 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20553, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 2.88/3.29 X ), X ), Y ) ] )
% 2.88/3.29 , clause( 20554, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.88/3.29 'tc_nat' ) ), =( Y, Z ) ] )
% 2.88/3.29 , clause( 20555, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.88/3.29 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20556, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.88/3.29 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.88/3.29 , clause( 20557, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20558, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20559, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.88/3.29 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20560, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.88/3.29 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20561, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20562, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20563, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.88/3.29 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20564, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 2.88/3.29 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20565, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.88/3.29 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 X ), T, X ) ) ] )
% 2.88/3.29 , clause( 20566, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 2.88/3.29 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20567, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.88/3.29 , Z, X ), X ) ) ] )
% 2.88/3.29 , clause( 20568, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.88/3.29 , T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20569, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 2.88/3.29 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.88/3.29 ) ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20570, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20571, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 Z, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20572, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 X, Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20573, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20574, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20575, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 2.88/3.29 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20576, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 2.88/3.29 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20577, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 2.88/3.29 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20578, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 2.88/3.29 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20579, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20580, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20581, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 2.88/3.29 Z, Y, X ) ) ] )
% 2.88/3.29 , clause( 20582, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 2.88/3.29 ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 2.88/3.29 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20583, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 2.88/3.29 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 2.88/3.29 , clause( 20584, [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 2.88/3.29 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, T ), 'c_Lambda_Olift'( Y, T ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.88/3.29 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.88/3.29 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20585, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.88/3.29 'tc_nat' ), X, 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20586, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 2.88/3.29 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20587, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 2.88/3.29 Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20588, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.88/3.29 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20589, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.88/3.29 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 2.88/3.29 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 2.88/3.29 , clause( 20590, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.88/3.29 ) ), =( Y, Z ) ] )
% 2.88/3.29 , clause( 20591, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.88/3.29 ) ), =( Y, Z ) ] )
% 2.88/3.29 , clause( 20592, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 X ), X ) ) ] )
% 2.88/3.29 , clause( 20593, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 X ), X ) ) ] )
% 2.88/3.29 , clause( 20594, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20595, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20596, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 2.88/3.29 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20597, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 2.88/3.29 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.88/3.29 , clause( 20598, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20599, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ] )
% 2.88/3.29 , clause( 20600, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 2.88/3.29 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20601, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 2.88/3.29 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.88/3.29 , clause( 20602, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 2.88/3.29 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20603, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 2.88/3.29 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20604, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.88/3.29 X, 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20605, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.88/3.29 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20606, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.88/3.29 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20607, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 2.88/3.29 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20608, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20609, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20610, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.88/3.29 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20611, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.88/3.29 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20612, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.88/3.29 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20613, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.88/3.29 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20614, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.88/3.29 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20615, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 2.88/3.29 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20616, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_Suc'( X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 2.88/3.29 Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20617, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 2.88/3.29 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20618, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 2.88/3.29 , clause( 20619, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 2.88/3.29 , clause( 20620, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 2.88/3.29 , clause( 20621, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.88/3.29 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 2.88/3.29 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 2.88/3.29 , clause( 20622, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20623, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20624, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.88/3.29 , clause( 20625, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.88/3.29 , clause( 20626, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.88/3.29 , clause( 20627, [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 2.88/3.29 , clause( 20628, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ] )
% 2.88/3.29 , clause( 20629, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 2.88/3.29 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20630, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'(
