TSTP Solution File: ALG428-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG428-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.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 : Thu Jul 14 12:10:54 EDT 2022
% Result : Unsatisfiable 1.43s 1.81s
% Output : Refutation 1.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG428-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Wed Jun 8 05:57:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.94/1.32 *** allocated 10000 integers for termspace/termends
% 0.94/1.32 *** allocated 10000 integers for clauses
% 0.94/1.32 *** allocated 10000 integers for justifications
% 0.94/1.32 *** allocated 15000 integers for termspace/termends
% 0.94/1.32 *** allocated 22500 integers for termspace/termends
% 0.94/1.32 Bliksem 1.12
% 0.94/1.32
% 0.94/1.32
% 0.94/1.32 Automatic Strategy Selection
% 0.94/1.32
% 0.94/1.32 Clauses:
% 0.94/1.32 [
% 0.94/1.32 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.94/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.32 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.94/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.94/1.32 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.94/1.32 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.94/1.32 X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.94/1.32 , Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.32 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.94/1.32 ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.32 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.94/1.32 X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.32 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.94/1.32 ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.32 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.94/1.32 X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.94/1.32 ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.94/1.32 ) ],
% 0.94/1.32 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.32 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.32 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.94/1.32 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.32 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.94/1.32 ), =( Z, Y ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.32 ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.94/1.32 ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.32 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.94/1.32 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.94/1.32 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 0.94/1.32 , Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.94/1.32 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.94/1.32 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.32 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.94/1.32 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.94/1.32 , X ) ) ), =( Y, Z ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.94/1.32 , X ) ) ), =( Y, Z ) ],
% 0.94/1.32 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.32 'tc_nat' ), Y, 'tc_nat' ), 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat'
% 0.94/1.32 ) ) ],
% 0.94/1.32 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.32 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 0.94/1.32 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.32 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.94/1.32 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.94/1.32 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.94/1.32 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.94/1.32 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.94/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.94/1.32 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.32 , X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.32 , X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.94/1.32 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.32 , X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.94/1.32 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.32 , X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ],
% 0.94/1.32 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.94/1.32 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Z, U ) ],
% 0.94/1.32 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.94/1.32 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Y, T ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.32 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.94/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.94/1.32 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 0.94/1.32 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 0.94/1.32 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.94/1.32 , Z, 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.94/1.32 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.94/1.32 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.94/1.32 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.94/1.32 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.94/1.32 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.94/1.32 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.94/1.32 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.94/1.32 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.94/1.32 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.94/1.32 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 0.94/1.32 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.32 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.94/1.32 ],
% 0.94/1.32 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.94/1.32 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 0.94/1.32 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.32 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.32 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.32 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.94/1.32 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.94/1.32 , 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 0.94/1.32 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.94/1.32 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.32 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.32 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.32 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.32 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.32 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.32 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.32 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.32 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.32 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.32 ) ) ],
% 0.94/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.94/1.32 ) ) ],
% 0.94/1.32 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.32 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.94/1.32 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.94/1.32 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.32 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.94/1.32 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.94/1.32 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.32 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.94/1.32 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.32 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.94/1.32 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.32 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.32 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.94/1.32 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.32 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.32 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.94/1.32 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.94/1.32 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.94/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.94/1.32 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.94/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.94/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.94/1.32 T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.94/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.94/1.32 X ), Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.94/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.94/1.32 T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.94/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.94/1.32 X ), T, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.94/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.94/1.32 T, X ), X ) ) ],
% 0.94/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.94/1.32 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.94/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.94/1.32 X ), T, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.94/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.94/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.94/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.32 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.94/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.94/1.32 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.32 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.94/1.32 , X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.94/1.32 , X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.94/1.32 , X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.94/1.32 , X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.32 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.94/1.32 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.94/1.32 ) ) ],
% 0.94/1.32 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 0.94/1.32 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.94/1.32 X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 0.94/1.32 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.94/1.32 X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.94/1.32 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.94/1.32 X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.94/1.32 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.94/1.32 X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.94/1.32 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.32 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.94/1.32 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.32 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.94/1.32 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.32 ), X ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 Z, Y, X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.94/1.32 , X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.94/1.32 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.94/1.32 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.32 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.32 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.32 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.32 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.94/1.32 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 0.94/1.32 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 0.94/1.32 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.94/1.32 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 0.94/1.32 'c_lessequals'( T, X, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 0.94/1.32 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U ) ],
% 0.94/1.32 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat'
% 0.94/1.32 ), 'tc_nat' ) ],
% 0.94/1.32 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.32 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.94/1.32 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.94/1.32 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.94/1.32 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.32 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ =( 'c_Orderings_Oord__class_Omin'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.94/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.32 ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.32 ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.94/1.32 ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.32 ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.32 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.94/1.32 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.94/1.32 , T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.94/1.32 , Z, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.94/1.32 , T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.94/1.32 , Z, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.32 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.94/1.32 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'(
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.94/1.32 , 'tc_Polynomial_Opoly'( X ) ), X ) ) ],
% 0.94/1.32 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 0.94/1.32 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.32 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.32 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 0.94/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.94/1.32 , X, 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.94/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.94/1.32 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.94/1.32 , X ), W, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 0.94/1.32 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 0.94/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.94/1.32 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.94/1.32 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.94/1.32 , X ), T, X ), W, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 0.94/1.32 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.94/1.32 ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.94/1.32 ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.94/1.32 Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.94/1.32 ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.94/1.32 ],
% 0.94/1.32 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.32 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.32 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.32 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 0.94/1.32 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.32 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.94/1.32 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.32 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.94/1.32 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.94/1.32 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.32 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.94/1.32 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.94/1.32 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.94/1.32 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.94/1.32 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.94/1.32 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.94/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.94/1.32 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ],
% 0.94/1.32 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z,
% 0.94/1.32 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 0.94/1.32 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.94/1.32 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.94/1.32 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.32 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.94/1.32 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.94/1.32 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.94/1.32 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 0.94/1.32 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.94/1.32 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.94/1.32 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.32 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 0.94/1.32 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.94/1.32 ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.32 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.94/1.32 , X ), X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.32 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 0.94/1.32 ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.94/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.32 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.94/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.94/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 0.94/1.32 , X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.94/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.94/1.32 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.94/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.94/1.32 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.94/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.94/1.32 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ],
% 0.94/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.94/1.32 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), Y, X ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 Y, Y, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.94/1.32 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.32 Y, Z, X ) ) ],
% 0.94/1.32 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.32 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.94/1.32 ],
% 0.94/1.32 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.94/1.32 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.94/1.32 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.94/1.32 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.94/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.94/1.32 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.94/1.32 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.94/1.32 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.32 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X
% 0.94/1.32 ), T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y
% 0.94/1.32 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 0.94/1.32 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 0.94/1.32 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.94/1.32 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.94/1.32 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.94/1.32 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.94/1.32 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.94/1.32 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.94/1.32 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.94/1.32 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 0.94/1.32 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.94/1.32 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 0.94/1.32 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 0.94/1.32 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 0.94/1.32 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 0.94/1.32 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 0.94/1.32 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.32 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.94/1.33 Y, 'tc_nat' ), 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.94/1.33 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.94/1.33 Y, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.94/1.33 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.94/1.33 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 0.94/1.33 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 0.94/1.33 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.33 'tc_nat' ), 'tc_nat' ) ],
