TSTP Solution File: ALG434-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG434-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 12:10:56 EDT 2022
% Result : Unsatisfiable 12.07s 12.43s
% Output : Refutation 12.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG434-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Wed Jun 8 02:45:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.82/1.22 *** allocated 10000 integers for termspace/termends
% 0.82/1.22 *** allocated 10000 integers for clauses
% 0.82/1.22 *** allocated 10000 integers for justifications
% 0.82/1.22 Bliksem 1.12
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 Automatic Strategy Selection
% 0.82/1.22
% 0.82/1.22 Clauses:
% 0.82/1.22 [
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_Polynomial_Osmult'( Z, T, X ),
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'( U, T, X ) ) ), =( U
% 0.82/1.22 , 'c_Polynomial_Opoly'( Y, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly'( 'c_Polynomial_OpCons'( Y, Z, X ), T, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 0.82/1.22 'c_Polynomial_Opoly'( Z, T, X ), X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Opoly'(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), Y, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.82/1.22 X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly'( 'c_Polynomial_Osmult'( Y, Z, X ), T, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Z, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.82/1.22 'c_Polynomial_Opoly'( Y, Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Ominus__class_Ominus'(
% 0.82/1.22 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.82/1.22 'c_Polynomial_OpCons'( T, U, X ), 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_Polynomial_OpCons'( 'c_HOL_Ominus__class_Ominus'( Y, T, X ),
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Z, U, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.82/1.22 , 'tc_Polynomial_Opoly'( X ) ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.82/1.22 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_OpCons'( T, Z, X ) ) ),
% 0.82/1.22 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.82/1.22 'c_Polynomial_OpCons'( T, U, X ), 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_Polynomial_OpCons'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Z, U, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Osmult'( Y, 'c_Polynomial_OpCons'( Z, T, X ), X ),
% 0.82/1.22 'c_Polynomial_OpCons'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_Polynomial_Osmult'( Y, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_OpCons'(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.82/1.22 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Y, T ) ],
% 0.82/1.22 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.82/1.22 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Z, U ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Opoly'( Y,
% 0.82/1.22 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_Polynomial_OpCons'(
% 0.82/1.22 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y, 'tc_Polynomial_Opoly'( X ) ) )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( 'c_Polynomial_Opoly'(
% 0.82/1.22 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_Polynomial_OpCons'(
% 0.82/1.22 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y, 'tc_Polynomial_Opoly'( X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( 'c_Polynomial_Opoly'(
% 0.82/1.22 Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'( Z,
% 0.82/1.22 'c_Polynomial_OpCons'( 'c_HOL_Oone__class_Oone'( X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Opoly'( Y,
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'( Z
% 0.82/1.22 , 'c_Polynomial_OpCons'( 'c_HOL_Oone__class_Oone'( X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 0.82/1.22 'c_Polynomial_OpCons'( T, Z, X ), 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.82/1.22 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.82/1.22 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.82/1.22 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.82/1.22 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.82/1.22 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.82/1.22 , X ) ) ), =( Y, Z ) ],
% 0.82/1.22 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.82/1.22 , X ) ) ), =( Y, Z ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, Z ), ~(
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( T, U, Z, W, X ) ), ~(
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( T, U, Y, V0, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, Z ), ~(
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( T, U, W, Z, X ) ), ~(
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( T, U, V0, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly__gcd'( 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.82/1.22 , Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.82/1.22 X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.82/1.22 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.82/1.22 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.82/1.22 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 0.82/1.22 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( T, U, X ), X ),
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, Z ), ~(