% 2.88/3.29 'c_Lambda_OdB_OAbs'( X ), Y ), 'c_Lambda_Osubst'( X, Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.88/3.29 , clause( 20631, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.88/3.29 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20632, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20633, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20634, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20635, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ),
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20636, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.88/3.29 ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20637, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 2.88/3.29 ), =( Z, Y ) ] )
% 2.88/3.29 , clause( 20638, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20639, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20640, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 2.88/3.29 , clause( 20641, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 2.88/3.29 , clause( 20642, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 2.88/3.29 , clause( 20643, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 2.88/3.29 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20644, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 2.88/3.29 ), =( Z, Y ) ] )
% 2.88/3.29 , clause( 20645, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 2.88/3.29 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20646, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 2.88/3.29 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 2.88/3.29 , clause( 20647, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 2.88/3.29 , clause( 20648, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20649, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 2.88/3.29 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 2.88/3.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 2.88/3.29 X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20650, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20651, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20652, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20653, [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20654, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ] )
% 2.88/3.29 , clause( 20655, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'(
% 2.88/3.29 Z, T ) ) ), =( Y, T ) ] )
% 2.88/3.29 , clause( 20656, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'(
% 2.88/3.29 Z, T ) ) ), =( X, Z ) ] )
% 2.88/3.29 , clause( 20657, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20658, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 2.88/3.29 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' )
% 2.88/3.29 , ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20659, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20660, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20661, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 2.88/3.29 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20662, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20663, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 2.88/3.29 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20664, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20665, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20666, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20667, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.88/3.29 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20668, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20669, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.88/3.29 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ) ) ] )
% 2.88/3.29 , clause( 20670, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 2.88/3.29 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20671, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 2.88/3.29 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20672, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 2.88/3.29 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20673, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20674, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 2.88/3.29 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20675, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 2.88/3.29 , clause( 20676, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 2.88/3.29 ), X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20677, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 2.88/3.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20678, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ), ~(
% 2.88/3.29 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20679, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 2.88/3.29 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20680, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 2.88/3.29 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20681, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 2.88/3.29 , clause( 20682, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 2.88/3.29 ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20683, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 2.88/3.29 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20684, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 2.88/3.29 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 2.88/3.29 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20685, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( T, 'c_HOL_Otimes__class_Otimes'( Y, U,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ) ) ), =( 'c_Divides_Odiv__class_Omod'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20686, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.88/3.29 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20687, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20688, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20689, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20690, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 2.88/3.29 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20691, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 2.88/3.29 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 2.88/3.29 , clause( 20692, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.88/3.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20693, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20694, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20695, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20696, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20697, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20698, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20699, [ 'c_HOL_Oord__class_Oless'( X,
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.88/3.29 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20700, [ 'c_HOL_Oord__class_Oless'( X,
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.88/3.29 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20701, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 2.88/3.29 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 2.88/3.29 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20702, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 2.88/3.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20703, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.88/3.29 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20704, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20705, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20706, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20707, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20708, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20709, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20710, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 2.88/3.29 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 2.88/3.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 2.88/3.29 , Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20711, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20712, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20713, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20714, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20715, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20716, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.88/3.29 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20717, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.88/3.29 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20718, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y, T,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20719, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 2.88/3.29 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20720, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 2.88/3.29 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20721, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20722, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 2.88/3.29 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 2.88/3.29 , clause( 20723, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 2.88/3.29 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 Y, T, X ) ) ), =( Z, T ) ] )
