TSTP Solution File: SWV824-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV824-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:28:41 EDT 2022
% Result : Unsatisfiable 181.31s 181.78s
% Output : Refutation 181.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV824-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n004.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 : Wed Jun 15 04:15:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.88/1.29 *** allocated 10000 integers for termspace/termends
% 0.88/1.29 *** allocated 10000 integers for clauses
% 0.88/1.29 *** allocated 10000 integers for justifications
% 0.88/1.29 *** allocated 15000 integers for termspace/termends
% 0.88/1.29 Bliksem 1.12
% 0.88/1.29
% 0.88/1.29
% 0.88/1.29 Automatic Strategy Selection
% 0.88/1.29
% 0.88/1.29 Clauses:
% 0.88/1.29 [
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.88/1.29 , X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.88/1.29 ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.88/1.29 X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.88/1.29 X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 X, T, 'tc_nat' ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.88/1.29 X ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 0.88/1.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.29 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.29 , T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 0.88/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.88/1.29 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.88/1.29 , X ), T, X ), W, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 0.88/1.29 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 0.88/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.88/1.29 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.88/1.29 , X ), W, X ), X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.88/1.29 ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.88/1.29 ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.88/1.29 Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.88/1.29 ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.88/1.29 ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.88/1.29 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.88/1.29 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 0.88/1.29 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.88/1.29 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.88/1.29 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.88/1.29 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.88/1.29 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.88/1.29 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.88/1.29 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ), =( X
% 0.88/1.29 , Z ) ],
% 0.88/1.29 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ), =( Y
% 0.88/1.29 , T ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.88/1.29 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.88/1.29 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.88/1.29 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.88/1.29 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z,
% 0.88/1.29 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.88/1.29 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.29 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.88/1.29 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.88/1.29 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.88/1.29 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.88/1.29 , X ), W, X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.88/1.29 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.88/1.29 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 0.88/1.29 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.88/1.29 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.88/1.29 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 0.88/1.29 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.88/1.29 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.88/1.29 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.88/1.29 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 0.88/1.29 'tc_nat' ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ),
% 0.88/1.29 T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.88/1.29 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 T, X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.29 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.88/1.29 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.88/1.29 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.29 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.88/1.29 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 Z, X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.88/1.29 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.88/1.29 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.29 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.29 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.88/1.29 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.88/1.29 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.88/1.29 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z,
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.88/1.29 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.88/1.29 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.88/1.29 ), Y ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.29 'tc_nat' ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ) ],
% 0.88/1.29 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSemi'( Y, Z ) ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.88/1.29 ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.88/1.29 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.88/1.29 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 0.88/1.29 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.29 , Y, X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.88/1.29 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.88/1.29 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.29 , Y, X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.29 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.29 , T, X ), X ), T, X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.29 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 0.88/1.29 X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 0.88/1.29 ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 0.88/1.29 X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.29 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.29 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.88/1.29 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.29 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.88/1.29 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.29 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.88/1.29 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.29 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.88/1.29 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 0.88/1.29 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.29 ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , Z, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.29 , T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , Z, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.88/1.29 ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.29 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.29 , T, X ), X ), T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.88/1.29 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.88/1.29 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.88/1.29 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.88/1.29 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.88/1.29 T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.88/1.29 T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.88/1.29 T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.88/1.29 T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.88/1.29 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.88/1.29 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ =( 'c_Orderings_Oord__class_Omin'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.88/1.29 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.88/1.29 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.88/1.29 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.88/1.29 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.88/1.29 , X ), W, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.88/1.29 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.88/1.29 W, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.88/1.29 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.88/1.29 , X ), T, X ), W, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.88/1.29 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.88/1.29 W, X ), X ) ) ],
% 0.88/1.29 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 0.88/1.29 'c_lessequals'( T, X, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 0.88/1.29 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.88/1.29 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.88/1.29 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.88/1.29 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 0.88/1.29 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 0.88/1.29 Z, X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.29 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.29 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.29 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.88/1.29 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.88/1.29 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.88/1.29 X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.88/1.29 X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.88/1.29 X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.88/1.29 X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.88/1.29 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.88/1.29 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 0.88/1.29 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), 'c_HOL_Oord__class_Oless'( Y, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Y, 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.29 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.88/1.29 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.88/1.29 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.88/1.29 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.88/1.29 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 0.88/1.29 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.88/1.29 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.88/1.29 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), Y,
% 0.88/1.29 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.29 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.29 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.29 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.29 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.88/1.29 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.88/1.29 , T ), =( X, Z ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.88/1.29 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.88/1.29 , T ), =( X, Z ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.88/1.29 ), X ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.88/1.29 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 0.88/1.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 0.88/1.29 X ), Z, X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.88/1.29 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 0.88/1.29 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.29 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.29 ), 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.88/1.29 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' )
% 0.88/1.29 ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.88/1.29 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.88/1.29 ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.29 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 0.88/1.29 X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 0.88/1.29 ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 0.88/1.29 X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ),
% 0.88/1.29 T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.88/1.29 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.88/1.29 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OBODY'( Z ) ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.88/1.29 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.88/1.29 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.29 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.88/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.88/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.29 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.29 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.88/1.29 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.88/1.29 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.88/1.29 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.29 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.29 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 0.88/1.29 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.88/1.29 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.88/1.29 ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.88/1.29 , T, X ) ) ), =( Y, Z ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.88/1.29 , T, X ) ) ), =( Z, T ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.88/1.29 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.88/1.29 X ), X ), Y ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ) ), =( Y, Z ) ],
% 0.88/1.29 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.29 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.88/1.29 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 0.88/1.29 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 X ), T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 0.88/1.29 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , Z, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.29 , T, X ), X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.88/1.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T ), ~(
% 0.88/1.29 'c_Natural_Oevalc'( Y, U, T ) ), ~( 'c_Natural_Oevalc'( X, Z, U ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.29 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.29 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.29 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, T
% 0.88/1.29 , X ), Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( T, Y
% 0.88/1.29 , X ), Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 0.88/1.29 Z, Y, X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.29 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.88/1.29 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.88/1.29 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 0.88/1.29 ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.88/1.29 ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.29 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 ) ), =( Y, Z ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 ) ), =( Y, Z ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 X ), X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.88/1.29 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z
% 0.88/1.29 , T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( T
% 0.88/1.29 , Z, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.88/1.29 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 0.88/1.29 ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 0.88/1.29 , 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.88/1.29 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.88/1.29 ) ],
% 0.88/1.29 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.29 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.29 , Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.29 , Y, X ) ) ],
% 0.88/1.29 [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 0.88/1.29 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ) ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ) ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ), 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat'
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', X, X ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.88/1.29 ), =( Z, Y ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.29 ) ],
% 0.88/1.29 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 0.88/1.29 , Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.88/1.29 [ =( X, Y ), ~( 'c_Natural_Oevalc'( Z, T, X ) ), ~( 'c_Natural_Oevalc'(
% 0.88/1.29 Z, T, Y ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.88/1.29 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.88/1.29 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.88/1.29 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.88/1.29 ) ],
% 0.88/1.29 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.88/1.29 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.88/1.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.88/1.29 X ), Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.88/1.29 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.88/1.29 ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.88/1.29 X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.88/1.29 ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.88/1.29 X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.88/1.29 ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.88/1.29 ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 0.88/1.29 ), X, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.88/1.29 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.88/1.29 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.29 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.88/1.29 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.88/1.29 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.88/1.29 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.88/1.29 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.88/1.29 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.88/1.29 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.29 ) ), X, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.29 ) ), X, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 0.88/1.29 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.88/1.29 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.88/1.29 ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.88/1.29 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.29 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.29 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.88/1.29 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 0.88/1.29 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 0.88/1.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.88/1.29 , Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.88/1.29 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.29 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.88/1.29 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.88/1.29 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.29 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.88/1.29 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.29 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.88/1.29 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.88/1.29 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.88/1.29 ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.29 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.29 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 0.88/1.29 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 0.88/1.29 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 0.88/1.29 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.88/1.29 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.29 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.88/1.29 X ) ) ), =( Z, T ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.88/1.29 X ) ) ), =( Z, T ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.88/1.29 X ) ) ), =( Y, T ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X