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( Z, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), T, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.82/1.22 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.82/1.22 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), T, 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_Divides_Odiv__class_Omod'( Y, Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.82/1.22 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Z, T, X ) ), =( Z,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Z, Y, T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Z, T, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( Z, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Y, T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.82/1.22 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.82/1.22 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.82/1.22 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 0.82/1.22 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 0.82/1.22 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 0.82/1.22 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.82/1.22 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y,
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Y ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( Z, Y, X ), X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), Z ) ],
% 0.82/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 0.82/1.22 Y, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.82/1.22 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Odiv'(
% 0.82/1.22 Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.82/1.22 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Odiv'(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.82/1.22 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.82/1.22 T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.82/1.22 X ), Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.82/1.22 T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.82/1.22 X ), T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.82/1.22 T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.82/1.22 X ), T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), T, 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 0.82/1.22 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 0.82/1.22 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Z, Y, X ),
% 0.82/1.22 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.82/1.22 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 0.82/1.22 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.82/1.22 X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 0.82/1.22 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.82/1.22 X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.82/1.22 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.82/1.22 X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.82/1.22 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.82/1.22 X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 Y, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 Y, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_Polynomial_OpCons'( Y, Z, X ), T,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_Polynomial_Osmult'( Y, T, X ), 'c_Polynomial_OpCons'(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_OpCons'( Z, T, X ),
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_Polynomial_Osmult'( Z, Y, X ), 'c_Polynomial_OpCons'(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.82/1.22 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.82/1.22 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.82/1.22 ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.82/1.22 ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.82/1.22 ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.82/1.22 ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.82/1.22 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.82/1.22 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.82/1.22 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 0.82/1.22 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 0.82/1.22 ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), U, 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( Y, T, Z, U, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Osmult'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_Osmult'( Y, T, X ),
% 0.82/1.22 'c_Polynomial_Osmult'( Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, T, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 0.82/1.22 , X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( Y, Z, 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_Divides_Odiv__class_Omod'( Y, Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.82/1.22 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.82/1.22 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly__gcd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T, X ), X ),
% 0.82/1.22 'c_Polynomial_Opoly__gcd'( Z, 'c_Polynomial_Opoly__gcd'( Y, T, X ), X ) )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly__gcd'( 'c_Polynomial_Opoly__gcd'( Y, Z, X ), T, X ),
% 0.82/1.22 'c_Polynomial_Opoly__gcd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T, X ), X ) )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.82/1.22 ), Y ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly__gcd'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Polynomial_Opoly__gcd'( Y, Z, X ) )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly__gcd'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Z, X ), 'c_Polynomial_Opoly__gcd'( Y, Z, X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.82/1.22 , Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.82/1.22 , Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.82/1.22 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.82/1.22 , T, X ), X ), T, X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.82/1.22 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.82/1.22 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.82/1.22 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.82/1.22 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.82/1.22 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.82/1.22 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.82/1.22 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.82/1.22 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.82/1.22 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.82/1.22 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Z, 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.82/1.22 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.82/1.22 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.82/1.22 , T, X ) ) ), =( Z, T ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.82/1.22 , T, X ) ) ), =( Y, Z ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_Polynomial_Opoly'( X ) ), T ),