% 2.88/3.29 , clause( 20724, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 2.88/3.29 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 T, Z, X ) ) ), =( Y, T ) ] )
% 2.88/3.29 , clause( 20725, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 2.88/3.29 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oplus__class_Oplus'( Z,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ] )
% 2.88/3.29 , clause( 20726, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 2.88/3.29 'tc_nat' ), X, 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20727, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T
% 2.88/3.29 , X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 2.88/3.29 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20728, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20729, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~(
% 2.88/3.29 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20730, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~(
% 2.88/3.29 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20731, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 2.88/3.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 2.88/3.29 , T, X ), X ), T, X ) ) ] )
% 2.88/3.29 , clause( 20732, [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 2.88/3.29 'tc_nat' ) ), Y ) ), =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20733, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X,
% 2.88/3.29 'c_Lambda_Olift'( Y, Z ), 'c_Suc'( T ) ), 'c_Lambda_Osubst'( U, Y, T ), Z
% 2.88/3.29 ), 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X, U, Z ), Y, T ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oplus__class_Oplus'( T,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20734, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 2.88/3.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 2.88/3.29 , clause( 20735, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 2.88/3.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 2.88/3.29 , clause( 20736, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20737, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.88/3.29 , clause( 20738, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ),
% 2.88/3.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 2.88/3.29 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20739, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X
% 2.88/3.29 ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20740, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20741, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20742, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20743, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 2.88/3.29 X ), X ) ) ] )
% 2.88/3.29 , clause( 20744, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ),
% 2.88/3.29 'c_Lambda_OdB_OApp'( X, Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ] )
% 2.88/3.29 , clause( 20745, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ),
% 2.88/3.29 'c_Lambda_OdB_OApp'( Z, Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ] )
% 2.88/3.29 , clause( 20746, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 2.88/3.29 Z, Y, X ) ) ] )
% 2.88/3.29 , clause( 20747, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 2.88/3.29 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 2.88/3.29 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 2.88/3.29 X ), X ), X ) ] )
% 2.88/3.29 , clause( 20748, [ =( 'c_Orderings_Oord__class_Omax'( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 2.88/3.29 , clause( 20749, [ =( 'c_Orderings_Oord__class_Omax'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 2.88/3.29 , clause( 20750, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 2.88/3.29 X ), X ), Y ) ] )
% 2.88/3.29 , clause( 20751, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20752, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20753, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 2.88/3.29 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 2.88/3.29 X ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 2.88/3.29 , clause( 20754, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 2.88/3.29 , clause( 20755, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 2.88/3.29 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 2.88/3.29 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20756, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 2.88/3.29 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20757, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 2.88/3.29 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20758, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 2.88/3.29 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20759, [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ),
% 2.88/3.29 'c_Lambda_Olift'( Z, Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ] )
% 2.88/3.29 , clause( 20760, [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 2.88/3.29 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( T,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), 'c_Lambda_Olift'( Y,
% 2.88/3.29 T ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 T, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20761, [ =( 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Y ), 'c_Suc'(
% 2.88/3.29 Z ) ), 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Z ), Y ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20762, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20763, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20764, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 2.88/3.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20765, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 2.88/3.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20766, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 2.88/3.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20767, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 2.88/3.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20768, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 2.88/3.29 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20769, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 2.88/3.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20770, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.88/3.29 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20771, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20772, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.88/3.29 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 X ), T, X ) ) ] )
% 2.88/3.29 , clause( 20773, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20774, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.88/3.29 , clause( 20775, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.88/3.29 , clause( 20776, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20777, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20778, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 2.88/3.29 , clause( 20779, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20780, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20781, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20782, [ ~(
% 2.88/3.29 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.88/3.29 , clause( 20783, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T
% 2.88/3.29 , X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 2.88/3.29 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20784, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat'