% 0.88/1.29 ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y
% 0.88/1.29 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.29 , T, X ), X ), T, X ) ) ],
% 0.88/1.29 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 0.88/1.29 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.29 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.88/1.29 X ), X ) ) ],
% 0.88/1.29 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OBODY'( Y ) ) ), =( X, Y )
% 0.88/1.29 ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 0.88/1.29 Z, Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.88/1.29 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 0.88/1.29 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.88/1.29 X ), X ), X ) ],
% 0.88/1.29 [ =( 'c_Orderings_Oord__class_Omax'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.88/1.29 [ =( 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), X, 'tc_nat' ), X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.88/1.29 X ), X ), Y ) ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 0.88/1.29 'tc_nat' ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.88/1.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.88/1.29 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.88/1.29 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.88/1.29 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.88/1.29 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 0.88/1.29 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.29 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.88/1.29 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.88/1.29 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 X ), T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.88/1.29 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OBODY'( X ) ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X
% 0.88/1.29 ), T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y
% 0.88/1.29 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.88/1.29 ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.88/1.29 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.88/1.29 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.88/1.29 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.88/1.29 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.88/1.29 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.88/1.29 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.88/1.29 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 0.88/1.29 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.88/1.29 ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.88/1.29 ],
% 0.88/1.29 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.88/1.29 , X, 'tc_nat' ), X ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.88/1.29 ), 'tc_nat' ), X ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.29 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.88/1.29 ), X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.88/1.29 ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.88/1.29 ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.88/1.29 ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.88/1.29 ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.88/1.29 ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.88/1.29 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ =( 'c_Fun_Oid'( X, Y ), X ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.88/1.29 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.88/1.29 ), Y ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.88/1.29 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.29 [ =( X, Y ), ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', Y, X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.88/1.29 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Y, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.88/1.29 X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Z, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Z, T, X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.88/1.29 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.88/1.29 X ), X ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 0.88/1.29 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.29 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.88/1.29 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.29 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.29 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.88/1.29 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 0.88/1.29 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.29 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 0.88/1.29 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 0.88/1.29 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.88/1.29 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.88/1.29 , 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 0.88/1.29 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.88/1.29 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.88/1.29 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.88/1.29 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.29 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.29 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.88/1.29 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , Y, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.29 , T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.29 , T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.29 , Y, X ), X ) ) ],
% 0.88/1.29 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.88/1.29 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.88/1.29 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.88/1.29 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.88/1.29 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.88/1.29 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.88/1.29 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 0.88/1.29 ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.88/1.29 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.88/1.29 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.88/1.29 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.88/1.29 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.88/1.29 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.88/1.29 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.29 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.29 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.88/1.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.88/1.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.29 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.29 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.29 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.88/1.29 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.29 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.29 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.88/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.29 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 0.88/1.29 , X ) ) ],
% 0.88/1.29 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.29 T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.88/1.29 X ), Z, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.29 T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.88/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.29 X ), T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.88/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.29 T, X ), X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.88/1.29 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.29 X ), T, X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.88/1.29 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.88/1.29 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.29 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OSemi'( X, Y ) ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.29 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.29 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.88/1.29 'c_lessequals'( Z, Y, X ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.29 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.88/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.29 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 0.88/1.29 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 0.88/1.29 ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_Natural_Oevaln'( X, Y, Z, T ), ~( 'c_lessequals'( U, Z, 'tc_nat' )
% 0.88/1.29 ), ~( 'c_Natural_Oevaln'( X, Y, U, T ) ) ],
% 0.88/1.29 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 0.88/1.29 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.88/1.29 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.88/1.29 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 0.88/1.29 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.29 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.29 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.29 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', X, Y, X ) ],
% 0.88/1.29 [ 'c_Natural_Oevaln'( X, Y, 'c_Suc'( Z ), T ), ~( 'c_Natural_Oevaln'( X
% 0.88/1.29 , Y, Z, T ) ) ],
% 0.88/1.29 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.88/1.29 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.88/1.29 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.88/1.29 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.88/1.29 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.88/1.29 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ =( 'c_Fun_Oid'( 'v_x', 't_a' ), 'v_x' ) ],
% 0.88/1.29 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.88/1.29 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.88/1.29 [ 'c_Natural_Oevaln'( X, Y,
% 0.88/1.29 'c_Natural_Osko__Natural__Xevaln__max2__1__1'( Z, X, T, Y, U, W ), W ),
% 0.88/1.29 ~( 'c_Natural_Oevaln'( X, Y, V0, W ) ), ~( 'c_Natural_Oevaln'( Z, T, V1,
% 0.88/1.29 U ) ) ],
% 0.88/1.29 [ 'c_Natural_Oevaln'( X, Y,
% 0.88/1.29 'c_Natural_Osko__Natural__Xevaln__max2__1__1'( X, Z, Y, T, U, W ), U ),
% 0.88/1.29 ~( 'c_Natural_Oevaln'( Z, T, V0, W ) ), ~( 'c_Natural_Oevaln'( X, Y, V1,
% 0.88/1.29 U ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.88/1.29 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.88/1.29 [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.88/1.29 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) )
% 0.88/1.29 ],
% 0.88/1.29 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 0.88/1.29 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 0.88/1.29 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T, U ), ~(
% 0.88/1.29 'c_Natural_Oevaln'( Y, W, T, U ) ), ~( 'c_Natural_Oevaln'( X, Z, T, W ) )
% 0.88/1.29 ],
% 0.88/1.29 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.88/1.29 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 0.88/1.29 , X, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 0.88/1.29 'tc_nat' ) ],
% 0.88/1.29 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.88/1.29 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.88/1.29 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.29 [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.88/1.29 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat' ) ) )
% 0.88/1.29 ],
% 0.88/1.29 [ =( X, 'c_Suc'( 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1'( Y
% 0.88/1.29 , X, Z, T ) ) ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OBODY'( Y ), Z, X, T
% 0.88/1.29 ) ) ],
% 0.88/1.29 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.29 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.88/1.29 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.88/1.29 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.88/1.29 [ =( X, Y ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', Y, Z, X ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.88/1.29 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.88/1.29 [ 'c_Natural_Oevalc'( X, Y, Z ), ~( 'c_Natural_Oevaln'( X, Y, T, Z ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ 'c_Natural_Oevalc'( X, Y, Z ), ~( 'c_Natural_Oevaln'( X, Y, T, Z ) ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ 'v_fun1'( 'v_x', 'v_xa' ) ],
% 0.88/1.29 [ 'c_Natural_Oevaln'( 'v_com', 'v_xa', 'v_n', 'v_xb' ) ],
% 0.88/1.29 [ ~( 'v_fun2'( 'v_x', 'v_xb' ) ) ],
% 0.88/1.29 [ 'v_fun2'( X, Y ), ~( 'c_Natural_Oevaln'( 'v_com', Z, 'c_Suc'( 'v_n' )
% 0.88/1.29 , Y ) ), ~( 'v_fun1'( X, Z ) ) ],
% 0.88/1.29 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.88/1.29 ],
% 0.88/1.29 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.88/1.29 ) ],
% 0.88/1.29 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.88/1.29 ],
% 0.88/1.29 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 0.88/1.29 ,
% 0.88/1.29 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.88/1.29 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.88/1.29 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.88/1.29 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.93/1.48 [ 'class_Orderings_Oorder'( 'tc_nat' ) ]
% 0.93/1.48 ] .
% 0.93/1.48
% 0.93/1.48
% 0.93/1.48 percentage equality = 0.239708, percentage horn = 0.895695
% 0.93/1.48 This is a problem with some equality
% 0.93/1.48
% 0.93/1.48
% 0.93/1.48
% 0.93/1.48 Options Used:
% 0.93/1.48
% 0.93/1.48 useres = 1
% 0.93/1.48 useparamod = 1
% 0.93/1.48 useeqrefl = 1
% 0.93/1.48 useeqfact = 1
% 0.93/1.48 usefactor = 1
% 0.93/1.48 usesimpsplitting = 0
% 0.93/1.48 usesimpdemod = 5
% 0.93/1.48 usesimpres = 3
% 0.93/1.48
% 0.93/1.48 resimpinuse = 1000
% 0.93/1.48 resimpclauses = 20000
% 0.93/1.48 substype = eqrewr
% 0.93/1.48 backwardsubs = 1
% 0.93/1.48 selectoldest = 5
% 0.93/1.48
% 0.93/1.48 litorderings [0] = split
% 0.93/1.48 litorderings [1] = extend the termordering, first sorting on arguments
% 0.93/1.48
% 0.93/1.48 termordering = kbo
% 0.93/1.48
% 0.93/1.48 litapriori = 0
% 0.93/1.48 termapriori = 1
% 0.93/1.48 litaposteriori = 0
% 0.93/1.48 termaposteriori = 0
% 0.93/1.48 demodaposteriori = 0
% 0.93/1.48 ordereqreflfact = 0
% 0.93/1.48
% 0.93/1.48 litselect = negord
% 0.93/1.48
% 0.93/1.48 maxweight = 15
% 0.93/1.48 maxdepth = 30000
% 0.93/1.48 maxlength = 115
% 0.93/1.48 maxnrvars = 195
% 0.93/1.48 excuselevel = 1
% 0.93/1.48 increasemaxweight = 1
% 0.93/1.48
% 0.93/1.48 maxselected = 10000000
% 0.93/1.48 maxnrclauses = 10000000
% 0.93/1.48
% 0.93/1.48 showgenerated = 0
% 0.93/1.48 showkept = 0
% 0.93/1.48 showselected = 0
% 0.93/1.48 showdeleted = 0
% 0.93/1.48 showresimp = 1
% 0.93/1.48 showstatus = 2000
% 0.93/1.48
% 0.93/1.48 prologoutput = 1
% 0.93/1.48 nrgoals = 5000000
% 0.93/1.48 totalproof = 1
% 0.93/1.48
% 0.93/1.48 Symbols occurring in the translation:
% 0.93/1.48
% 0.93/1.48 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.93/1.48 . [1, 2] (w:1, o:117, a:1, s:1, b:0),
% 0.93/1.48 ! [4, 1] (w:0, o:69, a:1, s:1, b:0),
% 0.93/1.48 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.93/1.48 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.93/1.48 'c_Suc' [40, 1] (w:1, o:74, a:1, s:1, b:0),
% 0.93/1.48 'tc_nat' [42, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.93/1.48 'c_HOL_Ominus__class_Ominus' [43, 3] (w:1, o:146, a:1, s:1, b:0),
% 0.93/1.48 'c_lessequals' [44, 3] (w:1, o:147, a:1, s:1, b:0),
% 0.93/1.48 'class_Ring__and__Field_Oordered__ring__strict' [46, 1] (w:1, o:79
% 0.93/1.48 , a:1, s:1, b:0),
% 0.93/1.48 'c_HOL_Ozero__class_Ozero' [47, 1] (w:1, o:80, a:1, s:1, b:0),
% 0.93/1.48 'c_HOL_Otimes__class_Otimes' [49, 3] (w:1, o:148, a:1, s:1, b:0),
% 0.93/1.48 'c_HOL_Oplus__class_Oplus' [51, 3] (w:1, o:150, a:1, s:1, b:0),
% 0.93/1.48 'class_Divides_Osemiring__div' [52, 1] (w:1, o:82, a:1, s:1, b:0),
% 0.93/1.48 'c_Divides_Odiv__class_Omod' [54, 3] (w:1, o:151, a:1, s:1, b:0),
% 0.93/1.48 'class_Ring__and__Field_Ocomm__semiring__1' [55, 1] (w:1, o:83, a:1
% 0.93/1.48 , s:1, b:0),
% 0.93/1.48 'class_OrderedGroup_Ocomm__monoid__add' [57, 1] (w:1, o:84, a:1, s:1
% 0.93/1.48 , b:0),
% 0.93/1.48 'c_HOL_Oord__class_Oless' [61, 3] (w:1, o:149, a:1, s:1, b:0),
% 0.93/1.48 'class_Ring__and__Field_Oidom' [62, 1] (w:1, o:85, a:1, s:1, b:0),
% 0.93/1.48 'class_Int_Onumber__ring' [63, 1] (w:1, o:86, a:1, s:1, b:0),
% 0.93/1.48 'class_Ring__and__Field_Oordered__semiring__strict' [64, 1] (w:1, o:
% 0.93/1.48 87, a:1, s:1, b:0),
% 0.93/1.48 'class_Ring__and__Field_Opordered__ring' [65, 1] (w:1, o:92, a:1, s:1
% 0.93/1.48 , b:0),
% 0.93/1.48 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [71, 1]
% 0.93/1.48 (w:1, o:93, a:1, s:1, b:0),
% 0.93/1.48 'class_Orderings_Olinorder' [72, 1] (w:1, o:94, a:1, s:1, b:0),
% 0.93/1.48 'c_Orderings_Oord__class_Omax' [73, 3] (w:1, o:153, a:1, s:1, b:0),
% 0.93/1.48 'c_Orderings_Oord__class_Omin' [74, 3] (w:1, o:154, a:1, s:1, b:0),
% 0.93/1.48 'c_Com_Ocom_OSemi' [77, 2] (w:1, o:142, a:1, s:1, b:0),
% 11.24/11.62 'class_Ring__and__Field_Oring' [80, 1] (w:1, o:95, a:1, s:1, b:0),
% 11.24/11.62 'class_OrderedGroup_Opordered__ab__group__add' [82, 1] (w:1, o:96, a:
% 11.24/11.62 1, s:1, b:0),
% 11.24/11.62 'class_OrderedGroup_Olordered__ab__group__add' [83, 1] (w:1, o:97, a:
% 11.24/11.62 1, s:1, b:0),
% 11.24/11.62 'class_OrderedGroup_Ogroup__add' [84, 1] (w:1, o:98, a:1, s:1, b:0),
% 11.24/11.62
% 11.24/11.62 'c_Com_Ocom_OBODY' [86, 1] (w:1, o:99, a:1, s:1, b:0),
% 11.24/11.62 'class_OrderedGroup_Opordered__ab__semigroup__add' [87, 1] (w:1, o:
% 11.24/11.62 100, a:1, s:1, b:0),