% 0.94/1.33 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 0.94/1.33 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 0.94/1.33 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 0.94/1.33 'tc_nat' ), 'tc_nat' ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.94/1.33 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.94/1.33 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.94/1.33 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.94/1.33 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.94/1.33 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.94/1.33 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.94/1.33 X ), X ), Y ) ],
% 0.94/1.33 [ =( 'c_Orderings_Oord__class_Omax'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.94/1.33 [ =( 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ), X, 'tc_nat' ), X ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.94/1.33 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.94/1.33 X ), X ), X ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 0.94/1.33 Z, Y, X ) ) ],
% 0.94/1.33 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 0.94/1.33 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.94/1.33 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.94/1.33 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.94/1.33 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 0.94/1.33 'c_Polynomial_OpCons'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_Polynomial_Opoly'( X ) ), X ), Z, X ), 'c_Polynomial_OpCons'( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.94/1.33 X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.33 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.33 Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 0.94/1.33 Z, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.33 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.33 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.94/1.33 , T, X ), X ), T, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.33 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X
% 0.94/1.33 ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y
% 0.94/1.33 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 0.94/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 0.94/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.94/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.33 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.94/1.33 X ) ) ), =( Z, T ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.94/1.33 X ) ) ), =( Z, T ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.94/1.33 X ) ) ), =( Y, T ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_OpCons'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.33 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.33 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.94/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.33 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.94/1.33 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.94/1.33 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.94/1.33 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.33 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.33 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.94/1.33 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ),
% 0.94/1.33 T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.94/1.33 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 0.94/1.33 X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 0.94/1.33 ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 0.94/1.33 X ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.33 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.94/1.33 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' )
% 0.94/1.33 ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.94/1.33 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.94/1.33 ) ],
% 0.94/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.94/1.33 ), 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.94/1.33 ), 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 0.94/1.33 X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 0.94/1.33 ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 0.94/1.33 X ) ) ],
% 0.94/1.33 [ ~( 'class_HOL_Ozero'( X ) ), =(
% 0.94/1.33 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.33 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.94/1.33 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.94/1.33 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 0.94/1.33 'c_Suc'( X ), 'tc_nat' ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.33 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.94/1.33 ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.94/1.33 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.94/1.33 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.94/1.33 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.94/1.33 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z,
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.94/1.33 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.94/1.33 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.33 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.33 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ),
% 0.94/1.33 T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.94/1.33 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.33 T, X ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.33 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.94/1.33 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.94/1.33 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.33 Z, X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.33 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.94/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.33 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.94/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.94/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.94/1.33 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.94/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.94/1.33 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.33 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.94/1.33 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.94/1.33 ), Y ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.33 'tc_nat' ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.94/1.33 'tc_nat' ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.94/1.33 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.94/1.33 , Y, X ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.94/1.33 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.94/1.33 , Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.33 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.94/1.33 , T, X ), X ), T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.33 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.94/1.33 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.33 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.94/1.33 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.33 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.94/1.33 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.33 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.94/1.33 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.33 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.94/1.33 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.33 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 0.94/1.33 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.94/1.33 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 0.94/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.94/1.33 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.94/1.33 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.94/1.33 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.94/1.33 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 0.94/1.33 ],
% 0.94/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.94/1.33 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.33 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.94/1.33 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.94/1.33 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.94/1.33 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.33 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.94/1.33 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.33 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.33 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.33 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.33 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.94/1.33 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.94/1.33 ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.33 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 0.94/1.33 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.33 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.33 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.33 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.94/1.33 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.94/1.33 , T, X ) ) ), =( Z, T ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.33 , T, X ) ) ), =( Y, Z ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.94/1.33 X ), X ), Y ) ],
% 0.94/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.33 'tc_nat' ) ), =( Y, Z ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.94/1.33 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.94/1.33 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.94/1.33 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.94/1.33 , T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.94/1.33 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.94/1.33 , Z, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 0.94/1.33 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.33 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.94/1.33 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 X ), T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 0.94/1.33 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.94/1.33 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.94/1.33 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.33 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.94/1.33 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.94/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.94/1.33 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.33 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.94/1.33 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.94/1.33 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.94/1.33 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.33 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 0.94/1.33 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.94/1.33 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.94/1.33 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.94/1.33 , 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat'
% 0.94/1.33 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.33 'c_Suc'( X ), 'tc_nat' ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.33 'c_Suc'( X ), 'tc_nat' ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( T, Y
% 0.94/1.33 , X ), Z, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, T
% 0.94/1.33 , X ), Z, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 0.94/1.33 Z, Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.94/1.33 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.94/1.33 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 0.94/1.33 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.94/1.33 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 0.94/1.33 'tc_nat' ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.94/1.33 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.94/1.33 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.94/1.33 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.94/1.33 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 0.94/1.33 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 0.94/1.33 'tc_nat' ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.33 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 0.94/1.33 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.33 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 0.94/1.33 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 0.94/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.94/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.94/1.33 'c_Polynomial_OpCons'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_Polynomial_Opoly'( X ) ), X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.94/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.94/1.33 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.94/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.94/1.33 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.94/1.33 , X ), W, X ) ) ],
% 0.94/1.33 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 0.94/1.33 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.94/1.33 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 0.94/1.33 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 0.94/1.33 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_HOL_Ozero'( X ) ), ~( =(
% 0.94/1.33 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( Y, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.94/1.33 ) ],
% 0.94/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.33 ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.94/1.33 X ) ) ],
% 0.94/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 X, T, 'tc_nat' ) ],
% 0.94/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.94/1.33 X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.94/1.33 X ) ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.33 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.33 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.94/1.33 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.94/1.33 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.94/1.33 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 0.94/1.33 X ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.94/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.94/1.33 , T, X ), X ), T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.94/1.33 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.94/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.94/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.94/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.33 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.33 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.94/1.33 T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.94/1.33 T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.94/1.33 T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.94/1.33 T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.33 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.33 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.94/1.33 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.94/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.94/1.33 W, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.94/1.33 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.94/1.33 , X ), T, X ), W, X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.94/1.33 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.94/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.94/1.33 W, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.94/1.33 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.94/1.33 , X ), W, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.94/1.33 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.94/1.33 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 0.94/1.33 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.94/1.33 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 0.94/1.33 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 0.94/1.33 Z, X ) ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.94/1.33 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.33 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.33 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.94/1.33 X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.94/1.33 X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.94/1.33 X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.94/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.94/1.33 X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.33 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.33 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 0.94/1.33 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.94/1.33 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.94/1.33 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 0.94/1.33 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.33 , X ), 'c_HOL_Oord__class_Oless'( Y, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 Y, 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.94/1.33 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ), 'tc_nat' ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.94/1.33 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.94/1.33 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.33 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 0.94/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.33 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.94/1.33 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.94/1.33 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 0.94/1.33 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.94/1.33 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 0.94/1.33 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 0.94/1.33 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 0.94/1.33 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 0.94/1.33 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), Y,
% 0.94/1.33 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.33 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.94/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.94/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.94/1.33 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.94/1.33 , T ), =( X, Z ) ],