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20785, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20786, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 2.88/3.29 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20787, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 2.88/3.29 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20788, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 2.88/3.29 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20789, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 2.88/3.29 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20790, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 2.88/3.29 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 2.88/3.29 , clause( 20791, [ =( 'c_Divides_Odiv__class_Omod'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 2.88/3.29 ), Z, 'tc_nat' ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20792, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20793, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20794, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20795, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20796, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20797, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20798, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 2.88/3.29 , clause( 20799, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 2.88/3.29 , clause( 20800, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.88/3.29 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20801, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20802, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20803, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20804, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20805, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 2.88/3.29 ) ] )
% 2.88/3.29 , clause( 20806, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 2.88/3.29 , clause( 20807, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 2.88/3.29 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20808, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.88/3.29 , clause( 20809, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 2.88/3.29 , clause( 20810, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.88/3.29 , clause( 20811, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 2.88/3.29 , clause( 20812, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ) ] )
% 2.88/3.29 , clause( 20813, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 2.88/3.29 , clause( 20814, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 2.88/3.29 ), Y ) ] )
% 2.88/3.29 , clause( 20815, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20816, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20817, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 2.88/3.29 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20818, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20819, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20820, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 2.88/3.29 , clause( 20821, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20822, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 2.88/3.29 , Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20823, [ 'c_HOL_Oord__class_Oless'( X,
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 2.88/3.29 Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20824, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20825, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20826, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 2.88/3.29 X ), X ) ) ] )
% 2.88/3.29 , clause( 20827, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 Z, T, X ) ) ] )
% 2.88/3.29 , clause( 20828, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 Z, T, X ) ) ] )
% 2.88/3.29 , clause( 20829, [ ~(
% 2.88/3.29 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 2.88/3.29 X ), X ) ) ] )
% 2.88/3.29 , clause( 20830, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 2.88/3.29 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 2.88/3.29 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20831, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20832, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 2.88/3.29 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 2.88/3.29 , ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20833, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 2.88/3.29 , ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y
% 2.88/3.29 , 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20834, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 2.88/3.29 , X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20835, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.88/3.29 , clause( 20836, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 2.88/3.29 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 2.88/3.29 , clause( 20837, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.88/3.29 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20838, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 2.88/3.29 ] )
% 2.88/3.29 , clause( 20839, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20840, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z,
% 2.88/3.29 Y, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20841, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20842, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y
% 2.88/3.29 , X ) ] )
% 2.88/3.29 , clause( 20843, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Y, X ) ] )
% 2.88/3.29 , clause( 20844, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 2.88/3.29 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20845, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20846, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.88/3.29 , 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 2.88/3.29 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ] )
% 2.88/3.29 , clause( 20847, [ =( 'c_Orderings_Oord__class_Omin'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 2.88/3.29 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20848, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.88/3.29 , clause( 20849, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 2.88/3.29 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 2.88/3.29 , clause( 20850, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 2.88/3.29 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20851, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 2.88/3.29 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.88/3.29 , clause( 20852, [ =( 'c_Divides_Odiv__class_Omod'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), X, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20853, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.88/3.29 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.88/3.29 , clause( 20854, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 2.88/3.29 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20855, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20856, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20857, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20858, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20859, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20860, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.88/3.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20861, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20862, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.88/3.29 , Y, X ), X ) ) ] )
% 2.88/3.29 , clause( 20863, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.88/3.29 , T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20864, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.88/3.29 , T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20865, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.88/3.29 , Y, X ), X ) ) ] )
% 2.88/3.29 , clause( 20866, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20867, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.88/3.29 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20868, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 2.88/3.29 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 2.88/3.29 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ] )
% 2.88/3.29 , clause( 20869, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.88/3.29 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 2.88/3.29 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 2.88/3.29 , clause( 20870, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.88/3.29 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 2.88/3.29 ~( 'c_lessequals'( U, T, X ) ) ] )