% 11.24/11.62 'class_OrderedGroup_Opordered__comm__monoid__add' [88, 1] (w:1, o:101
% 11.24/11.62 , a:1, s:1, b:0),
% 11.24/11.62 'class_Orderings_Opreorder' [89, 1] (w:1, o:103, a:1, s:1, b:0),
% 11.24/11.62 'class_Orderings_Oorder' [90, 1] (w:1, o:102, a:1, s:1, b:0),
% 11.24/11.62 'class_OrderedGroup_Oab__group__add' [91, 1] (w:1, o:104, a:1, s:1
% 11.24/11.62 , b:0),
% 11.24/11.62 'class_OrderedGroup_Oab__semigroup__add' [92, 1] (w:1, o:105, a:1, s:
% 11.24/11.62 1, b:0),
% 11.24/11.62 'class_Ring__and__Field_Oordered__semiring' [93, 1] (w:1, o:88, a:1
% 11.24/11.62 , s:1, b:0),
% 11.24/11.62 'class_Ring__and__Field_Oring__no__zero__divisors' [94, 1] (w:1, o:
% 11.24/11.62 106, a:1, s:1, b:0),
% 11.24/11.62 'class_Ring__and__Field_Ono__zero__divisors' [95, 1] (w:1, o:78, a:1
% 11.24/11.62 , s:1, b:0),
% 11.24/11.62 'class_Ring__and__Field_Oordered__idom' [98, 1] (w:1, o:89, a:1, s:1
% 11.24/11.62 , b:0),
% 11.24/11.62 'class_Ring__and__Field_Omult__zero' [104, 1] (w:1, o:75, a:1, s:1
% 11.24/11.62 , b:0),
% 11.24/11.62 'class_Divides_Oring__div' [105, 1] (w:1, o:81, a:1, s:1, b:0),
% 11.24/11.62 'c_Natural_Oevalc' [113, 3] (w:1, o:152, a:1, s:1, b:0),
% 11.24/11.62 'class_Ring__and__Field_Osemiring' [115, 1] (w:1, o:107, a:1, s:1, b:
% 11.24/11.62 0),
% 11.24/11.62 'class_Ring__and__Field_Opordered__cancel__semiring' [116, 1] (w:1
% 11.24/11.62 , o:108, a:1, s:1, b:0),
% 11.24/11.62 'c_Com_Ocom_OSKIP' [117, 0] (w:1, o:55, a:1, s:1, b:0),
% 11.24/11.62 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [120, 1]
% 11.24/11.62 (w:1, o:109, a:1, s:1, b:0),
% 11.24/11.62 'class_OrderedGroup_Oab__semigroup__idem__mult' [121, 1] (w:1, o:110
% 11.24/11.62 , a:1, s:1, b:0),
% 11.24/11.62 'class_Ring__and__Field_Oordered__semidom' [123, 1] (w:1, o:90, a:1
% 11.24/11.62 , s:1, b:0),
% 11.24/11.62 'class_Ring__and__Field_Omult__mono' [126, 1] (w:1, o:76, a:1, s:1
% 11.24/11.62 , b:0),
% 11.24/11.62 'class_Ring__and__Field_Omult__mono1' [127, 1] (w:1, o:77, a:1, s:1
% 11.24/11.62 , b:0),
% 11.24/11.62 'class_OrderedGroup_Ocancel__ab__semigroup__add' [128, 1] (w:1, o:111
% 11.24/11.62 , a:1, s:1, b:0),
% 11.24/11.62 'class_OrderedGroup_Ocancel__semigroup__add' [129, 1] (w:1, o:112, a:
% 11.24/11.62 1, s:1, b:0),
% 11.24/11.62 'class_Ring__and__Field_Oordered__comm__semiring__strict' [131, 1]
% 11.24/11.62 (w:1, o:91, a:1, s:1, b:0),
% 11.24/11.62 'class_Ring__and__Field_Opordered__semiring' [132, 1] (w:1, o:113, a:
% 11.24/11.62 1, s:1, b:0),
% 11.24/11.62 'class_OrderedGroup_Omonoid__add' [133, 1] (w:1, o:114, a:1, s:1, b:0
% 11.24/11.62 ),
% 11.24/11.62 'c_Fun_Oid' [134, 2] (w:1, o:143, a:1, s:1, b:0),
% 11.24/11.62 'class_OrderedGroup_Oab__semigroup__mult' [135, 1] (w:1, o:115, a:1
% 11.24/11.62 , s:1, b:0),
% 11.24/11.62 'class_Ring__and__Field_Ocomm__semiring' [136, 1] (w:1, o:116, a:1
% 11.24/11.62 , s:1, b:0),
% 11.24/11.62 'c_Natural_Oevaln' [137, 4] (w:1, o:155, a:1, s:1, b:0),
% 11.24/11.62 'v_x' [140, 0] (w:1, o:58, a:1, s:1, b:0),
% 11.24/11.62 't_a' [141, 0] (w:1, o:59, a:1, s:1, b:0),
% 11.24/11.62 'c_Natural_Osko__Natural__Xevaln__max2__1__1' [146, 6] (w:1, o:157
% 11.24/11.62 , a:1, s:1, b:0),
% 11.24/11.62 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1' [150, 4] (w:1
% 11.24/11.62 , o:156, a:1, s:1, b:0),
% 11.24/11.62 'v_xa' [151, 0] (w:1, o:64, a:1, s:1, b:0),
% 11.24/11.62 'v_fun1' [152, 2] (w:1, o:144, a:1, s:1, b:0),
% 11.24/11.62 'v_com' [153, 0] (w:1, o:65, a:1, s:1, b:0),
% 11.24/11.62 'v_n' [154, 0] (w:1, o:66, a:1, s:1, b:0),
% 11.24/11.62 'v_xb' [155, 0] (w:1, o:67, a:1, s:1, b:0),
% 11.24/11.62 'v_fun2' [156, 2] (w:1, o:145, a:1, s:1, b:0).
% 11.24/11.62
% 11.24/11.62
% 11.24/11.62 Starting Search:
% 11.24/11.62
% 11.24/11.62 Resimplifying inuse:
% 11.24/11.62 Done
% 11.24/11.62
% 11.24/11.62
% 11.24/11.62 Intermediate Status:
% 11.24/11.62 Generated: 3873
% 11.24/11.62 Kept: 2004
% 11.24/11.62 Inuse: 117
% 11.24/11.62 Deleted: 0
% 11.24/11.62 Deletedinuse: 0
% 11.24/11.62
% 11.24/11.62 Resimplifying inuse:
% 11.24/11.62 Done
% 11.24/11.62
% 11.24/11.62 Resimplifying inuse:
% 11.24/11.62 Done
% 11.24/11.62
% 11.24/11.62
% 11.24/11.62 Intermediate Status:
% 11.24/11.62 Generated: 10093
% 11.24/11.62 Kept: 4016
% 11.24/11.62 Inuse: 199
% 11.24/11.62 Deleted: 1
% 11.24/11.62 Deletedinuse: 1
% 11.24/11.62
% 11.24/11.62 Resimplifying inuse:
% 11.24/11.62 Done
% 11.24/11.62
% 11.24/11.62
% 11.24/11.62 Intermediate Status:
% 11.24/11.62 Generated: 15105
% 11.24/11.62 Kept: 6079
% 11.24/11.62 Inuse: 237
% 11.24/11.62 Deleted: 2
% 11.24/11.62 Deletedinuse: 1
% 11.24/11.62
% 11.24/11.62 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 19649
% 39.13/39.55 Kept: 8114
% 39.13/39.55 Inuse: 303
% 39.13/39.55 Deleted: 4
% 39.13/39.55 Deletedinuse: 1
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 25793
% 39.13/39.55 Kept: 10130
% 39.13/39.55 Inuse: 374
% 39.13/39.55 Deleted: 12
% 39.13/39.55 Deletedinuse: 1
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 33374
% 39.13/39.55 Kept: 12146
% 39.13/39.55 Inuse: 447
% 39.13/39.55 Deleted: 15
% 39.13/39.55 Deletedinuse: 1
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 46590
% 39.13/39.55 Kept: 14658
% 39.13/39.55 Inuse: 516
% 39.13/39.55 Deleted: 17
% 39.13/39.55 Deletedinuse: 2
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 59515
% 39.13/39.55 Kept: 16812
% 39.13/39.55 Inuse: 530
% 39.13/39.55 Deleted: 17
% 39.13/39.55 Deletedinuse: 2
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 68700
% 39.13/39.55 Kept: 18868
% 39.13/39.55 Inuse: 561
% 39.13/39.55 Deleted: 17
% 39.13/39.55 Deletedinuse: 2
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying clauses:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 74285
% 39.13/39.55 Kept: 20895
% 39.13/39.55 Inuse: 572
% 39.13/39.55 Deleted: 480
% 39.13/39.55 Deletedinuse: 2
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 81860
% 39.13/39.55 Kept: 22914
% 39.13/39.55 Inuse: 577
% 39.13/39.55 Deleted: 480
% 39.13/39.55 Deletedinuse: 2
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 87155
% 39.13/39.55 Kept: 24936
% 39.13/39.55 Inuse: 603
% 39.13/39.55 Deleted: 480
% 39.13/39.55 Deletedinuse: 2
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 98973
% 39.13/39.55 Kept: 27063
% 39.13/39.55 Inuse: 616
% 39.13/39.55 Deleted: 480
% 39.13/39.55 Deletedinuse: 2
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 114918
% 39.13/39.55 Kept: 29195
% 39.13/39.55 Inuse: 631
% 39.13/39.55 Deleted: 480
% 39.13/39.55 Deletedinuse: 2
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 126825
% 39.13/39.55 Kept: 31199
% 39.13/39.55 Inuse: 656
% 39.13/39.55 Deleted: 492
% 39.13/39.55 Deletedinuse: 14
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 139433
% 39.13/39.55 Kept: 33227
% 39.13/39.55 Inuse: 680
% 39.13/39.55 Deleted: 492
% 39.13/39.55 Deletedinuse: 14
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 147272
% 39.13/39.55 Kept: 35289
% 39.13/39.55 Inuse: 715
% 39.13/39.55 Deleted: 493
% 39.13/39.55 Deletedinuse: 14
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 155938
% 39.13/39.55 Kept: 37542
% 39.13/39.55 Inuse: 745
% 39.13/39.55 Deleted: 493
% 39.13/39.55 Deletedinuse: 14
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 181818
% 39.13/39.55 Kept: 40932
% 39.13/39.55 Inuse: 770
% 39.13/39.55 Deleted: 493
% 39.13/39.55 Deletedinuse: 14
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying clauses:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 204135
% 39.13/39.55 Kept: 42958
% 39.13/39.55 Inuse: 782
% 39.13/39.55 Deleted: 1049
% 39.13/39.55 Deletedinuse: 14
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 215737
% 39.13/39.55 Kept: 44976
% 39.13/39.55 Inuse: 816
% 39.13/39.55 Deleted: 1050
% 39.13/39.55 Deletedinuse: 15
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 227491
% 39.13/39.55 Kept: 46996
% 39.13/39.55 Inuse: 857
% 39.13/39.55 Deleted: 1050
% 39.13/39.55 Deletedinuse: 15
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 237471
% 39.13/39.55 Kept: 48997
% 39.13/39.55 Inuse: 878
% 39.13/39.55 Deleted: 1053
% 39.13/39.55 Deletedinuse: 18
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 248514
% 39.13/39.55 Kept: 51016
% 39.13/39.55 Inuse: 916
% 39.13/39.55 Deleted: 1054
% 39.13/39.55 Deletedinuse: 18
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 259435
% 39.13/39.55 Kept: 53138
% 39.13/39.55 Inuse: 954
% 39.13/39.55 Deleted: 1060
% 39.13/39.55 Deletedinuse: 19
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 281348
% 39.13/39.55 Kept: 55212
% 39.13/39.55 Inuse: 967
% 39.13/39.55 Deleted: 1068
% 39.13/39.55 Deletedinuse: 20
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 39.13/39.55 Done
% 39.13/39.55
% 39.13/39.55
% 39.13/39.55 Intermediate Status:
% 39.13/39.55 Generated: 303961
% 39.13/39.55 Kept: 57852
% 39.13/39.55 Inuse: 981
% 39.13/39.55 Deleted: 1070
% 39.13/39.55 Deletedinuse: 21
% 39.13/39.55
% 39.13/39.55 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 313986
% 93.78/94.27 Kept: 59859
% 93.78/94.27 Inuse: 1008
% 93.78/94.27 Deleted: 1073
% 93.78/94.27 Deletedinuse: 22
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying clauses:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 323936
% 93.78/94.27 Kept: 62049
% 93.78/94.27 Inuse: 1033
% 93.78/94.27 Deleted: 2245
% 93.78/94.27 Deletedinuse: 23
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 336272
% 93.78/94.27 Kept: 64102
% 93.78/94.27 Inuse: 1073
% 93.78/94.27 Deleted: 2246
% 93.78/94.27 Deletedinuse: 24
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 352658
% 93.78/94.27 Kept: 66491
% 93.78/94.27 Inuse: 1093
% 93.78/94.27 Deleted: 2246
% 93.78/94.27 Deletedinuse: 24
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 371254
% 93.78/94.27 Kept: 69343
% 93.78/94.27 Inuse: 1100
% 93.78/94.27 Deleted: 2254
% 93.78/94.27 Deletedinuse: 29
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 385423
% 93.78/94.27 Kept: 71391
% 93.78/94.27 Inuse: 1120
% 93.78/94.27 Deleted: 2254
% 93.78/94.27 Deletedinuse: 29
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 396833
% 93.78/94.27 Kept: 73599
% 93.78/94.27 Inuse: 1160
% 93.78/94.27 Deleted: 2254
% 93.78/94.27 Deletedinuse: 29
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 414431
% 93.78/94.27 Kept: 77971
% 93.78/94.27 Inuse: 1204
% 93.78/94.27 Deleted: 2255
% 93.78/94.27 Deletedinuse: 29
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 443317
% 93.78/94.27 Kept: 80496
% 93.78/94.27 Inuse: 1224
% 93.78/94.27 Deleted: 2255
% 93.78/94.27 Deletedinuse: 29
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying clauses:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 469380
% 93.78/94.27 Kept: 83514
% 93.78/94.27 Inuse: 1234
% 93.78/94.27 Deleted: 2944
% 93.78/94.27 Deletedinuse: 29
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 487738
% 93.78/94.27 Kept: 88207
% 93.78/94.27 Inuse: 1240
% 93.78/94.27 Deleted: 2946
% 93.78/94.27 Deletedinuse: 31
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 510274
% 93.78/94.27 Kept: 90282
% 93.78/94.27 Inuse: 1249
% 93.78/94.27 Deleted: 2946
% 93.78/94.27 Deletedinuse: 31
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 519429
% 93.78/94.27 Kept: 92326
% 93.78/94.27 Inuse: 1267
% 93.78/94.27 Deleted: 2946
% 93.78/94.27 Deletedinuse: 31
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 528581
% 93.78/94.27 Kept: 94361
% 93.78/94.27 Inuse: 1288
% 93.78/94.27 Deleted: 2946
% 93.78/94.27 Deletedinuse: 31
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 535448
% 93.78/94.27 Kept: 96655
% 93.78/94.27 Inuse: 1304
% 93.78/94.27 Deleted: 2956
% 93.78/94.27 Deletedinuse: 31
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 543671
% 93.78/94.27 Kept: 98787
% 93.78/94.27 Inuse: 1324
% 93.78/94.27 Deleted: 2961
% 93.78/94.27 Deletedinuse: 31
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 553349
% 93.78/94.27 Kept: 100803
% 93.78/94.27 Inuse: 1345
% 93.78/94.27 Deleted: 2961
% 93.78/94.27 Deletedinuse: 31
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 559103
% 93.78/94.27 Kept: 103490
% 93.78/94.27 Inuse: 1347
% 93.78/94.27 Deleted: 2961
% 93.78/94.27 Deletedinuse: 31
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying clauses:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 578264
% 93.78/94.27 Kept: 108330
% 93.78/94.27 Inuse: 1364
% 93.78/94.27 Deleted: 3775
% 93.78/94.27 Deletedinuse: 31
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 591320
% 93.78/94.27 Kept: 110390
% 93.78/94.27 Inuse: 1389
% 93.78/94.27 Deleted: 3775
% 93.78/94.27 Deletedinuse: 31
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 609700
% 93.78/94.27 Kept: 112421
% 93.78/94.27 Inuse: 1414
% 93.78/94.27 Deleted: 3775
% 93.78/94.27 Deletedinuse: 31
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 624743
% 93.78/94.27 Kept: 114437
% 93.78/94.27 Inuse: 1438
% 93.78/94.27 Deleted: 3777
% 93.78/94.27 Deletedinuse: 33
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 633625
% 93.78/94.27 Kept: 116586
% 93.78/94.27 Inuse: 1454
% 93.78/94.27 Deleted: 3779
% 93.78/94.27 Deletedinuse: 35
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27 Resimplifying inuse:
% 93.78/94.27 Done
% 93.78/94.27
% 93.78/94.27
% 93.78/94.27 Intermediate Status:
% 93.78/94.27 Generated: 671167
% 93.78/94.27 Kept: 119988
% 93.78/94.27 Inuse: 1474
% 181.31/181.78 Deleted: 3779
% 181.31/181.78 Deletedinuse: 35
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 702816
% 181.31/181.78 Kept: 122005
% 181.31/181.78 Inuse: 1483
% 181.31/181.78 Deleted: 3779
% 181.31/181.78 Deletedinuse: 35
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 720223
% 181.31/181.78 Kept: 124379
% 181.31/181.78 Inuse: 1489
% 181.31/181.78 Deleted: 3779
% 181.31/181.78 Deletedinuse: 35
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying clauses:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 738732
% 181.31/181.78 Kept: 126737
% 181.31/181.78 Inuse: 1504
% 181.31/181.78 Deleted: 4422
% 181.31/181.78 Deletedinuse: 35
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 767142
% 181.31/181.78 Kept: 129370
% 181.31/181.78 Inuse: 1514
% 181.31/181.78 Deleted: 4422
% 181.31/181.78 Deletedinuse: 35
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 794870
% 181.31/181.78 Kept: 131478
% 181.31/181.78 Inuse: 1524
% 181.31/181.78 Deleted: 4422
% 181.31/181.78 Deletedinuse: 35
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 815379
% 181.31/181.78 Kept: 133586
% 181.31/181.78 Inuse: 1544
% 181.31/181.78 Deleted: 4422
% 181.31/181.78 Deletedinuse: 35
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 836560
% 181.31/181.78 Kept: 136761
% 181.31/181.78 Inuse: 1559
% 181.31/181.78 Deleted: 4422
% 181.31/181.78 Deletedinuse: 35
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 850284
% 181.31/181.78 Kept: 138894
% 181.31/181.78 Inuse: 1589
% 181.31/181.78 Deleted: 4422
% 181.31/181.78 Deletedinuse: 35
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 862118
% 181.31/181.78 Kept: 140900
% 181.31/181.78 Inuse: 1612
% 181.31/181.78 Deleted: 4422
% 181.31/181.78 Deletedinuse: 35
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 871664
% 181.31/181.78 Kept: 142983
% 181.31/181.78 Inuse: 1629
% 181.31/181.78 Deleted: 4424
% 181.31/181.78 Deletedinuse: 37
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying clauses:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 882913
% 181.31/181.78 Kept: 145249
% 181.31/181.78 Inuse: 1649
% 181.31/181.78 Deleted: 4577
% 181.31/181.78 Deletedinuse: 37
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 895551
% 181.31/181.78 Kept: 147272
% 181.31/181.78 Inuse: 1673
% 181.31/181.78 Deleted: 4577
% 181.31/181.78 Deletedinuse: 37
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 913818
% 181.31/181.78 Kept: 149280
% 181.31/181.78 Inuse: 1697
% 181.31/181.78 Deleted: 4577
% 181.31/181.78 Deletedinuse: 37
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 928814
% 181.31/181.78 Kept: 151382
% 181.31/181.78 Inuse: 1729
% 181.31/181.78 Deleted: 4577
% 181.31/181.78 Deletedinuse: 37
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 947437
% 181.31/181.78 Kept: 153713
% 181.31/181.78 Inuse: 1759
% 181.31/181.78 Deleted: 4577
% 181.31/181.78 Deletedinuse: 37
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 962597
% 181.31/181.78 Kept: 155761
% 181.31/181.78 Inuse: 1784
% 181.31/181.78 Deleted: 4577
% 181.31/181.78 Deletedinuse: 37
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 974617
% 181.31/181.78 Kept: 157785
% 181.31/181.78 Inuse: 1804
% 181.31/181.78 Deleted: 4577
% 181.31/181.78 Deletedinuse: 37
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 986434
% 181.31/181.78 Kept: 159867
% 181.31/181.78 Inuse: 1824
% 181.31/181.78 Deleted: 4577
% 181.31/181.78 Deletedinuse: 37
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 999814
% 181.31/181.78 Kept: 161891
% 181.31/181.78 Inuse: 1847
% 181.31/181.78 Deleted: 4577
% 181.31/181.78 Deletedinuse: 37
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1015461
% 181.31/181.78 Kept: 164313
% 181.31/181.78 Inuse: 1869
% 181.31/181.78 Deleted: 4578
% 181.31/181.78 Deletedinuse: 38
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying clauses:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1031335
% 181.31/181.78 Kept: 166505
% 181.31/181.78 Inuse: 1894
% 181.31/181.78 Deleted: 5019
% 181.31/181.78 Deletedinuse: 38
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1044636
% 181.31/181.78 Kept: 168507
% 181.31/181.78 Inuse: 1917
% 181.31/181.78 Deleted: 5019
% 181.31/181.78 Deletedinuse: 38
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1070938
% 181.31/181.78 Kept: 172932
% 181.31/181.78 Inuse: 1934
% 181.31/181.78 Deleted: 5019
% 181.31/181.78 Deletedinuse: 38
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1082568
% 181.31/181.78 Kept: 175031
% 181.31/181.78 Inuse: 1954
% 181.31/181.78 Deleted: 5019
% 181.31/181.78 Deletedinuse: 38
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1093718
% 181.31/181.78 Kept: 177328
% 181.31/181.78 Inuse: 1974
% 181.31/181.78 Deleted: 5019
% 181.31/181.78 Deletedinuse: 38
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1105840
% 181.31/181.78 Kept: 179367
% 181.31/181.78 Inuse: 1995
% 181.31/181.78 Deleted: 5020
% 181.31/181.78 Deletedinuse: 39
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1128549
% 181.31/181.78 Kept: 182527
% 181.31/181.78 Inuse: 2009
% 181.31/181.78 Deleted: 5021
% 181.31/181.78 Deletedinuse: 40
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1147304
% 181.31/181.78 Kept: 186456
% 181.31/181.78 Inuse: 2014
% 181.31/181.78 Deleted: 5021
% 181.31/181.78 Deletedinuse: 40
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying clauses:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1165944
% 181.31/181.78 Kept: 188847
% 181.31/181.78 Inuse: 2019
% 181.31/181.78 Deleted: 5407
% 181.31/181.78 Deletedinuse: 40
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1178041
% 181.31/181.78 Kept: 190863
% 181.31/181.78 Inuse: 2040
% 181.31/181.78 Deleted: 5407
% 181.31/181.78 Deletedinuse: 40