% 0.82/1.22 ~( 'c_Polynomial_Opdivmod__rel'( Y, Z, U, T, X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.82/1.22 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 0.82/1.22 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.82/1.22 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.82/1.22 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.82/1.22 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.82/1.22 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.82/1.22 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.82/1.22 ) ), =( Y, Z ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.82/1.22 ) ), =( Y, Z ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.82/1.22 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.82/1.22 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.82/1.22 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.82/1.22 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.82/1.22 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.82/1.22 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.82/1.22 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.82/1.22 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.82/1.22 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.82/1.22 , U, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), T
% 0.82/1.22 , X ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.82/1.22 X ), Z, X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 0.82/1.22 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.82/1.22 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.82/1.22 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), U, 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, W, 'tc_Polynomial_Opoly'( X ) ), V0,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ), ~( 'c_Polynomial_Opdivmod__rel'( V1, T
% 0.82/1.22 , U, W, X ) ), ~( 'c_Polynomial_Opdivmod__rel'( Y, Z, V1, V0, X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.82/1.22 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 0.82/1.22 , X ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 0.82/1.22 , X ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.82/1.22 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ), Y ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.82/1.22 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.82/1.22 ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.82/1.22 ), Y ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.82/1.22 ), Y ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.82/1.22 ), Y ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.82/1.22 ), Y ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.82/1.22 ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.82/1.22 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.82/1.22 X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 0.82/1.22 Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 0.82/1.22 Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.82/1.22 , T, X ), X ), T, X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.82/1.22 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.82/1.22 X ) ) ), =( Z, T ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.82/1.22 X ) ) ), =( Z, T ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.82/1.22 X ) ) ), =( Y, T ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Y, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.82/1.22 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.82/1.22 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.82/1.22 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.82/1.22 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( 'c_Polynomial_Osmult'(
% 0.82/1.22 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 0.82/1.22 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), =( Y,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.82/1.22 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, 'c_Polynomial_Osmult'( Z, T, X ),
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_Divides_Odiv__class_Omod'( Y, T,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Y, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Y, X ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.82/1.22 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.82/1.22 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Osmult'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.82/1.22 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.82/1.22 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.82/1.22 , X ), W, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 0.82/1.22 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), T, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 0.82/1.22 , X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), T, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Z, T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Y, X ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.82/1.22 ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.82/1.22 ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.82/1.22 X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.82/1.22 X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.82/1.22 X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 0.82/1.22 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Z, X