% 2.88/3.29 , clause( 20871, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.88/3.29 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 2.88/3.29 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20872, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.88/3.29 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 2.88/3.29 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 2.88/3.29 , clause( 20873, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20874, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20875, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20876, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 X, 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20877, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.88/3.29 , clause( 20878, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.88/3.29 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20879, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 2.88/3.29 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 2.88/3.29 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20880, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.88/3.29 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 2.88/3.29 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 2.88/3.29 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20881, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20882, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 2.88/3.29 Z, Y ) ] )
% 2.88/3.29 , clause( 20883, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 2.88/3.29 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20884, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20885, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 2.88/3.29 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20886, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20887, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20888, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20889, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 2.88/3.29 Y, Z ) ] )
% 2.88/3.29 , clause( 20890, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 2.88/3.29 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 2.88/3.29 , clause( 20891, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.88/3.29 , clause( 20892, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.88/3.29 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20893, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20894, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20895, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.88/3.29 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ] )
% 2.88/3.29 , clause( 20896, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20897, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20898, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.88/3.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.88/3.29 , clause( 20899, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20900, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 2.88/3.29 , X ) ) ] )
% 2.88/3.29 , clause( 20901, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 2.88/3.29 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ] )
% 2.88/3.29 , clause( 20902, [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20903, [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20904, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 2.88/3.29 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 2.88/3.29 T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20905, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 2.88/3.29 T, X ), Z, X ) ) ] )
% 2.88/3.29 , clause( 20906, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.88/3.29 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 Z, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20907, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 2.88/3.29 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 2.88/3.29 , X ), T, X ) ) ] )
% 2.88/3.29 , clause( 20908, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 2.88/3.29 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 2.88/3.29 , T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20909, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 2.88/3.29 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20910, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 2.88/3.29 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 2.88/3.29 , X ), T, X ) ) ] )
% 2.88/3.29 , clause( 20911, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 2.88/3.29 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 2.88/3.29 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20912, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.88/3.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 2.88/3.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20913, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 2.88/3.29 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20914, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 2.88/3.29 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20915, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.88/3.29 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 2.88/3.29 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 2.88/3.29 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.88/3.29 , clause( 20916, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.88/3.29 Y, X ) ) ] )
% 2.88/3.29 , clause( 20917, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.88/3.29 Y, X ) ) ] )
% 2.88/3.29 , clause( 20918, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 2.88/3.29 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20919, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.88/3.29 , Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 2.88/3.29 , clause( 20920, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.88/3.29 Y, X ) ) ] )
% 2.88/3.29 , clause( 20921, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.88/3.29 Y, X ) ) ] )
% 2.88/3.29 , clause( 20922, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20923, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.88/3.29 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20924, [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 2.88/3.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) )
% 2.88/3.29 , =( Y, Z ) ] )
% 2.88/3.29 , clause( 20925, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T
% 2.88/3.29 ), 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubst'( X, Z, T ), 'c_Lambda_Osubst'(
% 2.88/3.29 Y, Z, T ) ) ) ] )
% 2.88/3.29 , clause( 20926, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 2.88/3.29 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20927, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20928, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y )
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20929, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OAbs'(
% 2.88/3.29 Z ) ) ) ] )
% 2.88/3.29 , clause( 20930, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y )
% 2.88/3.29 ) ), =( X, Y ) ] )
% 2.88/3.29 , clause( 20931, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OApp'( Y,
% 2.88/3.29 Z ) ) ) ] )
% 2.88/3.29 , clause( 20932, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ),
% 2.88/3.29 Y ) ] )
% 2.88/3.29 , clause( 20933, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 2.88/3.29 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 2.88/3.29 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20934, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 2.88/3.29 , clause( 20935, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 2.88/3.29 , clause( 20936, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 2.88/3.29 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20937, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20938, [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 2.88/3.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20939, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.88/3.29 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20940, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 2.88/3.29 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20941, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 2.88/3.29 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.88/3.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20942, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 2.88/3.29 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20943, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20944, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20945, [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20946, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.88/3.29 ) ) ) ] )
% 2.88/3.29 , clause( 20947, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.88/3.29 ) ) ) ] )
% 2.88/3.29 , clause( 20948, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 2.88/3.29 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20949, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X )