% 0.94/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.94/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.94/1.33 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.94/1.33 , T ), =( X, Z ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.33 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.94/1.33 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.33 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.94/1.33 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.94/1.33 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.94/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 0.94/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 0.94/1.33 X ), Z, X ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 0.94/1.33 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.94/1.33 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.94/1.33 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.94/1.33 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.33 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.94/1.33 ) ],
% 0.94/1.33 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.94/1.33 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.94/1.33 , Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.94/1.33 , X ) ) ],
% 0.94/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.94/1.33 , Y, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.33 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.94/1.33 ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 0.94/1.33 ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.33 ) ), =( Y, Z ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.33 ) ), =( Y, Z ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.33 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.94/1.33 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.33 X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.94/1.33 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.94/1.33 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.94/1.33 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.94/1.33 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.94/1.33 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.33 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.94/1.33 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.94/1.33 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.94/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.94/1.33 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.94/1.33 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.33 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.94/1.33 , U, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( T
% 0.94/1.33 , Z, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z
% 0.94/1.33 , T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.33 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.33 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.94/1.33 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 0.94/1.33 ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.33 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.33 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 0.94/1.33 , 'tc_nat' ) ) ],
% 0.94/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.94/1.33 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.97/1.33 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 0.97/1.33 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 0.97/1.33 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.97/1.33 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.97/1.33 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 0.97/1.33 'tc_nat' ) ],
% 0.97/1.33 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 0.97/1.33 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 0.97/1.33 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.97/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.97/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.97/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.97/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.97/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 0.97/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 0.97/1.33 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.97/1.33 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.97/1.33 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 0.97/1.33 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 0.97/1.33 'tc_nat' ) ],
% 0.97/1.33 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.97/1.33 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.97/1.33 ) ],
% 0.97/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.97/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.97/1.33 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 0.97/1.33 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.97/1.33 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.97/1.33 X ), T, X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.97/1.33 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.97/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.97/1.33 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.97/1.33 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.97/1.33 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.97/1.33 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.97/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.97/1.33 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.97/1.33 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.97/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.97/1.33 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.97/1.33 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.97/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.97/1.33 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.97/1.33 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.97/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.97/1.33 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.97/1.33 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.97/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.97/1.33 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 0.97/1.33 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.97/1.33 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.97/1.33 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 0.97/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.97/1.33 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ],
% 0.97/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.97/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 0.97/1.33 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 0.97/1.33 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.97/1.33 ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.97/1.33 ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.97/1.33 ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.97/1.33 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.97/1.33 ), X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.97/1.33 ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.97/1.33 ],
% 0.97/1.33 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.97/1.33 'tc_nat' ), 'tc_nat' ) ) ],
% 0.97/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.97/1.33 ), 'tc_nat' ), X ) ],
% 0.97/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.97/1.33 , X, 'tc_nat' ), X ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.97/1.33 ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.97/1.33 ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.97/1.33 ), Y ) ],
% 0.97/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.97/1.33 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.97/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.97/1.33 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.97/1.33 ), Y ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.97/1.33 ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.97/1.33 ) ) ],
% 0.97/1.33 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.97/1.33 ), Y ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.97/1.33 ), Y ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.97/1.33 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.97/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.97/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 0.97/1.33 , X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.97/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 0.97/1.33 , X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 0.97/1.33 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.97/1.33 , X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 0.97/1.33 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.97/1.33 , X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 0.97/1.33 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 0.97/1.33 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.97/1.33 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.97/1.33 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.97/1.33 [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.97/1.33 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.97/1.33 Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.97/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.97/1.33 'tc_nat' ) ],
% 0.97/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.97/1.33 'tc_nat' ) ],
% 0.97/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.97/1.33 'tc_nat' ) ],
% 0.97/1.33 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.97/1.33 'tc_nat' ) ],
% 0.97/1.33 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.97/1.33 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.97/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.97/1.33 X ), Z, X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.97/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.97/1.33 , X ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.97/1.33 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.97/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.97/1.33 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.97/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.97/1.33 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.97/1.33 , X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.97/1.33 , X ) ) ],
% 0.97/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.97/1.33 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.97/1.33 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 0.97/1.33 ), X, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.97/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.97/1.33 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.97/1.33 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.97/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.97/1.33 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.97/1.33 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.97/1.33 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.97/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.97/1.33 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.97/1.33 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 0.97/1.33 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.97/1.33 X ), X ) ) ],
% 0.97/1.33 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.97/1.33 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.97/1.33 ) ), X, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.97/1.33 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.97/1.33 ) ), X, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'(
% 0.97/1.33 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.97/1.33 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.97/1.33 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.97/1.33 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 0.97/1.33 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.97/1.33 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.97/1.33 ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.97/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.97/1.33 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.97/1.33 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.97/1.33 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.97/1.33 X ) ) ],
% 0.97/1.33 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.97/1.33 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.97/1.33 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.97/1.33 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.97/1.33 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.97/1.33 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.97/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.97/1.33 X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.97/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 Z, T, X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 Z, T, X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.97/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.97/1.33 X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.97/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 Y, T, X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 Y, T, X ) ) ],
% 0.97/1.33 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.97/1.33 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 0.97/1.33 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.97/1.33 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.97/1.33 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.97/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 0.97/1.33 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.97/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.97/1.33 , X ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.97/1.33 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.97/1.33 , X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 0.97/1.33 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.97/1.33 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.97/1.33 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.97/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.97/1.33 ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.97/1.33 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.97/1.33 ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.97/1.33 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.97/1.33 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 0.97/1.33 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.97/1.33 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.97/1.33 'tc_nat' ), 'tc_nat' ) ) ],
% 0.97/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.97/1.33 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.97/1.33 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.97/1.33 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.97/1.33 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.97/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.97/1.33 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.97/1.33 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.97/1.33 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.97/1.33 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.97/1.33 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.97/1.33 'tc_nat' ), 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.97/1.33 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 0.97/1.33 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.97/1.33 'tc_nat' ), 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.97/1.33 ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.97/1.33 , Y, X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.97/1.33 , T, X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.97/1.33 , T, X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.97/1.33 , Y, X ), X ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.97/1.33 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.97/1.33 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.97/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.97/1.33 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.97/1.33 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.97/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.97/1.33 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 0.97/1.33 ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.97/1.33 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 0.97/1.33 , X ) ) ],
% 0.97/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 0.97/1.33 , X ) ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 0.97/1.33 ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 0.97/1.33 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.97/1.33 ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 0.97/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 0.97/1.33 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.97/1.33 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.97/1.33 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.97/1.33 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.97/1.33 'c_lessequals'( Z, Y, X ) ],
% 0.97/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.97/1.33 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.97/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.97/1.33 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.97/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 0.97/1.33 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.97/1.33 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 0.97/1.33 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 0.97/1.33 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 0.97/1.33 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.97/1.33 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.97/1.33 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.97/1.33 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.97/1.33 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.97/1.33 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.97/1.33 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.97/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.97/1.33 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.97/1.33 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.97/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.97/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.97/1.33 [ ~( 'class_HOL_Ozero'( X ) ), 'c_lessequals'( 'c_Polynomial_Odegree'(
% 0.97/1.33 'c_Polynomial_OpCons'( Y, Z, X ), X ), 'c_Suc'( 'c_Polynomial_Odegree'( Z
% 0.97/1.33 , X ) ), 'tc_nat' ) ],
% 0.97/1.33 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.97/1.33 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.97/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.97/1.33 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.97/1.33 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.97/1.33 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.97/1.33 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.97/1.33 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.97/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.97/1.33 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.97/1.33 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.97/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 0.97/1.33 ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.97/1.33 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.97/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.97/1.33 'c_Polynomial_Odegree'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.97/1.33 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Polynomial_Odegree'( Y, X ) ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ ~( 'class_HOL_Ozero'( X ) ), =(