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1194157
% 181.31/181.78 Kept: 192886
% 181.31/181.78 Inuse: 2068
% 181.31/181.78 Deleted: 5411
% 181.31/181.78 Deletedinuse: 44
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1211427
% 181.31/181.78 Kept: 194901
% 181.31/181.78 Inuse: 2092
% 181.31/181.78 Deleted: 5411
% 181.31/181.78 Deletedinuse: 44
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1223654
% 181.31/181.78 Kept: 196966
% 181.31/181.78 Inuse: 2109
% 181.31/181.78 Deleted: 5411
% 181.31/181.78 Deletedinuse: 44
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1256560
% 181.31/181.78 Kept: 200230
% 181.31/181.78 Inuse: 2139
% 181.31/181.78 Deleted: 5411
% 181.31/181.78 Deletedinuse: 44
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1270180
% 181.31/181.78 Kept: 202237
% 181.31/181.78 Inuse: 2160
% 181.31/181.78 Deleted: 5411
% 181.31/181.78 Deletedinuse: 44
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1303484
% 181.31/181.78 Kept: 207366
% 181.31/181.78 Inuse: 2184
% 181.31/181.78 Deleted: 5411
% 181.31/181.78 Deletedinuse: 44
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying clauses:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1334375
% 181.31/181.78 Kept: 218916
% 181.31/181.78 Inuse: 2203
% 181.31/181.78 Deleted: 6468
% 181.31/181.78 Deletedinuse: 44
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1350894
% 181.31/181.78 Kept: 220936
% 181.31/181.78 Inuse: 2227
% 181.31/181.78 Deleted: 6468
% 181.31/181.78 Deletedinuse: 44
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1365800
% 181.31/181.78 Kept: 222944
% 181.31/181.78 Inuse: 2235
% 181.31/181.78 Deleted: 6468
% 181.31/181.78 Deletedinuse: 44
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1390812
% 181.31/181.78 Kept: 226436
% 181.31/181.78 Inuse: 2259
% 181.31/181.78 Deleted: 6469
% 181.31/181.78 Deletedinuse: 45
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying clauses:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1404680
% 181.31/181.78 Kept: 228494
% 181.31/181.78 Inuse: 2281
% 181.31/181.78 Deleted: 6749
% 181.31/181.78 Deletedinuse: 45
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Intermediate Status:
% 181.31/181.78 Generated: 1425643
% 181.31/181.78 Kept: 238541
% 181.31/181.78 Inuse: 2282
% 181.31/181.78 Deleted: 6749
% 181.31/181.78 Deletedinuse: 45
% 181.31/181.78
% 181.31/181.78 Resimplifying inuse:
% 181.31/181.78 Done
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 Bliksems!, er is een bewijs:
% 181.31/181.78 % SZS status Unsatisfiable
% 181.31/181.78 % SZS output start Refutation
% 181.31/181.78
% 181.31/181.78 clause( 11, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 181.31/181.78 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 181.31/181.78 , ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 48, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 96, [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 162, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 181.31/181.78 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 181.31/181.78 , T ), =( X, Z ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 195, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 494, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 181.31/181.78 'tc_nat' ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 502, [ 'c_Natural_Oevaln'( X, Y, Z, T ), ~( 'c_lessequals'( U, Z,
% 181.31/181.78 'tc_nat' ) ), ~( 'c_Natural_Oevaln'( X, Y, U, T ) ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 505, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 515, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 536, [ 'v_fun1'( 'v_x', 'v_xa' ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 537, [ 'c_Natural_Oevaln'( 'v_com', 'v_xa', 'v_n', 'v_xb' ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 538, [ ~( 'v_fun2'( 'v_x', 'v_xb' ) ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 539, [ 'v_fun2'( X, Y ), ~( 'c_Natural_Oevaln'( 'v_com', Z, 'c_Suc'(
% 181.31/181.78 'v_n' ), Y ) ), ~( 'v_fun1'( X, Z ) ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 565, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 615, [ ~( =( X, Y ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat'
% 181.31/181.78 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 181.31/181.78 , Z ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 618, [ ~( =( X, Y ) ), =( Y, X ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 905, [ 'v_fun1'( 'v_x', X ), ~( =( X, 'v_xa' ) ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 6291, [ ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 6294, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 9354, [ 'c_lessequals'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 9372, [ ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), X, 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 15773, [ ~( =( 'c_Suc'( X ), 'c_Suc'( 'v_xa' ) ) ), 'v_fun1'( 'v_x'
% 181.31/181.78 , X ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 50967, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 201372, [ 'c_Natural_Oevaln'( 'v_com', 'v_xa', X, 'v_xb' ), ~(
% 181.31/181.78 'c_lessequals'( 'v_n', X, 'tc_nat' ) ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 201482, [ 'c_Natural_Oevaln'( 'v_com', 'v_xa', X, 'v_xb' ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, 'v_n', 'tc_nat' ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 238595, [ 'v_fun2'( X, 'v_xb' ), ~( 'v_fun1'( X, 'v_xa' ) ) ] )
% 181.31/181.78 .
% 181.31/181.78 clause( 238951, [] )
% 181.31/181.78 .
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 % SZS output end Refutation
% 181.31/181.78 found a proof!
% 181.31/181.78
% 181.31/181.78 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 181.31/181.78
% 181.31/181.78 initialclauses(
% 181.31/181.78 [ clause( 238953, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y,
% 181.31/181.78 'tc_nat' ), 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ),
% 181.31/181.78 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238954, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ] )
% 181.31/181.78 , clause( 238955, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 238956, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 238957, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 181.31/181.78 Y, X ) ) ] )
% 181.31/181.78 , clause( 238958, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 181.31/181.78 X ) ) ] )
% 181.31/181.78 , clause( 238959, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238960, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 X, T, 'tc_nat' ) ] )
% 181.31/181.78 , clause( 238961, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 181.31/181.78 Y, X ) ) ] )
% 181.31/181.78 , clause( 238962, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 181.31/181.78 , clause( 238963, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 181.31/181.78 , clause( 238964, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 181.31/181.78 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238965, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 181.31/181.78 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238966, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 181.31/181.78 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 181.31/181.78 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 238967, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X )
% 181.31/181.78 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238968, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) )
% 181.31/181.78 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238969, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 181.31/181.78 , T, X ), X ) ) ] )
% 181.31/181.78 , clause( 238970, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ] )
% 181.31/181.78 , clause( 238971, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W, X ) ) ] )
% 181.31/181.78 , clause( 238972, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 181.31/181.78 , X ), W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X
% 181.31/181.78 ), X ) ) ] )
% 181.31/181.78 , clause( 238973, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 T, 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ), W, X ), X ) ) ] )
% 181.31/181.78 , clause( 238974, [ 'c_HOL_Oord__class_Oless'( X,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238975, [ 'c_HOL_Oord__class_Oless'( X,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238976, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 181.31/181.78 Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238977, [ 'c_HOL_Oord__class_Oless'( X,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238978, [ 'c_HOL_Oord__class_Oless'( X,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238979, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238980, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238981, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238982, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238983, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 181.31/181.78 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 181.31/181.78 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 181.31/181.78 , clause( 238984, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 181.31/181.78 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 181.31/181.78 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 181.31/181.78 , clause( 238985, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 181.31/181.78 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 181.31/181.78 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 238986, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 181.31/181.78 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 181.31/181.78 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 238987, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z
% 181.31/181.78 , T ) ) ), =( X, Z ) ] )
% 181.31/181.78 , clause( 238988, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z
% 181.31/181.78 , T ) ) ), =( Y, T ) ] )
% 181.31/181.78 , clause( 238989, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ] )
% 181.31/181.78 , clause( 238990, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ] )
% 181.31/181.78 , clause( 238991, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 238992, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 238993, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 238994, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X
% 181.31/181.78 , Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 238995, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 181.31/181.78 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 181.31/181.78 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238996, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 238997, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 238998, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 238999, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 181.31/181.78 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 181.31/181.78 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 181.31/181.78 , clause( 239000, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 181.31/181.78 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 181.31/181.78 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 181.31/181.78 , X ), W, X ) ) ] )
% 181.31/181.78 , clause( 239001, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 181.31/181.78 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239002, [ 'c_HOL_Oord__class_Oless'( X,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), T, 'tc_nat' ), U,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 181.31/181.78 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 181.31/181.78 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239003, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 181.31/181.78 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 181.31/181.78 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239004, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 181.31/181.78 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 181.31/181.78 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239005, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239006, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239007, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239008, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ] )
% 181.31/181.78 , clause( 239009, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ] )
% 181.31/181.78 , clause( 239010, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239011, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239012, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239013, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 181.31/181.78 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239014, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239015, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 181.31/181.78 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239016, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 181.31/181.78 ), =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z
% 181.31/181.78 , X ), T, X ), 'c_Orderings_Oord__class_Omin'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 181.31/181.78 , T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239017, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T,
% 181.31/181.78 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239018, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( Y
% 181.31/181.78 , Z, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239019, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 181.31/181.78 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X
% 181.31/181.78 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239020, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239021, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 181.31/181.78 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239022, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239023, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ),
% 181.31/181.78 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239024, [ =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 181.31/181.78 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239025, [ =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 181.31/181.78 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239026, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 181.31/181.78 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 181.31/181.78 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 181.31/181.78 , clause( 239027, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 181.31/181.78 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 181.31/181.78 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 181.31/181.78 , clause( 239028, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239029, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 181.31/181.78 , clause( 239030, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239031, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 181.31/181.78 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239032, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 181.31/181.78 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 181.31/181.78 , 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 181.31/181.78 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 181.31/181.78 X, T, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239033, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 181.31/181.78 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 181.31/181.78 , 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 181.31/181.78 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239034, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 181.31/181.78 ), Y ) ] )
% 181.31/181.78 , clause( 239035, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 181.31/181.78 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239036, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 181.31/181.78 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239037, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSemi'( Y, Z
% 181.31/181.78 ) ) ) ] )
% 181.31/181.78 , clause( 239038, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 181.31/181.78 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239039, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 181.31/181.78 X ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 181.31/181.78 ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239040, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' )
% 181.31/181.78 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239041, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239042, [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239043, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 Z, Y, X ) ) ] )
% 181.31/181.78 , clause( 239044, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239045, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 181.31/181.78 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239046, [ =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239047, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 181.31/181.78 ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239048, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 Z, Y, X ) ) ] )
% 181.31/181.78 , clause( 239049, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239050, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 181.31/181.78 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 181.31/181.78 , T, X ), X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239051, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 181.31/181.78 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239052, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 181.31/181.78 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239053, [ ~( 'class_Orderings_Oorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 181.31/181.78 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 181.31/181.78 , clause( 239054, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 181.31/181.78 X ) ) ] )
% 181.31/181.78 , clause( 239055, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239056, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 181.31/181.78 X ) ) ] )
% 181.31/181.78 , clause( 239057, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 181.31/181.78 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239058, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 181.31/181.78 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239059, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 181.31/181.78 ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239060, [ =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat'