% 0.82/1.22 ), 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.82/1.22 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.82/1.22 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 0.82/1.22 X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.82/1.22 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.82/1.22 , T, X ), X ), T, X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.82/1.22 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 0.82/1.22 Y, Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Z, 'c_Divides_Odiv__class_Odiv'( Y, T, X ), X
% 0.82/1.22 ) ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( T, 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), X
% 0.82/1.22 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.82/1.22 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_Polynomial_Opoly'( X ) ), T ),
% 0.82/1.22 ~( 'c_Polynomial_Opdivmod__rel'( Y, Z, T, U, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.82/1.22 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 0.82/1.22 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 0.82/1.22 Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Osmult'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_Osmult'( Y, T, X ),
% 0.82/1.22 'c_Polynomial_Osmult'( Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.82/1.22 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.82/1.22 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.82/1.22 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 0.82/1.22 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.82/1.22 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.82/1.22 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.82/1.22 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.82/1.22 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.82/1.22 , X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.82/1.22 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 0.82/1.22 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 0.82/1.22 X ), Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ),
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 0.82/1.22 ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 0.82/1.22 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.82/1.22 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 0.82/1.22 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 0.82/1.22 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.82/1.22 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.82/1.22 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.82/1.22 X ), Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_Polynomial_Opoly__gcd'( Z, Y, X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 0.82/1.22 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.82/1.22 X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_Polynomial_Opoly__gcd'( Z,
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_Polynomial_Opoly'( X ) ), X ) ),
% 0.82/1.22 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Osmult'(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.82/1.22 X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), T, 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.82/1.22 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.82/1.22 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.82/1.22 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.82/1.22 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 0.82/1.22 , X ), X ), Y ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 0.82/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ),
% 0.82/1.22 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Oplus__class_Oplus'(
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Y, Z, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), Z, 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Omod'( Y, Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 0.82/1.22 , X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.82/1.22 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 0.82/1.22 , X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 0.82/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.82/1.22 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 0.82/1.22 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Osmult'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Osmult'( Y
% 0.82/1.22 , 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 0.82/1.22 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T
% 0.82/1.22 , X ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 0.82/1.22 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'(
% 0.82/1.22 X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T
% 0.82/1.22 , X ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 0.82/1.22 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'(
% 0.82/1.22 X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Opoly__gcd'( Y, Z, X
% 0.82/1.22 ), Y, 'tc_Polynomial_Opoly'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Opoly__gcd'( Y, Z, X
% 0.82/1.22 ), Z, 'tc_Polynomial_Opoly'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'(
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Z, 'tc_Polynomial_Opoly'( X ) )