% 0.97/1.33 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( Y, X ), 'c_Suc'(
% 0.97/1.33 'c_Polynomial_Odegree'( Y, X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.97/1.33 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( =( 'v_p', 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.97/1.33 'tc_Complex_Ocomplex' ) ) ) ) ],
% 0.97/1.33 [ ~( =( 'c_Polynomial_Odegree'( 'v_p', 'tc_Complex_Ocomplex' ), 'c_Suc'(
% 0.97/1.33 X ) ) ), 'v_thesis____' ],
% 0.97/1.33 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.97/1.33 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.97/1.33 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.97/1.33 'c_Polynomial_OpCons'( Y, Z, X ), X ), 'c_Suc'( 'c_Polynomial_Odegree'( Z
% 0.97/1.33 , X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) )
% 0.97/1.33 ) ],
% 0.97/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.97/1.33 'c_Polynomial_Odegree'(
% 0.97/1.33 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ), X
% 0.97/1.33 ), 'c_Polynomial_Odegree'( Y, X ) ) ],
% 0.97/1.33 [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.97/1.33 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) )
% 0.97/1.33 ],
% 0.97/1.33 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 0.97/1.33 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.97/1.33 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 0.97/1.33 'tc_nat' ) ],
% 0.97/1.33 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 0.97/1.33 , X, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.97/1.33 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 0.97/1.33 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 0.97/1.33 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.97/1.33 [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.97/1.33 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat' ) ) )
% 0.97/1.33 ],
% 0.97/1.33 [ ~( =( 'c_Polynomial_Odegree'( 'v_p', 'tc_Complex_Ocomplex' ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.97/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.97/1.33 [ ~( =( 'c_Polynomial_Odegree'( 'v_p', 'tc_Complex_Ocomplex' ),
% 0.97/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.97/1.33 [ ~( 'v_thesis____' ) ],
% 0.97/1.33 [ ~( =( 'c_Polynomial_Odegree'( 'v_p', 'tc_Complex_Ocomplex' ), 'c_Suc'(
% 0.97/1.33 X ) ) ), 'v_thesis____' ],
% 0.97/1.33 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_Polynomial_Opoly'(
% 0.97/1.33 X ) ), ~( 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Polynomial_Opoly'( X ) ),
% 0.97/1.33 ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Polynomial_Opoly'( X ) )
% 0.97/1.33 , ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_Complex_Ocomplex'
% 0.97/1.33 ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.97/1.33 ],
% 0.97/1.33 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.97/1.33 ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.97/1.33 ],
% 0.97/1.33 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_HOL_Ozero'( 'tc_nat' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 0.97/1.33 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.97/1.33 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 0.97/1.33 ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 0.97/1.33 ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Complex_Ocomplex' ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_HOL_Ozero'( 'tc_Complex_Ocomplex' ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.97/1.33 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.97/1.33 X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 0.97/1.33 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.97/1.33 X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.97/1.33 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.97/1.33 X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.97/1.33 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.97/1.33 X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.97/1.33 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.97/1.33 X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 0.97/1.33 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.97/1.33 X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.97/1.33 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.97/1.33 X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 0.97/1.33 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 0.97/1.33 ,
% 0.97/1.33 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.97/1.33 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.97/1.33 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Polynomial_Opoly'(
% 0.97/1.33 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Polynomial_Opoly'(
% 0.97/1.33 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Polynomial_Opoly'(
% 0.97/1.33 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Polynomial_Opoly'( X
% 0.97/1.33 ) ), ~( 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Polynomial_Opoly'( X
% 0.97/1.33 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Polynomial_Opoly'( X
% 0.97/1.33 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Polynomial_Opoly'( X
% 0.97/1.33 ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Polynomial_Opoly'( X )
% 0.97/1.33 ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Polynomial_Opoly'( X
% 0.97/1.33 ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Polynomial_Opoly'( X
% 0.97/1.33 ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Polynomial_Opoly'( X )
% 0.97/1.33 ), ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Polynomial_Opoly'( X ) )
% 0.97/1.33 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Polynomial_Opoly'( X ) )
% 0.97/1.33 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Polynomial_Opoly'( X ) )
% 0.97/1.33 , ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Polynomial_Opoly'( X ) )
% 0.97/1.33 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Polynomial_Opoly'( X ) )
% 0.97/1.33 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Polynomial_Opoly'( X ) ),
% 0.97/1.33 ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Polynomial_Opoly'( X ) ),
% 0.97/1.33 ~( 'class_OrderedGroup_Oab__group__add'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.97/1.33 ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Polynomial_Opoly'( X ) ),
% 0.97/1.33 ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Osemiring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.97/1.33 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.97/1.33 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.97/1.33 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.97/1.33 'class_OrderedGroup_Oab__group__add'( X ) ) ],
% 0.97/1.33 [ 'class_Divides_Osemiring__div'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.97/1.33 'class_Ring__and__Field_Ofield'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.97/1.33 'class_Ring__and__Field_Ocomm__ring'( X ) ) ],
% 0.97/1.33 [ 'class_Ring__and__Field_Oidom'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.97/1.33 'class_Ring__and__Field_Oidom'( X ) ) ],
% 0.97/1.33 [ 'class_Orderings_Opreorder'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.97/1.33 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_Orderings_Olinorder'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.97/1.33 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_Divides_Oring__div'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.97/1.33 'class_Ring__and__Field_Ofield'( X ) ) ],
% 0.97/1.33 [ 'class_Orderings_Oorder'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.97/1.33 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.97/1.33 [ 'class_Int_Onumber__ring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.97/1.33 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ],
% 0.97/1.33 [ 'class_HOL_Ozero'( 'tc_Polynomial_Opoly'( X ) ), ~( 'class_HOL_Ozero'(
% 0.97/1.33 X ) ) ]
% 0.97/1.33 ] .
% 0.97/1.33
% 0.97/1.33
% 0.97/1.33 percentage equality = 0.233940, percentage horn = 0.902471
% 1.43/1.80 This is a problem with some equality
% 1.43/1.80
% 1.43/1.80
% 1.43/1.80
% 1.43/1.80 Options Used:
% 1.43/1.80
% 1.43/1.80 useres = 1
% 1.43/1.80 useparamod = 1
% 1.43/1.80 useeqrefl = 1
% 1.43/1.80 useeqfact = 1
% 1.43/1.80 usefactor = 1
% 1.43/1.80 usesimpsplitting = 0
% 1.43/1.80 usesimpdemod = 5
% 1.43/1.80 usesimpres = 3
% 1.43/1.80
% 1.43/1.80 resimpinuse = 1000
% 1.43/1.80 resimpclauses = 20000
% 1.43/1.80 substype = eqrewr
% 1.43/1.80 backwardsubs = 1
% 1.43/1.80 selectoldest = 5
% 1.43/1.80
% 1.43/1.80 litorderings [0] = split
% 1.43/1.80 litorderings [1] = extend the termordering, first sorting on arguments
% 1.43/1.80
% 1.43/1.80 termordering = kbo
% 1.43/1.80
% 1.43/1.80 litapriori = 0
% 1.43/1.80 termapriori = 1
% 1.43/1.80 litaposteriori = 0
% 1.43/1.80 termaposteriori = 0
% 1.43/1.80 demodaposteriori = 0
% 1.43/1.80 ordereqreflfact = 0
% 1.43/1.80
% 1.43/1.80 litselect = negord
% 1.43/1.80
% 1.43/1.80 maxweight = 15
% 1.43/1.80 maxdepth = 30000
% 1.43/1.80 maxlength = 115
% 1.43/1.80 maxnrvars = 195
% 1.43/1.80 excuselevel = 1
% 1.43/1.80 increasemaxweight = 1
% 1.43/1.80
% 1.43/1.80 maxselected = 10000000
% 1.43/1.80 maxnrclauses = 10000000
% 1.43/1.80
% 1.43/1.80 showgenerated = 0
% 1.43/1.80 showkept = 0
% 1.43/1.80 showselected = 0
% 1.43/1.80 showdeleted = 0
% 1.43/1.80 showresimp = 1
% 1.43/1.80 showstatus = 2000
% 1.43/1.81
% 1.43/1.81 prologoutput = 1
% 1.43/1.81 nrgoals = 5000000
% 1.43/1.81 totalproof = 1
% 1.43/1.81
% 1.43/1.81 Symbols occurring in the translation:
% 1.43/1.81
% 1.43/1.81 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.43/1.81 . [1, 2] (w:1, o:105, a:1, s:1, b:0),
% 1.43/1.81 ! [4, 1] (w:0, o:48, a:1, s:1, b:0),
% 1.43/1.81 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.43/1.81 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Oab__semigroup__idem__mult' [40, 1] (w:1, o:53
% 1.43/1.81 , a:1, s:1, b:0),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes' [43, 3] (w:1, o:134, a:1, s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Olordered__ab__group__add' [44, 1] (w:1, o:54, a:
% 1.43/1.81 1, s:1, b:0),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus' [47, 2] (w:1, o:130, a:1, s:1, b:0),
% 1.43/1.81 'c_lessequals' [48, 3] (w:1, o:135, a:1, s:1, b:0),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus' [49, 3] (w:1, o:137, a:1, s:1, b:0),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero' [50, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.43/1.81 'tc_nat' [53, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.43/1.81 'c_HOL_Oord__class_Oless' [54, 3] (w:1, o:136, a:1, s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Oring' [56, 1] (w:1, o:56, a:1, s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [57, 1]
% 1.43/1.81 (w:1, o:58, a:1, s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add' [59, 1] (w:1, o:59
% 1.43/1.81 , a:1, s:1, b:0),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus' [62, 3] (w:1, o:138, a:1, s:1, b:0),
% 1.43/1.81 'c_Suc' [63, 1] (w:1, o:60, a:1, s:1, b:0),
% 1.43/1.81 'class_Orderings_Olinorder' [64, 1] (w:1, o:61, a:1, s:1, b:0),
% 1.43/1.81 'c_Orderings_Oord__class_Omax' [65, 3] (w:1, o:139, a:1, s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Oordered__idom' [66, 1] (w:1, o:64, a:1, s:1
% 1.43/1.81 , b:0),
% 1.43/1.81 'class_Orderings_Oorder' [67, 1] (w:1, o:65, a:1, s:1, b:0),
% 1.43/1.81 'class_Lattices_Oboolean__algebra' [68, 1] (w:1, o:66, a:1, s:1, b:0)
% 1.43/1.81 ,
% 1.43/1.81 'class_OrderedGroup_Ogroup__add' [69, 1] (w:1, o:67, a:1, s:1, b:0),
% 1.43/1.81
% 1.43/1.81 'c_Orderings_Oord__class_Omin' [70, 3] (w:1, o:140, a:1, s:1, b:0),
% 1.43/1.81 'c_Divides_Odiv__class_Omod' [71, 3] (w:1, o:141, a:1, s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Ocomm__semiring__1' [72, 1] (w:1, o:71, a:1
% 1.43/1.81 , s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__group__add' [77, 1] (w:1, o:72, a:
% 1.43/1.81 1, s:1, b:0),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven' [78, 2] (w:1, o:131, a:1, s:1, b:0
% 1.43/1.81 ),
% 1.43/1.81 'class_Divides_Osemiring__div' [79, 1] (w:1, o:74, a:1, s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Oordered__ring__strict' [80, 1] (w:1, o:75
% 1.43/1.81 , a:1, s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Oordered__semiring__strict' [81, 1] (w:1, o:
% 1.43/1.81 76, a:1, s:1, b:0),
% 1.43/1.81 'class_HOL_Ozero' [82, 1] (w:1, o:77, a:1, s:1, b:0),
% 1.43/1.81 'c_Polynomial_OpCons' [84, 3] (w:1, o:142, a:1, s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Oordered__semidom' [86, 1] (w:1, o:78, a:1
% 1.43/1.81 , s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Omult__mono1' [88, 1] (w:1, o:79, a:1, s:1
% 1.43/1.81 , b:0),
% 1.43/1.81 'class_Ring__and__Field_Omult__mono' [89, 1] (w:1, o:80, a:1, s:1, b:
% 1.43/1.81 0),
% 1.43/1.81 'class_Ring__and__Field_Opordered__ring' [90, 1] (w:1, o:83, a:1, s:1
% 1.43/1.81 , b:0),
% 1.43/1.81 'class_Ring__and__Field_Oidom' [92, 1] (w:1, o:84, a:1, s:1, b:0),
% 1.43/1.81 'class_Int_Onumber__ring' [93, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Opordered__cancel__semiring' [97, 1] (w:1, o:
% 1.43/1.81 86, a:1, s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Oab__semigroup__mult' [98, 1] (w:1, o:87, a:1, s:
% 1.43/1.81 1, b:0),
% 1.43/1.81 'class_RealVector_Oreal__normed__algebra' [99, 1] (w:1, o:88, a:1, s:
% 1.43/1.81 1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Ocomm__semiring' [104, 1] (w:1, o:89, a:1, s:
% 1.43/1.81 1, b:0),
% 1.43/1.81 'class_OrderedGroup_Oordered__ab__group__add' [105, 1] (w:1, o:57, a:
% 1.43/1.81 1, s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Opordered__comm__monoid__add' [106, 1] (w:1, o:90
% 1.43/1.81 , a:1, s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Oring__no__zero__divisors' [107, 1] (w:1, o:
% 1.43/1.81 91, a:1, s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Ono__zero__divisors' [108, 1] (w:1, o:63, a:1
% 1.43/1.81 , s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Oab__group__add' [110, 1] (w:1, o:92, a:1, s:1
% 1.43/1.81 , b:0),
% 1.43/1.81 'class_Ring__and__Field_Oordered__semiring' [111, 1] (w:1, o:81, a:1
% 1.43/1.81 , s:1, b:0),
% 1.43/1.81 'tc_Polynomial_Opoly' [112, 1] (w:1, o:93, a:1, s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Ocomm__monoid__add' [114, 1] (w:1, o:94, a:1, s:1
% 1.43/1.81 , b:0),
% 1.43/1.81 'class_Ring__and__Field_Ocomm__semiring__0' [115, 1] (w:1, o:70, a:1
% 1.43/1.81 , s:1, b:0),
% 1.43/1.81 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly' [117, 3]
% 1.43/1.81 (w:1, o:143, a:1, s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Opordered__semiring' [119, 1] (w:1, o:95, a:1
% 1.43/1.81 , s:1, b:0),
% 1.43/1.81 'class_Divides_Oring__div' [120, 1] (w:1, o:73, a:1, s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Ocancel__ab__semigroup__add' [121, 1] (w:1, o:96
% 1.43/1.81 , a:1, s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Ocancel__semigroup__add' [122, 1] (w:1, o:97, a:1
% 1.43/1.81 , s:1, b:0),
% 1.43/1.81 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize' [123, 2] (w:1, o:
% 1.43/1.81 132, a:1, s:1, b:0),
% 1.43/1.81 'class_Orderings_Opreorder' [124, 1] (w:1, o:98, a:1, s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Oab__semigroup__add' [125, 1] (w:1, o:99, a:1, s:
% 1.43/1.81 1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Osemiring' [126, 1] (w:1, o:100, a:1, s:1, b:
% 1.43/1.81 0),
% 1.43/1.81 'c_Polynomial_Odegree' [127, 2] (w:1, o:133, a:1, s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Omult__zero' [129, 1] (w:1, o:62, a:1, s:1
% 1.43/1.81 , b:0),
% 1.43/1.81 'class_Ring__and__Field_Oordered__comm__semiring__strict' [130, 1]
% 1.43/1.81 (w:1, o:82, a:1, s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Omonoid__add' [131, 1] (w:1, o:101, a:1, s:1, b:0
% 1.43/1.81 ),
% 1.43/1.81 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [132, 1]
% 1.43/1.81 (w:1, o:102, a:1, s:1, b:0),
% 1.43/1.81 'v_p' [136, 0] (w:1, o:44, a:1, s:1, b:0),
% 1.43/1.81 'tc_Complex_Ocomplex' [137, 0] (w:1, o:45, a:1, s:1, b:0),
% 1.43/1.81 'v_thesis____' [138, 0] (w:1, o:46, a:1, s:1, b:0),
% 1.43/1.81 'class_OrderedGroup_Ocancel__comm__monoid__add' [140, 1] (w:1, o:103
% 1.43/1.81 , a:1, s:1, b:0),
% 1.43/1.81 'class_Ring__and__Field_Ocomm__ring' [141, 1] (w:1, o:68, a:1, s:1
% 1.43/1.81 , b:0),
% 1.43/1.81 'class_Ring__and__Field_Ocomm__ring__1' [142, 1] (w:1, o:69, a:1, s:1
% 1.43/1.81 , b:0),
% 1.43/1.81 'class_Ring__and__Field_Ofield' [143, 1] (w:1, o:104, a:1, s:1, b:0)
% 1.43/1.81 .
% 1.43/1.81
% 1.43/1.81
% 1.43/1.81 Starting Search:
% 1.43/1.81
% 1.43/1.81 Resimplifying inuse:
% 1.43/1.81 Done
% 1.43/1.81
% 1.43/1.81
% 1.43/1.81 Intermediate Status:
% 1.43/1.81 Generated: 5870
% 1.43/1.81 Kept: 2182
% 1.43/1.81 Inuse: 126
% 1.43/1.81 Deleted: 0
% 1.43/1.81 Deletedinuse: 0
% 1.43/1.81
% 1.43/1.81 Resimplifying inuse:
% 1.43/1.81 Done
% 1.43/1.81
% 1.43/1.81 Resimplifying inuse:
% 1.43/1.81 Done
% 1.43/1.81
% 1.43/1.81
% 1.43/1.81 Intermediate Status:
% 1.43/1.81 Generated: 11932
% 1.43/1.81 Kept: 4182
% 1.43/1.81 Inuse: 215
% 1.43/1.81 Deleted: 3
% 1.43/1.81 Deletedinuse: 0
% 1.43/1.81
% 1.43/1.81 Resimplifying inuse:
% 1.43/1.81 Done
% 1.43/1.81
% 1.43/1.81 Resimplifying inuse:
% 1.43/1.81 Done
% 1.43/1.81
% 1.43/1.81
% 1.43/1.81 Intermediate Status:
% 1.43/1.81 Generated: 19757
% 1.43/1.81 Kept: 6196
% 1.43/1.81 Inuse: 262
% 1.43/1.81 Deleted: 5
% 1.43/1.81 Deletedinuse: 0
% 1.43/1.81
% 1.43/1.81 Resimplifying inuse:
% 1.43/1.81 Done
% 1.43/1.81
% 1.43/1.81 Resimplifying inuse:
% 1.43/1.81 Done
% 1.43/1.81
% 1.43/1.81
% 1.43/1.81 Intermediate Status:
% 1.43/1.81 Generated: 33236
% 1.43/1.81 Kept: 8510
% 1.43/1.81 Inuse: 296
% 1.43/1.81 Deleted: 5
% 1.43/1.81 Deletedinuse: 0
% 1.43/1.81
% 1.43/1.81 Resimplifying inuse:
% 1.43/1.81 Done
% 1.43/1.81
% 1.43/1.81 Resimplifying inuse:
% 1.43/1.81 Done
% 1.43/1.81
% 1.43/1.81
% 1.43/1.81 Bliksems!, er is een bewijs:
% 1.43/1.81 % SZS status Unsatisfiable
% 1.43/1.81 % SZS output start Refutation
% 1.43/1.81
% 1.43/1.81 clause( 22, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 23, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 68, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 151, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 265, [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 344, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 630, [ ~( =( 'c_Polynomial_Odegree'( 'v_p', 'tc_Complex_Ocomplex' )
% 1.43/1.81 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 633, [ ~( 'v_thesis____' ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 634, [ ~( =( 'c_Polynomial_Odegree'( 'v_p', 'tc_Complex_Ocomplex' )
% 1.43/1.81 , 'c_Suc'( X ) ) ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 1843, [ ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~( =( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 9703, [ ~( =( 'c_Polynomial_Odegree'( 'v_p', 'tc_Complex_Ocomplex'
% 1.43/1.81 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 9723, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), 'c_Polynomial_Odegree'( 'v_p', 'tc_Complex_Ocomplex' ),
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 10039, [ ~( =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, 'c_Polynomial_Odegree'( 'v_p',
% 1.43/1.81 'tc_Complex_Ocomplex' ), 'tc_nat' ) ] )
% 1.43/1.81 .