% 181.31/181.78 ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239061, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 181.31/181.78 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239062, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 181.31/181.78 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239063, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 181.31/181.78 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239064, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 181.31/181.78 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239065, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 181.31/181.78 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239066, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 181.31/181.78 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239067, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 181.31/181.78 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239068, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239069, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239070, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 181.31/181.78 , Z, X ), X ) ) ] )
% 181.31/181.78 , clause( 239071, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 181.31/181.78 , T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239072, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 181.31/181.78 , Z, X ), X ) ) ] )
% 181.31/181.78 , clause( 239073, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239074, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239075, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239076, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239077, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239078, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 181.31/181.78 , clause( 239079, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 181.31/181.78 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 181.31/181.78 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239080, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 181.31/181.78 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 181.31/181.78 , T, X ), X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239081, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ] )
% 181.31/181.78 , clause( 239082, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 181.31/181.78 ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239083, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239084, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 181.31/181.78 , clause( 239085, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 181.31/181.78 , clause( 239086, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X
% 181.31/181.78 ), X ) ) ] )
% 181.31/181.78 , clause( 239087, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X
% 181.31/181.78 ), X ) ) ] )
% 181.31/181.78 , clause( 239088, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 T, X ) ) ] )
% 181.31/181.78 , clause( 239089, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 T, X ) ) ] )
% 181.31/181.78 , clause( 239090, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 T, X ) ) ] )
% 181.31/181.78 , clause( 239091, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 T, X ) ) ] )
% 181.31/181.78 , clause( 239092, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X
% 181.31/181.78 ), X ) ) ] )
% 181.31/181.78 , clause( 239093, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X
% 181.31/181.78 ), X ) ) ] )
% 181.31/181.78 , clause( 239094, [ =( 'c_Orderings_Oord__class_Omin'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239095, [ =( 'c_Orderings_Oord__class_Omin'( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239096, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 181.31/181.78 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239097, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 181.31/181.78 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239098, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239099, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239100, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 181.31/181.78 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239101, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 181.31/181.78 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 181.31/181.78 , X ), W, X ), X ) ) ] )
% 181.31/181.78 , clause( 239102, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 181.31/181.78 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 181.31/181.78 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 181.31/181.78 W, X ), X ) ) ] )
% 181.31/181.78 , clause( 239103, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 181.31/181.78 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 181.31/181.78 , X ), T, X ), W, X ) ) ] )
% 181.31/181.78 , clause( 239104, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 181.31/181.78 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 181.31/181.78 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 181.31/181.78 W, X ), X ) ) ] )
% 181.31/181.78 , clause( 239105, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 181.31/181.78 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239106, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 181.31/181.78 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 181.31/181.78 'tc_nat' ), U ) ] )
% 181.31/181.78 , clause( 239107, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 181.31/181.78 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239108, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ] )
% 181.31/181.78 , clause( 239109, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 181.31/181.78 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239110, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 181.31/181.78 X ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 181.31/181.78 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239111, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) )
% 181.31/181.78 , ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 181.31/181.78 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239112, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239113, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) )
% 181.31/181.78 , ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 181.31/181.78 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239114, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 181.31/181.78 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 181.31/181.78 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 181.31/181.78 Z, X ) ) ] )
% 181.31/181.78 , clause( 239115, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239116, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239117, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239118, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239119, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239120, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 181.31/181.78 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 181.31/181.78 , clause( 239121, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 181.31/181.78 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239122, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 181.31/181.78 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 181.31/181.78 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 181.31/181.78 , clause( 239123, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 181.31/181.78 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 181.31/181.78 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 181.31/181.78 , clause( 239124, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239125, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239126, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 181.31/181.78 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239127, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ),
% 181.31/181.78 Z, X ) ) ] )
% 181.31/181.78 , clause( 239128, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ),
% 181.31/181.78 Z, X ) ) ] )
% 181.31/181.78 , clause( 239129, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 T, X ) ) ] )
% 181.31/181.78 , clause( 239130, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 Z, X ) ) ] )
% 181.31/181.78 , clause( 239131, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 T, X ) ) ] )
% 181.31/181.78 , clause( 239132, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 Z, X ) ) ] )
% 181.31/181.78 , clause( 239133, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ),
% 181.31/181.78 Z, X ) ) ] )
% 181.31/181.78 , clause( 239134, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ),
% 181.31/181.78 Z, X ) ) ] )
% 181.31/181.78 , clause( 239135, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239136, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 181.31/181.78 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239137, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Y, T, X
% 181.31/181.78 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( T, Z
% 181.31/181.78 , X ), X ) ) ] )
% 181.31/181.78 , clause( 239138, [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ),
% 181.31/181.78 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239139, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239140, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 181.31/181.78 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239141, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 181.31/181.78 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 181.31/181.78 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239142, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 181.31/181.78 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 181.31/181.78 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239143, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 181.31/181.78 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 181.31/181.78 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 181.31/181.78 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239144, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 181.31/181.78 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239145, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 181.31/181.78 ), Z, 'tc_nat' ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 181.31/181.78 Z ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239146, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( T, Z, X
% 181.31/181.78 ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( T, Y, X
% 181.31/181.78 ), Z, X ) ) ] )
% 181.31/181.78 , clause( 239147, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 181.31/181.78 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 181.31/181.78 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 181.31/181.78 =( Y, T ) ] )
% 181.31/181.78 , clause( 239148, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 181.31/181.78 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 181.31/181.78 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 181.31/181.78 =( Y, T ) ] )
% 181.31/181.78 , clause( 239149, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 181.31/181.78 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 181.31/181.78 , T ), =( X, Z ) ] )
% 181.31/181.78 , clause( 239150, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 181.31/181.78 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 181.31/181.78 , T ), =( X, Z ) ] )
% 181.31/181.78 , clause( 239151, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 181.31/181.78 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239152, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 181.31/181.78 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239153, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), X
% 181.31/181.78 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 181.31/181.78 , clause( 239154, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 181.31/181.78 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 181.31/181.78 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 181.31/181.78 X ), Z, X ) ) ] )
% 181.31/181.78 , clause( 239155, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239156, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat'
% 181.31/181.78 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239157, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 181.31/181.78 , clause( 239158, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 181.31/181.78 , clause( 239159, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 181.31/181.78 , clause( 239160, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 181.31/181.78 , clause( 239161, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 181.31/181.78 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239162, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 181.31/181.78 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239163, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 181.31/181.78 X ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 181.31/181.78 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239164, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 181.31/181.78 X ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239165, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239166, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239167, [ =( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239168, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239169, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 181.31/181.78 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239170, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239171, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y
% 181.31/181.78 , X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239172, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 181.31/181.78 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239173, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 181.31/181.78 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 181.31/181.78 , clause( 239174, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239175, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239176, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239177, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239178, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239179, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239180, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 181.31/181.78 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239181, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 181.31/181.78 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239182, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 181.31/181.78 X ) ) ] )
% 181.31/181.78 , clause( 239183, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239184, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 181.31/181.78 X ) ) ] )
% 181.31/181.78 , clause( 239185, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 181.31/181.78 ), =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z
% 181.31/181.78 , X ), T, X ), 'c_Orderings_Oord__class_Omax'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 181.31/181.78 , T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239186, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OBODY'( Z
% 181.31/181.78 ) ) ) ] )
% 181.31/181.78 , clause( 239187, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'(
% 181.31/181.78 X, Y, 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239188, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 181.31/181.78 , clause( 239189, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 181.31/181.78 'c_lessequals'( Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239190, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 181.31/181.78 , clause( 239191, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239192, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 181.31/181.78 , clause( 239193, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 181.31/181.78 'c_lessequals'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239194, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 181.31/181.78 , clause( 239195, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 181.31/181.78 'c_lessequals'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239196, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 181.31/181.78 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239197, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 181.31/181.78 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239198, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 181.31/181.78 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239199, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 181.31/181.78 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239200, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 181.31/181.78 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239201, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 181.31/181.78 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 181.31/181.78 , clause( 239202, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239203, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239204, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat'
% 181.31/181.78 ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239205, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 181.31/181.78 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239206, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239207, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239208, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 181.31/181.78 , T, X ) ) ), =( Y, Z ) ] )
% 181.31/181.78 , clause( 239209, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 181.31/181.78 , T, X ) ) ), =( Z, T ) ] )
% 181.31/181.78 , clause( 239210, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 181.31/181.78 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ] )
% 181.31/181.78 , clause( 239211, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 181.31/181.78 X ), X ), Y ) ] )
% 181.31/181.78 , clause( 239212, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 181.31/181.78 'tc_nat' ) ), =( Y, Z ) ] )