% 2.88/3.29 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20950, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 2.88/3.29 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20951, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OApp'( Y,
% 2.88/3.29 Z ) ) ) ] )
% 2.88/3.29 , clause( 20952, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'(
% 2.88/3.29 Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20953, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 2.88/3.29 ) ), =( X, Y ) ] )
% 2.88/3.29 , clause( 20954, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 2.88/3.29 'c_InductTermi_OIT'( X ) ) ] )
% 2.88/3.29 , clause( 20955, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 2.88/3.29 ) ) ] )
% 2.88/3.29 , clause( 20956, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 2.88/3.29 , clause( 20957, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 2.88/3.29 , clause( 20958, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 2.88/3.29 ) ) ) ] )
% 2.88/3.29 , clause( 20959, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 2.88/3.29 ) ) ) ] )
% 2.88/3.29 , clause( 20960, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 2.88/3.29 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 2.88/3.29 , clause( 20961, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat'
% 2.88/3.29 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 2.88/3.29 , clause( 20962, [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ),
% 2.88/3.29 'c_Lambda_Osubst'( T, Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ] )
% 2.88/3.29 , clause( 20963, [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'(
% 2.88/3.29 Y ), 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat'
% 2.88/3.29 ) ) ) ] )
% 2.88/3.29 , clause( 20964, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 2.88/3.29 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 2.88/3.29 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20965, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 2.88/3.29 'tc_nat' ), 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ),
% 2.88/3.29 =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ] )
% 2.88/3.29 , clause( 20966, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 2.88/3.29 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ] )
% 2.88/3.29 , clause( 20967, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 2.88/3.29 ), 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20968, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 2.88/3.29 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20969, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 2.88/3.29 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20970, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 2.88/3.29 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20971, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.88/3.29 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 2.88/3.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 2.88/3.29 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20972, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 2.88/3.29 'c_InductTermi_OIT'( X ) ) ] )
% 2.88/3.29 , clause( 20973, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ]
% 2.88/3.29 )
% 2.88/3.29 , clause( 20974, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ),
% 2.88/3.29 X ) ] )
% 2.88/3.29 , clause( 20975, [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'(
% 2.88/3.29 Y ), 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat'
% 2.88/3.29 ) ) ) ] )
% 2.88/3.29 , clause( 20976, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ),
% 2.88/3.29 ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20977, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20978, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20979, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 2.88/3.29 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 2.88/3.29 , clause( 20980, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ),
% 2.88/3.29 'c_Lambda_OdB_OAbs'( Y ) ), ~( 'c_Lambda_Obeta'( X, Y ) ) ] )
% 2.88/3.29 , clause( 20981, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OVar'(
% 2.88/3.29 Z ) ) ) ] )
% 2.88/3.29 , clause( 20982, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 2.88/3.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20983, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.88/3.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20984, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 2.88/3.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.88/3.29 , clause( 20985, [ 'c_InductTermi_OIT'( 'v_ra' ) ] )
% 2.88/3.29 , clause( 20986, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra',
% 2.88/3.29 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 2.88/3.29 , clause( 20987, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'(
% 2.88/3.29 'c_Lambda_Osubst'( 'v_ra', 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' ) ),
% 2.96/3.30 'c_Suc'( 'v_ja' ) ) ) ) ) ] )
% 2.96/3.30 , clause( 20988, [
% 2.96/3.30 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 2.96/3.30 )
% 2.96/3.30 , clause( 20989, [
% 2.96/3.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 2.96/3.30 )
% 2.96/3.30 , clause( 20990, [
% 2.96/3.30 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' ) ]
% 2.96/3.30 )
% 2.96/3.30 , clause( 20991, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.96/3.30 'tc_nat' ) ] )
% 2.96/3.30 , clause( 20992, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.96/3.30 'tc_nat' ) ] )
% 2.96/3.30 , clause( 20993, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 2.96/3.30 'tc_nat' ) ] )
% 2.96/3.30 , clause( 20994, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 2.96/3.30 'tc_nat' ) ] )
% 2.96/3.30 , clause( 20995, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 2.96/3.30 'tc_nat' ) ] )
% 2.96/3.30 , clause( 20996, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 2.96/3.30 ] )
% 2.96/3.30 , clause( 20997, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' )
% 2.96/3.30 ] )
% 2.96/3.30 , clause( 20998, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' )
% 2.96/3.30 ] )
% 2.96/3.30 , clause( 20999, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 2.96/3.30 ] )
% 2.96/3.30 , clause( 21000, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 2.96/3.30 )
% 2.96/3.30 , clause( 21001, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 2.96/3.30 ] )
% 2.96/3.30 , clause( 21002, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 2.96/3.30 )
% 2.96/3.30 , clause( 21003, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ]
% 2.96/3.30 )
% 2.96/3.30 , clause( 21004, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 2.96/3.30 )
% 2.96/3.30 , clause( 21005, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ]
% 2.96/3.30 )
% 2.96/3.30 , clause( 21006, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 2.96/3.30 , clause( 21007, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ]
% 2.96/3.30 )
% 2.96/3.30 , clause( 21008, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 2.96/3.30 , clause( 21009, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 2.96/3.30 , clause( 21010, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 2.96/3.30 , clause( 21011, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 2.96/3.30 , clause( 21012, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 2.96/3.30 , clause( 21013, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 2.96/3.30 , clause( 21014, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 2.96/3.30 , clause( 21015, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 2.96/3.30 , clause( 21016, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 2.96/3.30 , clause( 21017, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 2.96/3.30 ] ).
% 2.96/3.30
% 2.96/3.30
% 2.96/3.30
% 2.96/3.30 subsumption(
% 2.96/3.30 clause( 571, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 2.96/3.30 'c_InductTermi_OIT'( X ) ) ] )
% 2.96/3.30 , clause( 20972, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 2.96/3.30 'c_InductTermi_OIT'( X ) ) ] )
% 2.96/3.30 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 2.96/3.30 1 )] ) ).
% 2.96/3.30
% 2.96/3.30
% 2.96/3.30 subsumption(
% 2.96/3.30 clause( 581, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra',
% 2.96/3.30 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 2.96/3.30 , clause( 20986, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra',
% 2.96/3.30 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 2.96/3.30 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.96/3.30 )] ) ).