% 0.82/1.22 ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 0.82/1.22 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 0.82/1.22 ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.82/1.22 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.82/1.22 Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.82/1.22 , X ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Osmult'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ominus__class_Ominus'(
% 0.82/1.22 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_Osmult'( Y, T, X ),
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 0.82/1.22 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'(
% 0.82/1.22 T, Z, X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 0.82/1.22 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'(
% 0.82/1.22 Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.82/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Osmult'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.82/1.22 'c_Polynomial_Osmult'( Y, Z, X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.82/1.22 , X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.82/1.22 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.82/1.22 , X ), Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 0.82/1.22 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 0.82/1.22 Z, X ), X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 0.82/1.22 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 0.82/1.22 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.82/1.22 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.82/1.22 'c_Polynomial_Osmult'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( 'c_Polynomial_Osmult'( Y, Z, X ), T,
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Y,
% 0.82/1.22 'c_Divides_Odiv__class_Omod'( Z, T, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 0.82/1.22 , =( T, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( T, Z, X
% 0.82/1.22 ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 0.82/1.22 T, 'tc_Polynomial_Opoly'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.82/1.22 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, 'tc_Polynomial_Opoly'(
% 0.82/1.22 X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 0.82/1.22 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( T,
% 0.82/1.22 Z, X ), 'tc_Polynomial_Opoly'( X ) ) ), =( T, 'c_HOL_Ozero__class_Ozero'(
% 0.82/1.22 X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( Z, T, X
% 0.82/1.22 ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 0.82/1.22 ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 0.82/1.22 , =( T, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( T, Y, X ),
% 0.82/1.22 Z, 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 0.82/1.22 T, 'tc_Polynomial_Opoly'( X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.82/1.22 Z, T, 'tc_Polynomial_Opoly'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.82/1.22 ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 0.82/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z
% 0.82/1.22 , 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.82/1.22 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.82/1.22 , X ), Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.82/1.22 , X ), Z, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.82/1.22 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.82/1.22 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 0.82/1.22 X ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.82/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 0.82/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'(
% 0.87/1.22 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.22 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ],
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.87/1.22 'c_Polynomial_Opdivmod__rel'( 'c_Polynomial_Osmult'( Y, Z, X ), T,
% 0.87/1.22 'c_Polynomial_Osmult'( Y, U, X ), 'c_Polynomial_Osmult'( Y, W, X ), X ),
% 0.87/1.22 ~( 'c_Polynomial_Opdivmod__rel'( Z, T, U, W, X ) ) ],
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 0.87/1.22 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.87/1.22 'c_Polynomial_Osmult'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.87/1.22 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.22 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_Osmult'( Y, T, X ),
% 0.87/1.22 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.87/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.87/1.22 , T, X ), X ) ) ],
% 0.87/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.87/1.22 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.87/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.87/1.22 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.87/1.22 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.87/1.22 'c_Divides_Odiv__class_Odiv'( 'c_Polynomial_Osmult'( Y, Z, X ), T,
% 0.87/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Y,
% 0.87/1.22 'c_Divides_Odiv__class_Odiv'( Z, T, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.22 , Y, X ), X ) ],
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.22 , Z, X ), X ) ],
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.22 , Z, X ), X ) ],
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 0.87/1.22 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( T, Y,
% 0.87/1.22 X ), Z, 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( Z, T, X
% 0.87/1.22 ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 0.87/1.22 ) ],
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 0.87/1.22 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 0.87/1.22 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.87/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_Osmult'( Z, T, X ),