% 1.43/1.81 clause( 10054, [] )
% 1.43/1.81 .
% 1.43/1.81
% 1.43/1.81
% 1.43/1.81 % SZS output end Refutation
% 1.43/1.81 found a proof!
% 1.43/1.81
% 1.43/1.81 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.43/1.81
% 1.43/1.81 initialclauses(
% 1.43/1.81 [ clause( 10056, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 1.43/1.81 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.43/1.81 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10057, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10058, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10059, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.43/1.81 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10060, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 1.43/1.81 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10061, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.43/1.81 X ), X ) ) ] )
% 1.43/1.81 , clause( 10062, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.43/1.81 , Z, X ) ) ] )
% 1.43/1.81 , clause( 10063, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10064, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.43/1.81 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10065, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10066, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.43/1.81 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10067, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 1.43/1.81 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10068, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 1.43/1.81 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10069, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10070, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10071, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10072, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.43/1.81 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10073, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ] )
% 1.43/1.81 , clause( 10074, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.43/1.81 ), =( Z, Y ) ] )
% 1.43/1.81 , clause( 10075, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10076, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10077, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 1.43/1.81 , clause( 10078, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.43/1.81 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.43/1.81 , clause( 10079, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10080, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 1.43/1.81 , clause( 10081, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 1.43/1.81 , clause( 10082, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 1.43/1.81 , clause( 10083, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.43/1.81 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10084, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.43/1.81 ), =( Z, Y ) ] )
% 1.43/1.81 , clause( 10085, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.43/1.81 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10086, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.43/1.81 , X ) ) ), =( Y, Z ) ] )
% 1.43/1.81 , clause( 10087, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.43/1.81 , X ) ) ), =( Y, Z ) ] )
% 1.43/1.81 , clause( 10088, [ =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ),
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10089, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.43/1.81 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10090, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ] )
% 1.43/1.81 , clause( 10091, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ),
% 1.43/1.81 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10092, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 1.43/1.81 , clause( 10093, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 1.43/1.81 , clause( 10094, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10095, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10096, [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10097, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10098, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.43/1.81 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 1.43/1.81 , clause( 10099, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.43/1.81 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10100, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10101, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10102, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10103, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.43/1.81 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10104, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10105, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10106, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10107, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ] )
% 1.43/1.81 , clause( 10108, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 1.43/1.81 Y, Z, X ), 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Z, U ) ] )
% 1.43/1.81 , clause( 10109, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 1.43/1.81 Y, Z, X ), 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Y, T ) ] )
% 1.43/1.81 , clause( 10110, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.43/1.81 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10111, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10112, [ =( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10113, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 1.43/1.81 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 1.43/1.81 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.43/1.81 , Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10114, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10115, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10116, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10117, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10118, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10119, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.43/1.81 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10120, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10121, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.43/1.81 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10122, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.43/1.81 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10123, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.43/1.81 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10124, [ =( 'c_Orderings_Oord__class_Omin'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 1.43/1.81 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10125, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 1.43/1.81 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 1.43/1.81 , clause( 10126, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10127, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10128, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10129, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10130, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10131, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10132, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10133, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10134, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 1.43/1.81 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 1.43/1.81 , clause( 10135, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 1.43/1.81 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10136, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 1.43/1.81 ~( 'c_lessequals'( U, T, X ) ) ] )
% 1.43/1.81 , clause( 10137, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 1.43/1.81 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.43/1.81 , clause( 10138, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10139, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10140, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10141, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.43/1.81 , clause( 10142, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.43/1.81 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.43/1.81 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10143, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.43/1.81 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.43/1.81 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10144, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10145, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10146, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 1.43/1.81 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10147, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 1.43/1.81 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10148, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 1.43/1.81 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10149, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10150, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 1.43/1.81 Y, Z ) ] )
% 1.43/1.81 , clause( 10151, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 1.43/1.81 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 1.43/1.81 , clause( 10152, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10153, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 1.43/1.81 Z, Y ) ] )
% 1.43/1.81 , clause( 10154, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10155, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10156, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10157, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10158, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ] )
% 1.43/1.81 , clause( 10159, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10160, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10161, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.43/1.81 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10162, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.43/1.81 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.43/1.81 T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10163, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.43/1.81 T, X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10164, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10165, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 1.43/1.81 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.43/1.81 , X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10166, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 1.43/1.81 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 1.43/1.81 , T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10167, [ =( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10168, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 1.43/1.81 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.43/1.81 , X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10169, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.43/1.81 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 1.43/1.81 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10170, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10171, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10172, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10173, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10174, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 1.43/1.81 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10175, [ =( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.43/1.81 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10176, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 1.43/1.81 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 1.43/1.81 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10177, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10178, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10179, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10180, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10181, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10182, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10183, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10184, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10185, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10186, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.43/1.81 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10187, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 1.43/1.81 , ~( =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10188, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 1.43/1.81 , clause( 10189, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10190, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.43/1.81 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.43/1.81 X ), X ) ) ] )
% 1.43/1.81 , clause( 10191, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.43/1.81 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.43/1.81 X ), X ) ) ] )
% 1.43/1.81 , clause( 10192, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.43/1.81 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.43/1.81 X ), X ) ) ] )
% 1.43/1.81 , clause( 10193, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.43/1.81 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.43/1.81 X ), X ) ) ] )
% 1.43/1.81 , clause( 10194, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 1.43/1.81 , clause( 10195, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.43/1.81 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10196, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10197, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat'
% 1.43/1.81 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10198, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), X
% 1.43/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 1.43/1.81 , clause( 10199, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 1.43/1.81 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10200, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 1.43/1.81 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10201, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Z, Y, X ) ) ] )
% 1.43/1.81 , clause( 10202, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.43/1.81 , X ), X ) ) ] )
% 1.43/1.81 , clause( 10203, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.43/1.81 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10204, [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ),
% 1.43/1.81 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10205, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10206, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.43/1.81 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.43/1.81 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10207, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.43/1.81 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.43/1.81 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10208, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10209, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10210, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.43/1.81 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10211, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10212, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10213, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10214, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10215, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 1.43/1.81 ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.43/1.81 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10216, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 1.43/1.81 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10217, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 1.43/1.81 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10218, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10219, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.43/1.81 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z,
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10220, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.43/1.81 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.43/1.81 'tc_nat' ), U ) ] )
% 1.43/1.81 , clause( 10221, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ), 'tc_nat' ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10222, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.43/1.81 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10223, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 1.43/1.81 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10224, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 1.43/1.81 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10225, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10226, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10227, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10228, [ =( 'c_Orderings_Oord__class_Omin'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10229, [ =( 'c_Orderings_Oord__class_Omin'( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10230, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 1.43/1.81 ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10231, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10232, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10233, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10234, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10235, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.43/1.81 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 1.43/1.81 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10236, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10237, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 1.43/1.81 , clause( 10238, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.43/1.81 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10239, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.43/1.81 , T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10240, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.43/1.81 , Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10241, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.43/1.81 , T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10242, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.43/1.81 , Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10243, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.43/1.81 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 1.43/1.81 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10244, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) )
% 1.43/1.81 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10245, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X )
% 1.43/1.81 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10246, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 1.43/1.81 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.43/1.81 , 'tc_Polynomial_Opoly'( X ) ), X ) ) ] )
% 1.43/1.81 , clause( 10247, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.43/1.81 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10248, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.43/1.81 , clause( 10249, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.43/1.81 , clause( 10250, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ] )
% 1.43/1.81 , clause( 10251, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y,
% 1.43/1.81 'tc_nat' ), 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ),
% 1.43/1.81 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10252, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 T, 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ), W, X ), X ) ) ] )
% 1.43/1.81 , clause( 10253, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.43/1.81 , X ), W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X
% 1.43/1.81 ), X ) ) ] )
% 1.43/1.81 , clause( 10254, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W, X ) ) ] )
% 1.43/1.81 , clause( 10255, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ] )
% 1.43/1.81 , clause( 10256, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10257, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10258, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 1.43/1.81 Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10259, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10260, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10261, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10262, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10263, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10264, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10265, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.43/1.81 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 1.43/1.81 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10266, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.43/1.81 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.43/1.81 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10267, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.43/1.81 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 1.43/1.81 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10268, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.43/1.81 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 1.43/1.81 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10269, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10270, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10271, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10272, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ] )
% 1.43/1.81 , clause( 10273, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ] )
% 1.43/1.81 , clause( 10274, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.43/1.81 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.43/1.81 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10275, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X
% 1.43/1.81 , Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10276, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10277, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10278, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10279, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.43/1.81 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10280, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.43/1.81 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 1.43/1.81 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10281, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.43/1.81 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.43/1.81 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10282, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.43/1.81 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 1.43/1.81 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10283, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10284, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.43/1.81 , X ), X ) ) ] )
% 1.43/1.81 , clause( 10285, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10286, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10287, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10288, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 1.43/1.81 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10289, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 1.43/1.81 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10290, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 1.43/1.81 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10291, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ] )
% 1.43/1.81 , clause( 10292, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ] )
% 1.43/1.81 , clause( 10293, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.43/1.81 =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.43/1.81 , clause( 10294, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 Y, Y, X ) ) ] )