% 181.31/181.78 , clause( 239213, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 181.31/181.78 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239214, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 181.31/181.78 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 181.31/181.78 , clause( 239215, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239216, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239217, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 181.31/181.78 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239218, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 181.31/181.78 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239219, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239220, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239221, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 181.31/181.78 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239222, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 181.31/181.78 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239223, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 181.31/181.78 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239224, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 181.31/181.78 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239225, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 181.31/181.78 , Z, X ), X ) ) ] )
% 181.31/181.78 , clause( 239226, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 181.31/181.78 , T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239227, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 181.31/181.78 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 181.31/181.78 ) ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239228, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T )
% 181.31/181.78 , ~( 'c_Natural_Oevalc'( Y, U, T ) ), ~( 'c_Natural_Oevalc'( X, Z, U ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239229, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239230, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 Z, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239231, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 X, Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239232, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239233, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239234, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 181.31/181.78 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239235, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 181.31/181.78 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239236, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 181.31/181.78 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239237, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 181.31/181.78 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239238, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ] )
% 181.31/181.78 , clause( 239239, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ] )
% 181.31/181.78 , clause( 239240, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 181.31/181.78 Z, Y, X ) ) ] )
% 181.31/181.78 , clause( 239241, [ =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 181.31/181.78 ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 181.31/181.78 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239242, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 181.31/181.78 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 181.31/181.78 , clause( 239243, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 181.31/181.78 'tc_nat' ), X, 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239244, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 181.31/181.78 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239245, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 181.31/181.78 Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239246, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 181.31/181.78 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239247, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 181.31/181.78 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 181.31/181.78 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 181.31/181.78 , clause( 239248, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 181.31/181.78 ) ), =( Y, Z ) ] )
% 181.31/181.78 , clause( 239249, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 181.31/181.78 ) ), =( Y, Z ) ] )
% 181.31/181.78 , clause( 239250, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 X ), X ) ) ] )
% 181.31/181.78 , clause( 239251, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 X ), X ) ) ] )
% 181.31/181.78 , clause( 239252, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239253, [ =( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239254, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 181.31/181.78 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239255, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 181.31/181.78 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 181.31/181.78 , clause( 239256, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239257, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ] )
% 181.31/181.78 , clause( 239258, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 181.31/181.78 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239259, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 181.31/181.78 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 181.31/181.78 , clause( 239260, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 181.31/181.78 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239261, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 181.31/181.78 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239262, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 181.31/181.78 , X, 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239263, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 181.31/181.78 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239264, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 181.31/181.78 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239265, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 181.31/181.78 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239266, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239267, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239268, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 181.31/181.78 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239269, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 181.31/181.78 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239270, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 181.31/181.78 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239271, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239272, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239273, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X )
% 181.31/181.78 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239274, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 181.31/181.78 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239275, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 181.31/181.78 'c_lessequals'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239276, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239277, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239278, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 181.31/181.78 , clause( 239279, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 181.31/181.78 , clause( 239280, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 181.31/181.78 , clause( 239281, [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X
% 181.31/181.78 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 181.31/181.78 , clause( 239282, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ] )
% 181.31/181.78 , clause( 239283, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 181.31/181.78 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239284, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 181.31/181.78 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239285, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239286, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239287, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239288, [ =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ),
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239289, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', X, X ) ] )
% 181.31/181.78 , clause( 239290, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 181.31/181.78 ), =( Z, Y ) ] )
% 181.31/181.78 , clause( 239291, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239292, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239293, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 181.31/181.78 , clause( 239294, [ =( X, Y ), ~( 'c_Natural_Oevalc'( Z, T, X ) ), ~(
% 181.31/181.78 'c_Natural_Oevalc'( Z, T, Y ) ) ] )
% 181.31/181.78 , clause( 239295, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 181.31/181.78 , clause( 239296, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 181.31/181.78 , clause( 239297, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 181.31/181.78 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239298, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 181.31/181.78 ), =( Z, Y ) ] )
% 181.31/181.78 , clause( 239299, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 181.31/181.78 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239300, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 181.31/181.78 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 181.31/181.78 , clause( 239301, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 181.31/181.78 , clause( 239302, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239303, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 181.31/181.78 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 181.31/181.78 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 181.31/181.78 X ), Z, X ) ) ] )
% 181.31/181.78 , clause( 239304, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239305, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239306, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ] )
% 181.31/181.78 , clause( 239307, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239308, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat'
% 181.31/181.78 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239309, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239310, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239311, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 181.31/181.78 Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239312, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239313, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 181.31/181.78 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239314, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239315, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239316, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239317, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 181.31/181.78 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239318, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239319, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 181.31/181.78 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ) ) ] )
% 181.31/181.78 , clause( 239320, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 181.31/181.78 X ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239321, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 181.31/181.78 X ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239322, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 181.31/181.78 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239323, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239324, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 181.31/181.78 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239325, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 181.31/181.78 ), X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239326, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 181.31/181.78 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239327, [ =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ), ~(
% 181.31/181.78 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239328, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 181.31/181.78 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239329, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 181.31/181.78 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239330, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 181.31/181.78 ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239331, [ =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 181.31/181.78 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239332, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 181.31/181.78 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 181.31/181.78 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239333, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( T, 'c_HOL_Otimes__class_Otimes'( Y, U,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ) ), =( 'c_Divides_Odiv__class_Omod'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239334, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 181.31/181.78 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239335, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239336, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239337, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSKIP' )
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239338, [ ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239339, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 181.31/181.78 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239340, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 181.31/181.78 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 181.31/181.78 , clause( 239341, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 181.31/181.78 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239342, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239343, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239344, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239345, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 181.31/181.78 , clause( 239346, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239347, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239348, [ 'c_HOL_Oord__class_Oless'( X,
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 181.31/181.78 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239349, [ 'c_HOL_Oord__class_Oless'( X,
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 181.31/181.78 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239350, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 181.31/181.78 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 181.31/181.78 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239351, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 181.31/181.78 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239352, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 181.31/181.78 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 181.31/181.78 , clause( 239353, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239354, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239355, [ =( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239356, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239357, [ ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239358, [ ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239359, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 181.31/181.78 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 181.31/181.78 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 181.31/181.78 , Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239360, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239361, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239362, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239363, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239364, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239365, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 181.31/181.78 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239366, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 181.31/181.78 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239367, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y, T,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239368, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 181.31/181.78 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239369, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 181.31/181.78 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239370, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 181.31/181.78 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239371, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 181.31/181.78 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239372, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 181.31/181.78 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 181.31/181.78 , clause( 239373, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 181.31/181.78 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239374, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_Suc'( X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 181.31/181.78 Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239375, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 181.31/181.78 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239376, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 181.31/181.78 , clause( 239377, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 181.31/181.78 , clause( 239378, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 181.31/181.78 , clause( 239379, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 181.31/181.78 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 181.31/181.78 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 181.31/181.78 , clause( 239380, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X
% 181.31/181.78 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 181.31/181.78 , clause( 239381, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) )
% 181.31/181.78 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 Y, T, X ) ) ), =( Z, T ) ] )
% 181.31/181.78 , clause( 239382, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) )
% 181.31/181.78 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 T, Z, X ) ) ), =( Y, T ) ] )
% 181.31/181.78 , clause( 239383, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 181.31/181.78 'tc_nat' ), X, 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239384, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T