% 2.96/3.30
% 2.96/3.30
% 2.96/3.30 subsumption(
% 2.96/3.30 clause( 582, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'(
% 2.96/3.30 'c_Lambda_Osubst'( 'v_ra', 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' ) ),
% 2.96/3.30 'c_Suc'( 'v_ja' ) ) ) ) ) ] )
% 2.96/3.30 , clause( 20987, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'(
% 2.96/3.30 'c_Lambda_Osubst'( 'v_ra', 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' ) ),
% 2.96/3.30 'c_Suc'( 'v_ja' ) ) ) ) ) ] )
% 2.96/3.30 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.96/3.30
% 2.96/3.30
% 2.96/3.30 resolution(
% 2.96/3.30 clause( 23234, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'(
% 2.96/3.30 'c_Lambda_Osubst'( 'v_ra', 'c_Lambda_OdB_OVar'( X ), Y ) ) ) ] )
% 2.96/3.30 , clause( 571, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 2.96/3.30 'c_InductTermi_OIT'( X ) ) ] )
% 2.96/3.30 , 1, clause( 581, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_ra',
% 2.96/3.30 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 2.96/3.30 , 0, substitution( 0, [ :=( X, 'c_Lambda_Osubst'( 'v_ra',
% 2.96/3.30 'c_Lambda_OdB_OVar'( X ), Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y
% 2.96/3.30 , Y )] )).
% 2.96/3.30
% 2.96/3.30
% 2.96/3.30 subsumption(
% 2.96/3.30 clause( 1053, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'(
% 2.96/3.30 'v_ra', 'c_Lambda_OdB_OVar'( X ), Y ) ) ) ] )
% 2.96/3.30 , clause( 23234, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'(
% 2.96/3.30 'c_Lambda_Osubst'( 'v_ra', 'c_Lambda_OdB_OVar'( X ), Y ) ) ) ] )
% 2.96/3.30 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.96/3.30 )] ) ).
% 2.96/3.30
% 2.96/3.30
% 2.96/3.30 resolution(
% 2.96/3.30 clause( 23235, [] )
% 2.96/3.30 , clause( 582, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'(
% 2.96/3.30 'c_Lambda_Osubst'( 'v_ra', 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' ) ),
% 2.96/3.30 'c_Suc'( 'v_ja' ) ) ) ) ) ] )
% 2.96/3.30 , 0, clause( 1053, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'(
% 2.96/3.30 'c_Lambda_Osubst'( 'v_ra', 'c_Lambda_OdB_OVar'( X ), Y ) ) ) ] )
% 2.96/3.30 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_Suc'( 'v_ia' ) ),
% 2.96/3.30 :=( Y, 'c_Suc'( 'v_ja' ) )] )).
% 2.96/3.30
% 2.96/3.30
% 2.96/3.30 subsumption(
% 2.96/3.30 clause( 20261, [] )
% 2.96/3.30 , clause( 23235, [] )
% 2.96/3.30 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.96/3.30
% 2.96/3.30
% 2.96/3.30 end.
% 2.96/3.30
% 2.96/3.30 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.96/3.30
% 2.96/3.30 Memory use:
% 2.96/3.30
% 2.96/3.30 space for terms: 486239
% 2.96/3.30 space for clauses: 1040578
% 2.96/3.30
% 2.96/3.30
% 2.96/3.30 clauses generated: 87653
% 2.96/3.30 clauses kept: 20262
% 2.96/3.30 clauses selected: 674
% 2.96/3.30 clauses deleted: 1016
% 2.96/3.30 clauses inuse deleted: 13
% 2.96/3.30
% 2.96/3.30 subsentry: 457653
% 2.96/3.30 literals s-matched: 305703
% 2.96/3.30 literals matched: 296511
% 2.96/3.30 full subsumption: 166681
% 2.96/3.30
% 2.96/3.30 checksum: -917317368
% 2.96/3.30
% 2.96/3.30
% 2.96/3.30 Bliksem ended
%------------------------------------------------------------------------------