% 1.43/1.81 , clause( 10295, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10296, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat'
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10297, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10298, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.43/1.81 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10299, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 1.43/1.81 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.43/1.81 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10300, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T
% 1.43/1.81 , X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.43/1.81 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10301, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10302, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10303, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10304, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10305, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10306, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10307, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10308, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10309, [ ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ) ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10310, [ ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10311, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10312, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.43/1.81 ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10313, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 1.43/1.81 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10314, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10315, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 1.43/1.81 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.43/1.81 X ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10316, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10317, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 1.43/1.81 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.43/1.81 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10318, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.43/1.81 X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10319, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.43/1.81 X ), X ), Y ) ] )
% 1.43/1.81 , clause( 10320, [ =( 'c_Orderings_Oord__class_Omax'( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 1.43/1.81 , clause( 10321, [ =( 'c_Orderings_Oord__class_Omax'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 1.43/1.81 , clause( 10322, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.43/1.81 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.43/1.81 X ), X ), X ) ] )
% 1.43/1.81 , clause( 10323, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 1.43/1.81 Z, Y, X ) ) ] )
% 1.43/1.81 , clause( 10324, [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10325, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10326, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ] )
% 1.43/1.81 , clause( 10327, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.43/1.81 =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 1.43/1.81 'c_Polynomial_OpCons'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_Polynomial_Opoly'( X ) ), X ), Z, X ), 'c_Polynomial_OpCons'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ) ) ] )
% 1.43/1.81 , clause( 10328, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.43/1.81 X ), X ) ) ] )
% 1.43/1.81 , clause( 10329, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10330, [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10331, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10332, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10333, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.43/1.81 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.43/1.81 , T, X ), X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10334, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T
% 1.43/1.81 , X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.43/1.81 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10335, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 1.43/1.81 , clause( 10336, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 1.43/1.81 , clause( 10337, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 1.43/1.81 , clause( 10338, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.43/1.81 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.43/1.81 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 1.43/1.81 , clause( 10339, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 1.43/1.81 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 1.43/1.81 , clause( 10340, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 1.43/1.81 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 Y, T, X ) ) ), =( Z, T ) ] )
% 1.43/1.81 , clause( 10341, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 1.43/1.81 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 T, Z, X ) ) ), =( Y, T ) ] )
% 1.43/1.81 , clause( 10342, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 1.43/1.81 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10343, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10344, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10345, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.43/1.81 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10346, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.43/1.81 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10347, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.43/1.81 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10348, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.43/1.81 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10349, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.43/1.81 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10350, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 1.43/1.81 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10351, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 1.43/1.81 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10352, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_OpCons'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.43/1.81 , clause( 10353, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 Z, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10354, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 X, Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10355, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 1.43/1.81 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.43/1.81 ) ), Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10356, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.43/1.81 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10357, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.43/1.81 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.43/1.81 , clause( 10358, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.43/1.81 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10359, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.43/1.81 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10360, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.43/1.81 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10361, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.43/1.81 ~( =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X
% 1.43/1.81 ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.43/1.81 , clause( 10362, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10363, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10364, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'(
% 1.43/1.81 X, Y, 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10365, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.43/1.81 X ), T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10366, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 1.43/1.81 X ) ) ] )
% 1.43/1.81 , clause( 10367, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10368, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 1.43/1.81 X ) ) ] )
% 1.43/1.81 , clause( 10369, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.43/1.81 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10370, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.43/1.81 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10371, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.43/1.81 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 1.43/1.81 , clause( 10372, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.43/1.81 , X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10373, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 1.43/1.81 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10374, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10375, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10376, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 1.43/1.81 X ) ) ] )
% 1.43/1.81 , clause( 10377, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10378, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 1.43/1.81 X ) ) ] )
% 1.43/1.81 , clause( 10379, [ ~( 'class_HOL_Ozero'( X ) ), =(
% 1.43/1.81 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10380, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 1.43/1.81 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10381, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 X, Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10382, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10383, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10384, [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10385, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10386, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 1.43/1.81 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.43/1.81 ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10387, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 1.43/1.81 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.43/1.81 , 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 1.43/1.81 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10388, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 1.43/1.81 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.43/1.81 , 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 1.43/1.81 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.43/1.81 X, T, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10389, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10390, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10391, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.43/1.81 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10392, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.43/1.81 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X
% 1.43/1.81 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10393, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.43/1.81 X ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10394, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T,
% 1.43/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10395, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( Y
% 1.43/1.81 , Z, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10396, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10397, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10398, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10399, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10400, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ),
% 1.43/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10401, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.43/1.81 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.43/1.81 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10402, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.43/1.81 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.43/1.81 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10403, [ =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.43/1.81 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10404, [ =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.43/1.81 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10405, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10406, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.43/1.81 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10407, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 1.43/1.81 ), Y ) ] )
% 1.43/1.81 , clause( 10408, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.43/1.81 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10409, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.43/1.81 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10410, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 1.43/1.81 ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10411, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 Z, Y, X ) ) ] )
% 1.43/1.81 , clause( 10412, [ =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10413, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10414, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10415, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 Z, Y, X ) ) ] )
% 1.43/1.81 , clause( 10416, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.43/1.81 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.43/1.81 , T, X ), X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10417, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.43/1.81 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 1.43/1.81 , clause( 10418, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 1.43/1.81 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10419, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.43/1.81 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10420, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.43/1.81 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10421, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 1.43/1.81 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10422, [ =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat'
% 1.43/1.81 ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10423, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.43/1.81 ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10424, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.43/1.81 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10425, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.43/1.81 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10426, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 1.43/1.81 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10427, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 1.43/1.81 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10428, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 1.43/1.81 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10429, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 1.43/1.81 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10430, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10431, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.43/1.81 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ] )
% 1.43/1.81 , clause( 10432, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10433, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10434, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10435, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10436, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10437, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10438, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10439, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 1.43/1.81 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 1.43/1.81 , clause( 10440, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.43/1.81 , clause( 10441, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 1.43/1.81 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.43/1.81 , clause( 10442, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 1.43/1.81 , clause( 10443, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10444, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 1.43/1.81 , clause( 10445, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.43/1.81 , clause( 10446, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 1.43/1.81 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 1.43/1.81 , clause( 10447, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.43/1.81 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10448, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.43/1.81 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10449, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.43/1.81 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10450, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.43/1.81 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10451, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat'
% 1.43/1.81 ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10452, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10453, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10454, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10455, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10456, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.43/1.81 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ] )
% 1.43/1.81 , clause( 10457, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.43/1.81 , T, X ) ) ), =( Z, T ) ] )
% 1.43/1.81 , clause( 10458, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.43/1.81 , T, X ) ) ), =( Y, Z ) ] )
% 1.43/1.81 , clause( 10459, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.43/1.81 X ), X ), Y ) ] )
% 1.43/1.81 , clause( 10460, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.43/1.81 'tc_nat' ) ), =( Y, Z ) ] )
% 1.43/1.81 , clause( 10461, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10462, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10463, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.43/1.81 , T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10464, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.43/1.81 , Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10465, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.43/1.81 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10466, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.43/1.81 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10467, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.43/1.81 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10468, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.43/1.81 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10469, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10470, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10471, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.43/1.81 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10472, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.43/1.81 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10473, [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.43/1.81 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10474, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10475, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.43/1.81 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ] )
% 1.43/1.81 , clause( 10476, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10477, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10478, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10479, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10480, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10481, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10482, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 1.43/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10483, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 1.43/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10484, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 1.43/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10485, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 1.43/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10486, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 1.43/1.81 Z, Y, X ) ) ] )
% 1.43/1.81 , clause( 10487, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.43/1.81 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 1.43/1.81 , clause( 10488, [ =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 1.43/1.81 ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.43/1.81 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10489, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10490, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.43/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10491, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.43/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10492, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.43/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10493, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.43/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10494, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10495, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.43/1.81 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10496, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.43/1.81 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10497, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.43/1.81 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10498, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10499, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10500, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.43/1.81 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10501, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.43/1.81 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10502, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10503, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10504, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10505, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 1.43/1.81 'c_Polynomial_OpCons'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_Polynomial_Opoly'( X ) ), X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10506, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.43/1.81 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 1.43/1.81 , clause( 10507, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.43/1.81 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.43/1.81 , X ), W, X ) ) ] )
% 1.43/1.81 , clause( 10508, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10509, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10510, [ ~( 'class_HOL_Ozero'( X ) ), ~( =(
% 1.43/1.81 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.43/1.81 , clause( 10511, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10512, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10513, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 1.43/1.81 Y, X ) ) ] )
% 1.43/1.81 , clause( 10514, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 X, T, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10515, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10516, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 1.43/1.81 Y, X ) ) ] )
% 1.43/1.81 , clause( 10517, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.43/1.81 X ) ) ] )
% 1.43/1.81 , clause( 10518, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.43/1.81 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10519, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 1.43/1.81 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 1.43/1.81 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.43/1.81 , clause( 10520, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 1.43/1.81 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 1.43/1.81 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10521, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.43/1.81 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.43/1.81 X ) ) ] )