% 181.31/181.78 , X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 181.31/181.78 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239385, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239386, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 181.31/181.78 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 181.31/181.78 , T, X ), X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239387, [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 181.31/181.78 'tc_nat' ) ), Y ) ), =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239388, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 181.31/181.78 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239389, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 181.31/181.78 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239390, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239391, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 181.31/181.78 , clause( 239392, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 181.31/181.78 X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239393, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239394, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239395, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239396, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 181.31/181.78 X ), X ) ) ] )
% 181.31/181.78 , clause( 239397, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OBODY'( Y )
% 181.31/181.78 ) ), =( X, Y ) ] )
% 181.31/181.78 , clause( 239398, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 181.31/181.78 Z, Y, X ) ) ] )
% 181.31/181.78 , clause( 239399, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 181.31/181.78 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 181.31/181.78 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 181.31/181.78 X ), X ), X ) ] )
% 181.31/181.78 , clause( 239400, [ =( 'c_Orderings_Oord__class_Omax'( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 181.31/181.78 , clause( 239401, [ =( 'c_Orderings_Oord__class_Omax'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 181.31/181.78 , clause( 239402, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 181.31/181.78 X ), X ), Y ) ] )
% 181.31/181.78 , clause( 239403, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239404, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239405, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 181.31/181.78 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 181.31/181.78 X ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 181.31/181.78 , clause( 239406, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 181.31/181.78 , clause( 239407, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 181.31/181.78 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 181.31/181.78 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239408, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 181.31/181.78 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239409, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239410, [ =( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239411, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 181.31/181.78 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239412, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 181.31/181.78 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239413, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 181.31/181.78 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239414, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 181.31/181.78 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239415, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 181.31/181.78 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239416, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 181.31/181.78 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239417, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 181.31/181.78 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239418, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239419, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 181.31/181.78 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239420, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239421, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 181.31/181.78 , clause( 239422, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 181.31/181.78 , clause( 239423, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239424, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239425, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 181.31/181.78 , clause( 239426, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239427, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 181.31/181.78 , clause( 239428, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239429, [ ~(
% 181.31/181.78 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 181.31/181.78 , clause( 239430, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OBODY'( X ) ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239431, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T
% 181.31/181.78 , X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 181.31/181.78 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239432, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat'
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239433, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239434, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) )
% 181.31/181.78 , 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 181.31/181.78 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239435, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) )
% 181.31/181.78 , 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 181.31/181.78 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239436, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 181.31/181.78 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239437, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 181.31/181.78 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239438, [ =( 'c_Divides_Odiv__class_Omod'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 181.31/181.78 ), Z, 'tc_nat' ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239439, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239440, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239441, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239442, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239443, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239444, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239445, [ =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 181.31/181.78 , clause( 239446, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 181.31/181.78 , clause( 239447, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 181.31/181.78 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239448, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239449, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239450, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239451, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239452, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239453, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 181.31/181.78 , clause( 239454, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 181.31/181.78 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239455, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 181.31/181.78 , clause( 239456, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 181.31/181.78 , clause( 239457, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 181.31/181.78 , clause( 239458, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 181.31/181.78 , clause( 239459, [ =( 'c_Fun_Oid'( X, Y ), X ) ] )
% 181.31/181.78 , clause( 239460, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ) ] )
% 181.31/181.78 , clause( 239461, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 181.31/181.78 , clause( 239462, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 181.31/181.78 ), Y ) ] )
% 181.31/181.78 , clause( 239463, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239464, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 181.31/181.78 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239465, [ =( X, Y ), ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', Y
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239466, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239467, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239468, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 181.31/181.78 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 181.31/181.78 , clause( 239469, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239470, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 181.31/181.78 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239471, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239472, [ 'c_HOL_Oord__class_Oless'( X,
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 181.31/181.78 Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239473, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239474, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239475, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 181.31/181.78 X ), X ) ) ] )
% 181.31/181.78 , clause( 239476, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 Z, T, X ) ) ] )
% 181.31/181.78 , clause( 239477, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 Z, T, X ) ) ] )
% 181.31/181.78 , clause( 239478, [ ~(
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 181.31/181.78 X ), X ) ) ] )
% 181.31/181.78 , clause( 239479, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat'
% 181.31/181.78 ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239480, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239481, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat'
% 181.31/181.78 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239482, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 181.31/181.78 , ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y
% 181.31/181.78 , 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239483, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 181.31/181.78 Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239484, [ ~( 'class_Orderings_Oorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 181.31/181.78 , clause( 239485, [ ~( 'class_Orderings_Oorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 181.31/181.78 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 181.31/181.78 , clause( 239486, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 181.31/181.78 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239487, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239488, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239489, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z
% 181.31/181.78 , Y, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239490, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239491, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 181.31/181.78 Y, X ) ] )
% 181.31/181.78 , clause( 239492, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Y, X ) ] )
% 181.31/181.78 , clause( 239493, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 181.31/181.78 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239494, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239495, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 181.31/181.78 ), 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 181.31/181.78 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ] )
% 181.31/181.78 , clause( 239496, [ =( 'c_Orderings_Oord__class_Omin'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 181.31/181.78 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239497, [ =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 181.31/181.78 , clause( 239498, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 181.31/181.78 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 181.31/181.78 , clause( 239499, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 181.31/181.78 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239500, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 181.31/181.78 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 181.31/181.78 , clause( 239501, [ =( 'c_Divides_Odiv__class_Omod'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), X, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239502, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 181.31/181.78 , clause( 239503, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y
% 181.31/181.78 ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239504, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSKIP' ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239505, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239506, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239507, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239508, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239509, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239510, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239511, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239512, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 181.31/181.78 , Y, X ), X ) ) ] )
% 181.31/181.78 , clause( 239513, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 181.31/181.78 , T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239514, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 181.31/181.78 , T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239515, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 181.31/181.78 , Y, X ), X ) ) ] )
% 181.31/181.78 , clause( 239516, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239517, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239518, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 181.31/181.78 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 181.31/181.78 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ] )
% 181.31/181.78 , clause( 239519, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 181.31/181.78 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 181.31/181.78 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 181.31/181.78 , clause( 239520, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 181.31/181.78 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 181.31/181.78 ~( 'c_lessequals'( U, T, X ) ) ] )
% 181.31/181.78 , clause( 239521, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 181.31/181.78 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 181.31/181.78 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239522, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 181.31/181.78 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 181.31/181.78 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 181.31/181.78 , clause( 239523, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239524, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 181.31/181.78 ) ) ] )
% 181.31/181.78 , clause( 239525, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239526, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 X, 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239527, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 181.31/181.78 , clause( 239528, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239529, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 181.31/181.78 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 181.31/181.78 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239530, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 181.31/181.78 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 181.31/181.78 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 181.31/181.78 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239531, [ ~( 'class_Orderings_Oorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239532, [ ~( 'class_Orderings_Oorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 181.31/181.78 Z, Y ) ] )
% 181.31/181.78 , clause( 239533, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y )
% 181.31/181.78 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239534, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 181.31/181.78 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239535, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y )
% 181.31/181.78 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239536, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239537, [ ~( 'class_Orderings_Oorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239538, [ ~( 'class_Orderings_Oorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239539, [ ~( 'class_Orderings_Oorder'( X ) ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 181.31/181.78 Y, Z ) ] )
% 181.31/181.78 , clause( 239540, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 181.31/181.78 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 181.31/181.78 , clause( 239541, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 181.31/181.78 , clause( 239542, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 181.31/181.78 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239543, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239544, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239545, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 181.31/181.78 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ] )
% 181.31/181.78 , clause( 239546, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239547, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239548, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 181.31/181.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 181.31/181.78 , clause( 239549, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239550, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 181.31/181.78 , X ) ) ] )
% 181.31/181.78 , clause( 239551, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 Z, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239552, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 181.31/181.78 T, X ), Z, X ) ) ] )
% 181.31/181.78 , clause( 239553, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 181.31/181.78 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 Z, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239554, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 181.31/181.78 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 181.31/181.78 , X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239555, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 181.31/181.78 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 181.31/181.78 , T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239556, [ =( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239557, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 181.31/181.78 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 181.31/181.78 , X ), T, X ) ) ] )
% 181.31/181.78 , clause( 239558, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 181.31/181.78 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 181.31/181.78 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239559, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 181.31/181.78 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 181.31/181.78 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239560, [ =( 'c_HOL_Otimes__class_Otimes'(