% 1.43/1.81 , clause( 10522, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.43/1.81 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.43/1.81 , T, X ), X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10523, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10524, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 1.43/1.81 , clause( 10525, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 1.43/1.81 , clause( 10526, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10527, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X )
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10528, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X )
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10529, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 1.43/1.81 T, X ) ) ] )
% 1.43/1.81 , clause( 10530, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 T, X ) ) ] )
% 1.43/1.81 , clause( 10531, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 1.43/1.81 T, X ) ) ] )
% 1.43/1.81 , clause( 10532, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 T, X ) ) ] )
% 1.43/1.81 , clause( 10533, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X )
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10534, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X )
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10535, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.43/1.81 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 1.43/1.81 W, X ), X ) ) ] )
% 1.43/1.81 , clause( 10536, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.43/1.81 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.43/1.81 , X ), T, X ), W, X ) ) ] )
% 1.43/1.81 , clause( 10537, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.43/1.81 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 1.43/1.81 W, X ), X ) ) ] )
% 1.43/1.81 , clause( 10538, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.43/1.81 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.43/1.81 , X ), W, X ), X ) ) ] )
% 1.43/1.81 , clause( 10539, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10540, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10541, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.43/1.81 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 1.43/1.81 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 1.43/1.81 Z, X ) ) ] )
% 1.43/1.81 , clause( 10542, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10543, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.43/1.81 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10544, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.43/1.81 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.43/1.81 , clause( 10545, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10546, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10547, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10548, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10549, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10550, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10551, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10552, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10553, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.43/1.81 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10554, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10555, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Y, T, X
% 1.43/1.81 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( T, Z
% 1.43/1.81 , X ), X ) ) ] )
% 1.43/1.81 , clause( 10556, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10557, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.43/1.81 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ] )
% 1.43/1.81 , clause( 10558, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.43/1.81 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ] )
% 1.43/1.81 , clause( 10559, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.43/1.81 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.43/1.81 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10560, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.43/1.81 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.43/1.81 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10561, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.43/1.81 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 1.43/1.81 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.43/1.81 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10562, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.43/1.81 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10563, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 1.43/1.81 ), Z, 'tc_nat' ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 1.43/1.81 Z ), Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10564, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.43/1.81 ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( T, Y, X
% 1.43/1.81 ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10565, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.43/1.81 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.43/1.81 , T ), =( X, Z ) ] )
% 1.43/1.81 , clause( 10566, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.43/1.81 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.43/1.81 , T ), =( X, Z ) ] )
% 1.43/1.81 , clause( 10567, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.43/1.81 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.43/1.81 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 1.43/1.81 =( Y, T ) ] )
% 1.43/1.81 , clause( 10568, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.43/1.81 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.43/1.81 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 1.43/1.81 =( Y, T ) ] )
% 1.43/1.81 , clause( 10569, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.43/1.81 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 1.43/1.81 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 1.43/1.81 X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10570, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.43/1.81 , clause( 10571, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.43/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10572, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.43/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10573, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10574, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10575, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10576, [ =( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10577, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10578, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10579, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.43/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10580, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10581, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10582, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 1.43/1.81 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.43/1.81 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10583, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 1.43/1.81 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.43/1.81 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10584, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.43/1.81 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10585, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10586, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10587, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.43/1.81 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10588, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.43/1.81 , clause( 10589, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.43/1.81 , clause( 10590, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10591, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10592, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.43/1.81 , clause( 10593, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 1.43/1.81 'c_lessequals'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10594, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.43/1.81 Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10595, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.43/1.81 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10596, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 1.43/1.81 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10597, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.43/1.81 ) ), =( Y, Z ) ] )
% 1.43/1.81 , clause( 10598, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.43/1.81 ) ), =( Y, Z ) ] )
% 1.43/1.81 , clause( 10599, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.43/1.81 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.43/1.81 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 1.43/1.81 , clause( 10600, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 X ), X ) ) ] )
% 1.43/1.81 , clause( 10601, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 X ), X ) ) ] )
% 1.43/1.81 , clause( 10602, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.43/1.81 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.43/1.81 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10603, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.43/1.81 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.43/1.81 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10604, [ =( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10605, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10606, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.43/1.81 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.43/1.81 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10607, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.43/1.81 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.43/1.81 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10608, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.43/1.81 , U, X ), X ) ) ] )
% 1.43/1.81 , clause( 10609, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 1.43/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.43/1.81 , clause( 10610, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 1.43/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10611, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ] )
% 1.43/1.81 , clause( 10612, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.43/1.81 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10613, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 1.43/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.43/1.81 , clause( 10614, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 1.43/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10615, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 1.43/1.81 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10616, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.43/1.81 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10617, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.43/1.81 X, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10618, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 1.43/1.81 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10619, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 1.43/1.81 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10620, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_Suc'( X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 1.43/1.81 Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10621, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.43/1.81 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10622, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10623, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10624, [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.43/1.81 'tc_nat' ) ), Y ) ), =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10625, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.43/1.81 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10626, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.43/1.81 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10627, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.43/1.81 , clause( 10628, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.43/1.81 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10629, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10630, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X
% 1.43/1.81 ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10631, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10632, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10633, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10634, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.43/1.81 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ] )
% 1.43/1.81 , clause( 10635, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10636, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10637, [ =( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10638, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10639, [ ~(
% 1.43/1.81 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.43/1.81 , clause( 10640, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10641, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10642, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10643, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 1.43/1.81 , clause( 10644, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10645, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10646, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.43/1.81 , clause( 10647, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 1.43/1.81 , clause( 10648, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10649, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.43/1.81 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 X ), T, X ) ) ] )
% 1.43/1.81 , clause( 10650, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10651, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.43/1.81 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10652, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.43/1.81 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10653, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.43/1.81 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10654, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 1.43/1.81 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10655, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.43/1.81 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10656, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.43/1.81 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10657, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 1.43/1.81 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10658, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.43/1.81 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10659, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.43/1.81 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10660, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.43/1.81 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10661, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10662, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10663, [ =( 'c_Divides_Odiv__class_Omod'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 1.43/1.81 ), Z, 'tc_nat' ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10664, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10665, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10666, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10667, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.43/1.81 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10668, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10669, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10670, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10671, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 1.43/1.81 , clause( 10672, [ =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 1.43/1.81 , clause( 10673, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10674, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.43/1.81 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10675, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.43/1.81 ), Y ) ] )
% 1.43/1.81 , clause( 10676, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 1.43/1.81 , clause( 10677, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ) ] )
% 1.43/1.81 , clause( 10678, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.43/1.81 ), Y ) ] )
% 1.43/1.81 , clause( 10679, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10680, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10681, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.43/1.81 ), Y ) ] )
% 1.43/1.81 , clause( 10682, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.43/1.81 ), Y ) ] )
% 1.43/1.81 , clause( 10683, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.43/1.81 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ] )
% 1.43/1.81 , clause( 10684, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.43/1.81 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10685, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10686, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X
% 1.43/1.81 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X )
% 1.43/1.81 , Y, X ) ) ] )
% 1.43/1.81 , clause( 10687, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X
% 1.43/1.81 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X )
% 1.43/1.81 , Y, X ) ) ] )
% 1.43/1.81 , clause( 10688, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X
% 1.43/1.81 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.43/1.81 ), X ) ) ] )
% 1.43/1.81 , clause( 10689, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X
% 1.43/1.81 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.43/1.81 ), X ) ) ] )
% 1.43/1.81 , clause( 10690, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10691, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10692, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.43/1.81 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10693, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.43/1.81 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10694, [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 1.43/1.81 , clause( 10695, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 1.43/1.81 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.43/1.81 , clause( 10696, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10697, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10698, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10699, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10700, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.43/1.81 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.43/1.81 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.43/1.81 X ), Z, X ) ) ] )
% 1.43/1.81 , clause( 10701, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10702, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10703, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 1.43/1.81 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' )
% 1.43/1.81 , ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10704, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10705, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 1.43/1.81 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10706, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10707, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.43/1.81 , clause( 10708, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10709, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ] )
% 1.43/1.81 , clause( 10710, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ] )
% 1.43/1.81 , clause( 10711, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10712, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10713, [ =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ), ~(
% 1.43/1.81 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10714, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 1.43/1.81 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10715, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 1.43/1.81 ), X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10716, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10717, [ =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.43/1.81 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10718, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.43/1.81 ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10719, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( T, 'c_HOL_Otimes__class_Otimes'( Y, U,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ), =( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.43/1.81 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10720, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10721, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.81 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.43/1.81 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.43/1.81 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10722, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10723, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.43/1.81 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.43/1.81 X ), X ) ) ] )
% 1.43/1.81 , clause( 10724, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10725, [ 'c_HOL_Oord__class_Oless'( X,
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.43/1.81 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10726, [ 'c_HOL_Oord__class_Oless'( X,
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.43/1.81 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10727, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10728, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 1.43/1.81 , =( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.43/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10729, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.43/1.81 , clause( 10730, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 1.43/1.81 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10731, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.43/1.81 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.43/1.81 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10732, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.43/1.81 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10733, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10734, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10735, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10736, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.43/1.81 X ) ) ] )
% 1.43/1.81 , clause( 10737, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10738, [ 'c_HOL_Oord__class_Oless'( X,
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 1.43/1.81 Y, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10739, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 1.43/1.81 , Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10740, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 1.43/1.81 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.43/1.81 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10741, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10742, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 1.43/1.81 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 1.43/1.81 , ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10743, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.43/1.81 X ), X ) ) ] )
% 1.43/1.81 , clause( 10744, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Z, T, X ) ) ] )
% 1.43/1.81 , clause( 10745, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Z, T, X ) ) ] )
% 1.43/1.81 , clause( 10746, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.43/1.81 X ), X ) ) ] )
% 1.43/1.81 , clause( 10747, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10748, [ ~(
% 1.43/1.81 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10749, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.43/1.81 , ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y
% 1.43/1.81 , 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.81 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10750, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Y, X ) ] )
% 1.43/1.81 , clause( 10751, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y
% 1.43/1.81 , X ) ] )
% 1.43/1.81 , clause( 10752, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10753, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z,
% 1.43/1.81 Y, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10754, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10755, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 1.43/1.81 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10756, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.43/1.81 , clause( 10757, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.43/1.81 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ] )
% 1.43/1.81 , clause( 10758, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.81 , Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10759, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 1.43/1.81 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10760, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.43/1.81 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 1.43/1.81 , clause( 10761, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 1.43/1.81 , clause( 10762, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 1.43/1.81 , X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.43/1.81 )
% 1.43/1.81 , clause( 10763, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10764, [ =( 'c_HOL_Oplus__class_Oplus'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.43/1.81 , clause( 10765, [ =( 'c_Divides_Odiv__class_Omod'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), X, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10766, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.43/1.81 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10767, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.43/1.81 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.43/1.81 , clause( 10768, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 1.43/1.81 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10769, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10770, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.43/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.43/1.81 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10771, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.43/1.81 ) ) ] )
% 1.43/1.81 , clause( 10772, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.43/1.81 , Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10773, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.43/1.81 , T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10774, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.43/1.81 , T, X ), X ) ) ] )
% 1.43/1.81 , clause( 10775, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.43/1.81 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.43/1.81 , Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10776, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.43/1.81 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10777, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.43/1.81 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.43/1.81 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.43/1.81 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ] )
% 1.43/1.81 , clause( 10778, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10779, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.43/1.81 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.43/1.81 , clause( 10780, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 1.43/1.81 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 1.43/1.81 , clause( 10781, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.81 X, 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.43/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 1.43/1.81 , clause( 10782, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10783, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.43/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.43/1.81 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 1.43/1.81 , X ) ) ] )
% 1.43/1.81 , clause( 10784, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.43/1.81 ) ] )
% 1.43/1.81 , clause( 10785, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.43/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.43/1.81 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.43/1.81 ] )
% 1.43/1.81 , clause( 10786, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.43/1.81 , clause( 10787, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.81 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.43/1.81 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.43/1.82 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.43/1.82 , clause( 10788, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 1.43/1.82 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.43/1.82 Y, X ) ) ] )
% 1.43/1.82 , clause( 10789, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 1.43/1.82 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.43/1.82 Y, X ) ) ] )
% 1.43/1.82 , clause( 10790, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.43/1.82 , Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.43/1.82 , clause( 10791, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.43/1.82 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10792, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.43/1.82 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.43/1.82 Y, X ) ) ] )
% 1.43/1.82 , clause( 10793, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 1.43/1.82 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.43/1.82 Y, X ) ) ] )
% 1.43/1.82 , clause( 10794, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.43/1.82 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10795, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ),
% 1.43/1.82 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10796, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 1.43/1.82 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 1.43/1.82 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10797, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10798, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.43/1.82 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10799, [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.43/1.82 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10800, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.43/1.82 ) ) ) ] )
% 1.43/1.82 , clause( 10801, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.43/1.82 ) ) ) ] )
% 1.43/1.82 , clause( 10802, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 1.43/1.82 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10803, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X )
% 1.43/1.82 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10804, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 1.43/1.82 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10805, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'(
% 1.43/1.82 Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10806, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 1.43/1.82 , clause( 10807, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 1.43/1.82 , clause( 10808, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat'
% 1.43/1.82 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 1.43/1.82 , clause( 10809, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 1.43/1.82 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 1.43/1.82 , clause( 10810, [ ~( 'class_HOL_Ozero'( X ) ), 'c_lessequals'(
% 1.43/1.82 'c_Polynomial_Odegree'( 'c_Polynomial_OpCons'( Y, Z, X ), X ), 'c_Suc'(
% 1.43/1.82 'c_Polynomial_Odegree'( Z, X ) ), 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10811, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 1.43/1.82 ), 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10812, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.43/1.82 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 1.43/1.82 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 1.43/1.82 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10813, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ),
% 1.43/1.82 ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10814, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.43/1.82 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10815, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.43/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10816, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 1.43/1.82 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10817, [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 1.43/1.82 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) )
% 1.43/1.82 , =( Y, Z ) ] )
% 1.43/1.82 , clause( 10818, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.82 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10819, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.43/1.82 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10820, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 1.43/1.82 , clause( 10821, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 1.43/1.82 , clause( 10822, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.43/1.82 'c_Polynomial_Odegree'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Polynomial_Odegree'( Y, X ) ) ] )
% 1.43/1.82 , clause( 10823, [ ~( 'class_HOL_Ozero'( X ) ), =(
% 1.43/1.82 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( Y, X ), 'c_Suc'(
% 1.43/1.82 'c_Polynomial_Odegree'( Y, X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.43/1.82 , clause( 10824, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10825, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10826, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.43/1.82 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.43/1.82 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10827, [ ~( =( 'v_p', 'c_HOL_Ozero__class_Ozero'(
% 1.43/1.82 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ) ) ] )
% 1.43/1.82 , clause( 10828, [ ~( =( 'c_Polynomial_Odegree'( 'v_p',
% 1.43/1.82 'tc_Complex_Ocomplex' ), 'c_Suc'( X ) ) ), 'v_thesis____' ] )
% 1.43/1.82 , clause( 10829, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 1.43/1.82 ) ) ) ] )
% 1.43/1.82 , clause( 10830, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 1.43/1.82 ) ) ) ] )
% 1.43/1.82 , clause( 10831, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 1.43/1.82 'c_Polynomial_OpCons'( Y, Z, X ), X ), 'c_Suc'( 'c_Polynomial_Odegree'( Z
% 1.43/1.82 , X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) )
% 1.43/1.82 ) ] )
% 1.43/1.82 , clause( 10832, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.43/1.82 =( 'c_Polynomial_Odegree'(
% 1.43/1.82 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ), X
% 1.43/1.82 ), 'c_Polynomial_Odegree'( Y, X ) ) ] )
% 1.43/1.82 , clause( 10833, [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'(
% 1.43/1.82 Y ), 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat'
% 1.43/1.82 ) ) ) ] )
% 1.43/1.82 , clause( 10834, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 1.43/1.82 'tc_nat' ), 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ),
% 1.43/1.82 =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ] )
% 1.43/1.82 , clause( 10835, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.43/1.82 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10836, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.43/1.82 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10837, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.43/1.82 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10838, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10839, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.43/1.82 ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10840, [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ),
% 1.43/1.82 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10841, [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'(
% 1.43/1.82 Y ), 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat'
% 1.43/1.82 ) ) ) ] )
% 1.43/1.82 , clause( 10842, [ ~( =( 'c_Polynomial_Odegree'( 'v_p',
% 1.43/1.82 'tc_Complex_Ocomplex' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.43/1.82 , clause( 10843, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 1.43/1.82 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10844, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.43/1.82 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10845, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 1.43/1.82 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.43/1.82 , clause( 10846, [ ~( =( 'c_Polynomial_Odegree'( 'v_p',
% 1.43/1.82 'tc_Complex_Ocomplex' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.43/1.82 , clause( 10847, [ ~( 'v_thesis____' ) ] )
% 1.43/1.82 , clause( 10848, [ ~( =( 'c_Polynomial_Odegree'( 'v_p',
% 1.43/1.82 'tc_Complex_Ocomplex' ), 'c_Suc'( X ) ) ), 'v_thesis____' ] )
% 1.43/1.82 , clause( 10849, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.43/1.82 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 1.43/1.82 , clause( 10850, [ 'class_Ring__and__Field_Ocomm__ring'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Ocomm__ring'( X
% 1.43/1.82 ) ) ] )
% 1.43/1.82 , clause( 10851, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Ocomm__ring__1'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10852, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10853, [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' )
% 1.43/1.82 ] )
% 1.43/1.82 , clause( 10854, [ 'class_Ring__and__Field_Ocomm__ring'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10855, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10856, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 1.43/1.82 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10857, [
% 1.43/1.82 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10858, [
% 1.43/1.82 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10859, [
% 1.43/1.82 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10860, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.43/1.82 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10861, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.82 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10862, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 1.43/1.82 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10863, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 1.43/1.82 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10864, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.43/1.82 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10865, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 1.43/1.82 ] )
% 1.43/1.82 , clause( 10866, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' )
% 1.43/1.82 ] )
% 1.43/1.82 , clause( 10867, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' )
% 1.43/1.82 ] )
% 1.43/1.82 , clause( 10868, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 1.43/1.82 ] )
% 1.43/1.82 , clause( 10869, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10870, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 1.43/1.82 ] )
% 1.43/1.82 , clause( 10871, [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' )
% 1.43/1.82 ] )
% 1.43/1.82 , clause( 10872, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10873, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10874, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10875, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10876, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10877, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10878, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10879, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10880, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10881, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10882, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10883, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10884, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10885, [ 'class_HOL_Ozero'( 'tc_nat' ) ] )
% 1.43/1.82 , clause( 10886, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10887, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10888, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10889, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10890, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10891, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10892, [ 'class_RealVector_Oreal__normed__algebra'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10893, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10894, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10895, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10896, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10897, [ 'class_OrderedGroup_Oab__group__add'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10898, [ 'class_Ring__and__Field_Omult__zero'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10899, [ 'class_Ring__and__Field_Osemiring'(
% 1.43/1.82 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10900, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex'
% 1.43/1.82 ) ] )
% 1.43/1.82 , clause( 10901, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex'
% 1.43/1.82 ) ] )
% 1.43/1.82 , clause( 10902, [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' )
% 1.43/1.82 ] )
% 1.43/1.82 , clause( 10903, [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' )
% 1.43/1.82 ] )
% 1.43/1.82 , clause( 10904, [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10905, [ 'class_HOL_Ozero'( 'tc_Complex_Ocomplex' ) ] )
% 1.43/1.82 , clause( 10906, [
% 1.43/1.82 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10907, [
% 1.43/1.82 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10908, [
% 1.43/1.82 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10909, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10910, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10911, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10912, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10913, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10914, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.43/1.82 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 1.43/1.82 , clause( 10915, [ 'class_Ring__and__Field_Oordered__ring__strict'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10916, [ 'class_OrderedGroup_Opordered__ab__group__add'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10917, [ 'class_OrderedGroup_Oordered__ab__group__add'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10918, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.43/1.82 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 1.43/1.82 , clause( 10919, [ 'class_Ring__and__Field_Opordered__semiring'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10920, [ 'class_Ring__and__Field_Oordered__semiring'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10921, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 1.43/1.82 )
% 1.43/1.82 , clause( 10922, [ 'class_Ring__and__Field_Oordered__semidom'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10923, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.43/1.82 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 1.43/1.82 , clause( 10924, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.43/1.82 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 1.43/1.82 , clause( 10925, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.43/1.82 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 1.43/1.82 , clause( 10926, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10927, [ 'class_Ring__and__Field_Opordered__ring'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10928, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.43/1.82 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 1.43/1.82 , clause( 10929, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10930, [ 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10931, [ 'class_Ring__and__Field_Omult__mono1'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10932, [ 'class_OrderedGroup_Oab__group__add'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Oab__group__add'( X
% 1.43/1.82 ) ) ] )
% 1.43/1.82 , clause( 10933, [ 'class_Ring__and__Field_Omult__zero'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.43/1.82 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 1.43/1.82 , clause( 10934, [ 'class_Ring__and__Field_Omult__mono'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.43/1.82 X ) ) ] )
% 1.43/1.82 , clause( 10935, [ 'class_Ring__and__Field_Osemiring'(
% 1.43/1.82 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.43/1.82 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 1.43/1.82 , clause( 10936, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Polynomial_Opoly'(
% 1.43/1.82 X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ] )
% 1.43/1.82 , clause( 10937, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Polynomial_Opoly'(
% 1.43/1.82 X ) ), ~( 'class_OrderedGroup_Oab__group__add'( X ) ) ] )
% 1.43/1.82 , clause( 10938, [ 'class_Divides_Osemiring__div'( 'tc_Polynomial_Opoly'( X
% 1.43/1.82 ) ), ~( 'class_Ring__and__Field_Ofield'( X ) ) ] )
% 1.43/1.82 , clause( 10939, [ 'class_Ring__and__Field_Oring'( 'tc_Polynomial_Opoly'( X
% 1.43/1.82 ) ), ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ) ] )
% 1.43/1.82 , clause( 10940, [ 'class_Ring__and__Field_Oidom'( 'tc_Polynomial_Opoly'( X
% 1.43/1.82 ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ] )
% 1.43/1.82 , clause( 10941, [ 'class_Orderings_Opreorder'( 'tc_Polynomial_Opoly'( X )
% 1.43/1.82 ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.43/1.82 , clause( 10942, [ 'class_Orderings_Olinorder'( 'tc_Polynomial_Opoly'( X )
% 1.43/1.82 ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.43/1.82 , clause( 10943, [ 'class_Divides_Oring__div'( 'tc_Polynomial_Opoly'( X ) )
% 1.43/1.82 , ~( 'class_Ring__and__Field_Ofield'( X ) ) ] )
% 1.43/1.82 , clause( 10944, [ 'class_Orderings_Oorder'( 'tc_Polynomial_Opoly'( X ) ),
% 1.43/1.82 ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.43/1.82 , clause( 10945, [ 'class_Int_Onumber__ring'( 'tc_Polynomial_Opoly'( X ) )
% 1.43/1.82 , ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ] )
% 1.43/1.82 , clause( 10946, [ 'class_HOL_Ozero'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.43/1.82 'class_HOL_Ozero'( X ) ) ] )
% 1.43/1.82 ] ).
% 1.43/1.82
% 1.43/1.82
% 1.43/1.82
% 1.43/1.82 subsumption(
% 1.43/1.82 clause( 22, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 1.43/1.82 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 1.43/1.82 , clause( 10080, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 1.43/1.82 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 1.43/1.82 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.43/1.82 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.43/1.82
% 1.43/1.82
% 1.43/1.82 subsumption(
% 1.43/1.82 clause( 23, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.43/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.43/1.82 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.43/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 1.43/1.82 , clause( 10081, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.43/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.43/1.82 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.43/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 1.43/1.82 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.43/1.82 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.43/1.82
% 1.43/1.82
% 1.43/1.82 subsumption(
% 1.43/1.82 clause( 68, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.43/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ),Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------