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 181.31/181.78 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239561, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 181.31/181.78 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239562, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 181.31/181.78 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 181.31/181.78 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 181.31/181.78 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 181.31/181.78 , clause( 239563, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OSemi'( X, Y ) )
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239564, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 181.31/181.78 Y, X ) ) ] )
% 181.31/181.78 , clause( 239565, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 181.31/181.78 Y, X ) ) ] )
% 181.31/181.78 , clause( 239566, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X
% 181.31/181.78 , 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239567, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 181.31/181.78 Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 181.31/181.78 , clause( 239568, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 181.31/181.78 Y, X ) ) ] )
% 181.31/181.78 , clause( 239569, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 181.31/181.78 Y, X ) ) ] )
% 181.31/181.78 , clause( 239570, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' )
% 181.31/181.78 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239571, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 181.31/181.78 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239572, [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) )
% 181.31/181.78 , =( Y, Z ) ] )
% 181.31/181.78 , clause( 239573, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' )
% 181.31/181.78 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239574, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239575, [ 'c_Natural_Oevaln'( X, Y, Z, T ), ~( 'c_lessequals'( U
% 181.31/181.78 , Z, 'tc_nat' ) ), ~( 'c_Natural_Oevaln'( X, Y, U, T ) ) ] )
% 181.31/181.78 , clause( 239576, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 181.31/181.78 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 181.31/181.78 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239577, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 181.31/181.78 , clause( 239578, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 181.31/181.78 , clause( 239579, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239580, [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 181.31/181.78 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239581, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 181.31/181.78 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239582, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' )
% 181.31/181.78 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239583, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239584, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239585, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ) ) ) ] )
% 181.31/181.78 , clause( 239586, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ) ) ) ] )
% 181.31/181.78 , clause( 239587, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', X, Y, X ) ] )
% 181.31/181.78 , clause( 239588, [ 'c_Natural_Oevaln'( X, Y, 'c_Suc'( Z ), T ), ~(
% 181.31/181.78 'c_Natural_Oevaln'( X, Y, Z, T ) ) ] )
% 181.31/181.78 , clause( 239589, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y
% 181.31/181.78 ), 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239590, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X
% 181.31/181.78 ), 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239591, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 181.31/181.78 , ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239592, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'(
% 181.31/181.78 Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239593, [ =( 'c_Fun_Oid'( 'v_x', 't_a' ), 'v_x' ) ] )
% 181.31/181.78 , clause( 239594, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 181.31/181.78 , clause( 239595, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 181.31/181.78 , clause( 239596, [ 'c_Natural_Oevaln'( X, Y,
% 181.31/181.78 'c_Natural_Osko__Natural__Xevaln__max2__1__1'( Z, X, T, Y, U, W ), W ),
% 181.31/181.78 ~( 'c_Natural_Oevaln'( X, Y, V0, W ) ), ~( 'c_Natural_Oevaln'( Z, T, V1,
% 181.31/181.78 U ) ) ] )
% 181.31/181.78 , clause( 239597, [ 'c_Natural_Oevaln'( X, Y,
% 181.31/181.78 'c_Natural_Osko__Natural__Xevaln__max2__1__1'( X, Z, Y, T, U, W ), U ),
% 181.31/181.78 ~( 'c_Natural_Oevaln'( Z, T, V0, W ) ), ~( 'c_Natural_Oevaln'( X, Y, V1,
% 181.31/181.78 U ) ) ] )
% 181.31/181.78 , clause( 239598, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 181.31/181.78 X ) ) ) ] )
% 181.31/181.78 , clause( 239599, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 181.31/181.78 X ) ) ) ] )
% 181.31/181.78 , clause( 239600, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y,
% 181.31/181.78 'tc_nat' ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239601, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ),
% 181.31/181.78 'tc_nat' ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239602, [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ),
% 181.31/181.78 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y,
% 181.31/181.78 'tc_nat' ) ) ) ] )
% 181.31/181.78 , clause( 239603, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 181.31/181.78 'tc_nat' ), 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ),
% 181.31/181.78 =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ] )
% 181.31/181.78 , clause( 239604, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T, U
% 181.31/181.78 ), ~( 'c_Natural_Oevaln'( Y, W, T, U ) ), ~( 'c_Natural_Oevaln'( X, Z, T
% 181.31/181.78 , W ) ) ] )
% 181.31/181.78 , clause( 239605, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y,
% 181.31/181.78 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239606, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' )
% 181.31/181.78 , =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239607, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_lessequals'( 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239608, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 181.31/181.78 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239609, [ =( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 181.31/181.78 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 181.31/181.78 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239610, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239611, [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ),
% 181.31/181.78 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y,
% 181.31/181.78 'tc_nat' ) ) ) ] )
% 181.31/181.78 , clause( 239612, [ =( X, 'c_Suc'(
% 181.31/181.78 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1'( Y, X, Z, T ) ) ),
% 181.31/181.78 ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OBODY'( Y ), Z, X, T ) ) ] )
% 181.31/181.78 , clause( 239613, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' )
% 181.31/181.78 , ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239614, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239615, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239616, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' )
% 181.31/181.78 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239617, [ =( X, Y ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', Y
% 181.31/181.78 , Z, X ) ) ] )
% 181.31/181.78 , clause( 239618, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 181.31/181.78 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239619, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239620, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 181.31/181.78 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239621, [ 'c_Natural_Oevalc'( X, Y, Z ), ~( 'c_Natural_Oevaln'( X
% 181.31/181.78 , Y, T, Z ) ) ] )
% 181.31/181.78 , clause( 239622, [ 'c_Natural_Oevalc'( X, Y, Z ), ~( 'c_Natural_Oevaln'( X
% 181.31/181.78 , Y, T, Z ) ) ] )
% 181.31/181.78 , clause( 239623, [ 'v_fun1'( 'v_x', 'v_xa' ) ] )
% 181.31/181.78 , clause( 239624, [ 'c_Natural_Oevaln'( 'v_com', 'v_xa', 'v_n', 'v_xb' ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239625, [ ~( 'v_fun2'( 'v_x', 'v_xb' ) ) ] )
% 181.31/181.78 , clause( 239626, [ 'v_fun2'( X, Y ), ~( 'c_Natural_Oevaln'( 'v_com', Z,
% 181.31/181.78 'c_Suc'( 'v_n' ), Y ) ), ~( 'v_fun1'( X, Z ) ) ] )
% 181.31/181.78 , clause( 239627, [
% 181.31/181.78 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239628, [
% 181.31/181.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239629, [
% 181.31/181.78 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239630, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 181.31/181.78 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239631, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 181.31/181.78 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239632, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 181.31/181.78 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239633, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 181.31/181.78 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239634, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 181.31/181.78 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239635, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat'
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239636, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat'
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239637, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239638, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat'
% 181.31/181.78 ) ] )
% 181.31/181.78 , clause( 239639, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239640, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 181.31/181.78 ] )
% 181.31/181.78 , clause( 239641, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239642, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239643, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239644, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ]
% 181.31/181.78 )
% 181.31/181.78 , clause( 239645, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239646, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239647, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239648, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239649, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239650, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239651, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239652, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 181.31/181.78 , clause( 239653, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 181.31/181.78 ] ).
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 subsumption(
% 181.31/181.78 clause( 11, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 181.31/181.78 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 181.31/181.78 , ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 238965, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 181.31/181.78 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 181.31/181.78 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 181.31/181.78 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 181.31/181.78 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 181.31/181.78 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 subsumption(
% 181.31/181.78 clause( 48, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239014, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 181.31/181.78 'tc_nat' ) ) ] )
% 181.31/181.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 181.31/181.78 ), ==>( 1, 1 )] ) ).
% 181.31/181.78
% 181.31/181.78
% 181.31/181.78 subsumption(
% 181.31/181.78 clause( 96, [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'(
% 181.31/181.78 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , clause( 239069, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 181.31/181.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 181.31/181.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 subsumption(
% 181.31/181.81 clause( 162, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 181.31/181.81 , T ), =( X, Z ) ] )
% 181.31/181.81 , clause( 239149, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 181.31/181.81 , T ), =( X, Z ) ] )
% 181.31/181.81 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 181.31/181.81 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 subsumption(
% 181.31/181.81 clause( 195, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 181.31/181.81 , clause( 239188, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 181.31/181.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 181.31/181.81 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 181.31/181.81 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 subsumption(
% 181.31/181.81 clause( 494, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 181.31/181.81 'tc_nat' ) ] )
% 181.31/181.81 , clause( 239566, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X
% 181.31/181.81 , 'tc_nat' ) ] )
% 181.31/181.81 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 181.31/181.81 ), ==>( 1, 1 )] ) ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 subsumption(
% 181.31/181.81 clause( 502, [ 'c_Natural_Oevaln'( X, Y, Z, T ), ~( 'c_lessequals'( U, Z,
% 181.31/181.81 'tc_nat' ) ), ~( 'c_Natural_Oevaln'( X, Y, U, T ) ) ] )
% 181.31/181.81 , clause( 239575, [ 'c_Natural_Oevaln'( X, Y, Z, T ), ~( 'c_lessequals'( U
% 181.31/181.81 , Z, 'tc_nat' ) ), ~( 'c_Natural_Oevaln'( X, Y, U, T ) ) ] )
% 181.31/181.81 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 181.31/181.81 , U )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] )
% 181.31/181.81 ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 subsumption(
% 181.31/181.81 clause( 505, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 181.31/181.81 , clause( 239579, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 181.31/181.81 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 subsumption(
% 181.31/181.81 clause( 515, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 181.31/181.81 , clause( 239594, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 181.31/181.81 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 181.31/181.81 ), ==>( 1, 1 )] ) ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 subsumption(
% 181.31/181.81 clause( 536, [ 'v_fun1'( 'v_x', 'v_xa' ) ] )
% 181.31/181.81 , clause( 239623, [ 'v_fun1'( 'v_x', 'v_xa' ) ] )
% 181.31/181.81 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 subsumption(
% 181.31/181.81 clause( 537, [ 'c_Natural_Oevaln'( 'v_com', 'v_xa', 'v_n', 'v_xb' ) ] )
% 181.31/181.81 , clause( 239624, [ 'c_Natural_Oevaln'( 'v_com', 'v_xa', 'v_n', 'v_xb' ) ]
% 181.31/181.81 )
% 181.31/181.81 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 subsumption(
% 181.31/181.81 clause( 538, [ ~( 'v_fun2'( 'v_x', 'v_xb' ) ) ] )
% 181.31/181.81 , clause( 239625, [ ~( 'v_fun2'( 'v_x', 'v_xb' ) ) ] )
% 181.31/181.81 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 subsumption(
% 181.31/181.81 clause( 539, [ 'v_fun2'( X, Y ), ~( 'c_Natural_Oevaln'( 'v_com', Z, 'c_Suc'(
% 181.31/181.81 'v_n' ), Y ) ), ~( 'v_fun1'( X, Z ) ) ] )
% 181.31/181.81 , clause( 239626, [ 'v_fun2'( X, Y ), ~( 'c_Natural_Oevaln'( 'v_com', Z,
% 181.31/181.81 'c_Suc'( 'v_n' ), Y ) ), ~( 'v_fun1'( X, Z ) ) ] )
% 181.31/181.81 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 181.31/181.81 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 subsumption(
% 181.31/181.81 clause( 565, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 181.31/181.81 , clause( 239652, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 181.31/181.81 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 eqswap(
% 181.31/181.81 clause( 246262, [ =( Y, X ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 181.31/181.81 , T ) ] )
% 181.31/181.81 , clause( 162, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 181.31/181.81 , T ), =( X, Z ) ] )
% 181.31/181.81 , 2, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] )
% 181.31/181.81 ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 eqswap(
% 181.31/181.81 clause( 246263, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat' ),
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 181.31/181.81 , X ), =( Y, T ) ] )
% 181.31/181.81 , clause( 246262, [ =( Y, X ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 181.31/181.81 , T ) ] )
% 181.31/181.81 , 1, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] )
% 181.31/181.81 ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 eqfact(
% 181.31/181.81 clause( 246281, [ ~( =( X, Y ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 181.31/181.81 , Y ) ] )
% 181.31/181.81 , clause( 246263, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat' ),
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 181.31/181.81 , X ), =( Y, T ) ] )
% 181.31/181.81 , 2, 1, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, Z ), :=( T, X )] )
% 181.31/181.81 ).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 eqswap(
% 181.31/181.81 clause( 246284, [ =( Y, X ), ~( =( Z, Y ) ), ~( =(
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ) ] )
% 181.31/181.81 , clause( 246281, [ ~( =( X, Y ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ), =( Z
% 181.31/181.81 , Y ) ] )
% 181.31/181.81 , 2, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] )).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 eqswap(
% 181.31/181.81 clause( 246286, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( X
% 181.31/181.81 , Z ), ~( =( Y, X ) ) ] )
% 181.31/181.81 , clause( 246284, [ =( Y, X ), ~( =( Z, Y ) ), ~( =(
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ) ] )
% 181.31/181.81 , 2, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 181.31/181.81
% 181.31/181.81
% 181.31/181.81 subsumption(
% 181.31/181.81 clause( 615, [ ~( =( X, Y ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ),
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 181.31/181.81 , Z ) ] )
% 181.31/181.81 , clause( 246286, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 181.31/181.81 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 181.31/181.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 181.31/181.81 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, 'tc_nat' ), 'tc_nat' ) ) ), =( X
% 181.31/181.81 , Z ), ~( =( Y, X ) ) ] )
% 181.31/181.81 , substitution( 0, [ Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------