% 0.87/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Z,
% 0.87/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.87/1.22 'c_HOL_Otimes__class_Otimes'( 'c_Polynomial_Osmult'( Y, Z, X ), T,
% 0.87/1.22 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Y,
% 0.87/1.22 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p', 'v_q',
% 0.87/1.22 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ],
% 0.87/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.87/1.22 'c_Polynomial_Osmult'( Y, 'c_Polynomial_Osmult'( Z, T, X ), X ),
% 0.87/1.22 'c_Polynomial_Osmult'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ) )
% 0.87/1.22 ],
% 0.87/1.22 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_q', 'c_Polynomial_Osmult'(
% 0.87/1.22 'v_a', 'v_q', 'tc_Complex_Ocomplex' ), 'tc_Polynomial_Opoly'(
% 0.87/1.22 'tc_Complex_Ocomplex' ) ) ],
% 0.87/1.22 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p', 'v_q',
% 0.87/1.22 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ],
% 0.87/1.22 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p', 'c_Polynomial_Osmult'(
% 0.87/1.22 'v_a', 'v_q', 'tc_Complex_Ocomplex' ), 'tc_Polynomial_Opoly'(
% 0.87/1.22 'tc_Complex_Ocomplex' ) ) ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_Polynomial_Opoly'(
% 0.87/1.22 X ) ), ~( 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_Complex_Ocomplex'
% 0.87/1.22 ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.87/1.22 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 0.87/1.22 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.87/1.22 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 0.87/1.22 ],
% 0.87/1.22 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 0.87/1.22 ],
% 0.87/1.22 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_HOL_Ozero'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.87/1.22 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 0.87/1.22 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.87/1.22 X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 0.87/1.22 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 0.87/1.22 ,
% 0.87/1.22 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.87/1.22 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.87/1.22 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Polynomial_Opoly'(
% 0.87/1.22 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Polynomial_Opoly'(
% 0.87/1.22 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Polynomial_Opoly'( X
% 0.87/1.22 ) ), ~( 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Polynomial_Opoly'( X
% 0.87/1.22 ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Polynomial_Opoly'( X
% 0.87/1.22 ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Polynomial_Opoly'( X
% 0.87/1.22 ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Polynomial_Opoly'( X )
% 0.87/1.22 ), ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Polynomial_Opoly'( X ) )
% 0.87/1.22 , ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Polynomial_Opoly'( X ) )
% 0.87/1.22 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Polynomial_Opoly'( X ) )
% 0.87/1.22 , ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Polynomial_Opoly'( X ) )
% 0.87/1.22 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Polynomial_Opoly'( X ) )
% 0.87/1.22 , ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Polynomial_Opoly'( X ) )
% 0.87/1.22 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Polynomial_Opoly'( X ) )
% 0.87/1.22 , ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Polynomial_Opoly'( X ) ),
% 0.87/1.22 ~( 'class_OrderedGroup_Oab__group__add'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.87/1.22 ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Polynomial_Opoly'( X ) ),
% 0.87/1.22 ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.87/1.22 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Osemiring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.87/1.22 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.87/1.22 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.87/1.22 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.87/1.22 'class_OrderedGroup_Oab__group__add'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Oring__1'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.87/1.22 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ],
% 0.87/1.22 [ 'class_Divides_Osemiring__div'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.87/1.22 'class_Ring__and__Field_Ofield'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Oring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.87/1.22 'class_Ring__and__Field_Ocomm__ring'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Oidom'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.87/1.22 'class_Ring__and__Field_Oidom'( X ) ) ],
% 0.87/1.22 [ 'class_Ring__and__Field_Odvd'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.87/1.22 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 1.95/2.34 [ 'class_Divides_Oring__div'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.95/2.34 'class_Ring__and__Field_Ofield'( X ) ) ],
% 1.95/2.34 [ 'class_Int_Onumber__ring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.95/2.34 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ],
% 1.95/2.34 [ 'class_Power_Opower'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.95/2.34 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 1.95/2.34 [ 'class_HOL_Ozero'( 'tc_Polynomial_Opoly'( X ) ), ~( 'class_HOL_Ozero'(
% 1.95/2.34 X ) ) ]
% 1.95/2.34 ] .
% 1.95/2.34
% 1.95/2.34
% 1.95/2.34 percentage equality = 0.373695, percentage horn = 0.941606
% 1.95/2.34 This is a problem with some equality
% 1.95/2.34
% 1.95/2.34
% 1.95/2.34
% 1.95/2.34 Options Used:
% 1.95/2.34
% 1.95/2.34 useres = 1
% 1.95/2.34 useparamod = 1
% 1.95/2.34 useeqrefl = 1
% 1.95/2.34 useeqfact = 1
% 1.95/2.34 usefactor = 1
% 1.95/2.34 usesimpsplitting = 0
% 1.95/2.34 usesimpdemod = 5
% 1.95/2.34 usesimpres = 3
% 1.95/2.34
% 1.95/2.34 resimpinuse = 1000
% 1.95/2.34 resimpclauses = 20000
% 1.95/2.34 substype = eqrewr
% 1.95/2.34 backwardsubs = 1
% 1.95/2.34 selectoldest = 5
% 1.95/2.34
% 1.95/2.34 litorderings [0] = split
% 1.95/2.34 litorderings [1] = extend the termordering, first sorting on arguments
% 1.95/2.34
% 1.95/2.34 termordering = kbo
% 1.95/2.34
% 1.95/2.34 litapriori = 0
% 1.95/2.34 termapriori = 1
% 1.95/2.34 litaposteriori = 0
% 1.95/2.34 termaposteriori = 0
% 1.95/2.34 demodaposteriori = 0
% 1.95/2.34 ordereqreflfact = 0
% 1.95/2.34
% 1.95/2.34 litselect = negord
% 1.95/2.34
% 1.95/2.34 maxweight = 15
% 1.95/2.34 maxdepth = 30000
% 1.95/2.34 maxlength = 115
% 1.95/2.34 maxnrvars = 195
% 1.95/2.34 excuselevel = 1
% 1.95/2.34 increasemaxweight = 1
% 1.95/2.34
% 1.95/2.34 maxselected = 10000000
% 1.95/2.34 maxnrclauses = 10000000
% 1.95/2.34
% 1.95/2.34 showgenerated = 0
% 1.95/2.34 showkept = 0
% 1.95/2.34 showselected = 0
% 1.95/2.34 showdeleted = 0
% 1.95/2.34 showresimp = 1
% 1.95/2.34 showstatus = 2000
% 1.95/2.34
% 1.95/2.34 prologoutput = 1
% 1.95/2.34 nrgoals = 5000000
% 1.95/2.34 totalproof = 1
% 1.95/2.34
% 1.95/2.34 Symbols occurring in the translation:
% 1.95/2.34
% 1.95/2.34 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.95/2.34 . [1, 2] (w:1, o:98, a:1, s:1, b:0),
% 1.95/2.34 ! [4, 1] (w:0, o:50, a:1, s:1, b:0),
% 1.95/2.34 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.95/2.34 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.95/2.34 'class_Ring__and__Field_Ocomm__semiring__0' [40, 1] (w:1, o:57, a:1
% 1.95/2.34 , s:1, b:0),
% 1.95/2.34 'c_Polynomial_Osmult' [44, 3] (w:1, o:125, a:1, s:1, b:0),
% 1.95/2.34 'tc_Polynomial_Opoly' [45, 1] (w:1, o:58, a:1, s:1, b:0),
% 1.95/2.34 'c_HOL_Oplus__class_Oplus' [46, 3] (w:1, o:126, a:1, s:1, b:0),
% 1.95/2.34 'c_Polynomial_OpCons' [48, 3] (w:1, o:127, a:1, s:1, b:0),
% 1.95/2.34 'c_Polynomial_Opoly' [49, 3] (w:1, o:128, a:1, s:1, b:0),
% 1.95/2.34 'c_HOL_Otimes__class_Otimes' [52, 3] (w:1, o:129, a:1, s:1, b:0),
% 1.95/2.34 'class_Ring__and__Field_Oidom' [53, 1] (w:1, o:59, a:1, s:1, b:0),
% 1.95/2.34 'c_HOL_Ozero__class_Ozero' [54, 1] (w:1, o:60, a:1, s:1, b:0),
% 1.95/2.34 'class_Ring__and__Field_Ocomm__ring' [55, 1] (w:1, o:55, a:1, s:1, b:
% 1.95/2.34 0),
% 1.95/2.34 'c_HOL_Ouminus__class_Ouminus' [56, 2] (w:1, o:123, a:1, s:1, b:0),
% 1.95/2.34 'c_HOL_Ominus__class_Ominus' [57, 3] (w:1, o:130, a:1, s:1, b:0),
% 1.95/2.34 'class_OrderedGroup_Oab__group__add' [58, 1] (w:1, o:61, a:1, s:1, b:
% 1.95/2.34 0),
% 1.95/2.34 'class_OrderedGroup_Ocomm__monoid__add' [60, 1] (w:1, o:62, a:1, s:1
% 1.95/2.34 , b:0),
% 1.95/2.34 'class_HOL_Ozero' [61, 1] (w:1, o:63, a:1, s:1, b:0),
% 1.95/2.34 'c_HOL_Oone__class_Oone' [62, 1] (w:1, o:64, a:1, s:1, b:0),
% 1.95/2.34 'c_Ring__and__Field_Odvd__class_Odvd' [63, 3] (w:1, o:131, a:1, s:1
% 1.95/2.34 , b:0),
% 1.95/2.34 'class_Ring__and__Field_Ono__zero__divisors' [64, 1] (w:1, o:66, a:1
% 1.95/2.34 , s:1, b:0),
% 1.95/2.34 'class_Ring__and__Field_Oring__no__zero__divisors' [65, 1] (w:1, o:67
% 1.95/2.34 , a:1, s:1, b:0),
% 1.95/2.34 'class_Ring__and__Field_Ozero__neq__one' [66, 1] (w:1, o:68, a:1, s:1
% 1.95/2.34 , b:0),
% 1.95/2.34 'class_Divides_Osemiring__div' [67, 1] (w:1, o:70, a:1, s:1, b:0),
% 1.95/2.34 'c_Divides_Odiv__class_Odiv' [68, 3] (w:1, o:132, a:1, s:1, b:0),
% 1.95/2.34 'class_OrderedGroup_Ogroup__add' [69, 1] (w:1, o:71, a:1, s:1, b:0),
% 1.95/2.34
% 1.95/2.34 'class_Ring__and__Field_Ocomm__semiring__1' [70, 1] (w:1, o:72, a:1
% 1.95/2.34 , s:1, b:0),
% 1.95/2.34 'class_Lattices_Oboolean__algebra' [75, 1] (w:1, o:73, a:1, s:1, b:0)
% 1.95/2.34 ,
% 1.95/2.34 'class_Ring__and__Field_Ofield' [77, 1] (w:1, o:74, a:1, s:1, b:0),
% 1.95/2.34 'c_Polynomial_Opdivmod__rel' [81, 5] (w:1, o:136, a:1, s:1, b:0),
% 1.95/2.34 'c_Polynomial_Opoly__gcd' [83, 3] (w:1, o:133, a:1, s:1, b:0),
% 1.95/2.34 'class_Ring__and__Field_Oordered__idom' [84, 1] (w:1, o:75, a:1, s:1
% 1.95/2.34 , b:0),
% 1.95/2.34 'c_HOL_Oabs__class_Oabs' [85, 2] (w:1, o:124, a:1, s:1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Oring' [86, 1] (w:1, o:76, a:1, s:1, b:0),
% 11.60/11.98 'class_OrderedGroup_Oab__semigroup__idem__mult' [87, 1] (w:1, o:77
% 11.60/11.98 , a:1, s:1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Omult__zero' [88, 1] (w:1, o:65, a:1, s:1, b:
% 11.60/11.98 0),
% 11.60/11.98 'class_Power_Opower' [89, 1] (w:1, o:89, a:1, s:1, b:0),
% 11.60/11.98 'c_Power_Opower__class_Opower' [91, 3] (w:1, o:134, a:1, s:1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Oring__1__no__zero__divisors' [92, 1] (w:1
% 11.60/11.98 , o:90, a:1, s:1, b:0),
% 11.60/11.98 'c_Divides_Odiv__class_Omod' [95, 3] (w:1, o:135, a:1, s:1, b:0),
% 11.60/11.98 'class_Int_Onumber__ring' [96, 1] (w:1, o:91, a:1, s:1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Oordered__ring__strict' [98, 1] (w:1, o:92
% 11.60/11.98 , a:1, s:1, b:0),
% 11.60/11.98 'class_OrderedGroup_Ocomm__monoid__mult' [99, 1] (w:1, o:78, a:1, s:1
% 11.60/11.98 , b:0),
% 11.60/11.98 'class_Ring__and__Field_Odvd' [100, 1] (w:1, o:94, a:1, s:1, b:0),
% 11.60/11.98 'class_Divides_Oring__div' [104, 1] (w:1, o:69, a:1, s:1, b:0),
% 11.60/11.98 'class_OrderedGroup_Oab__semigroup__mult' [105, 1] (w:1, o:79, a:1
% 11.60/11.98 , s:1, b:0),
% 11.60/11.98 'class_RealVector_Oreal__normed__algebra' [106, 1] (w:1, o:95, a:1
% 11.60/11.98 , s:1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Ocomm__semiring' [111, 1] (w:1, o:93, a:1, s:
% 11.60/11.98 1, b:0),
% 11.60/11.98 'class_OrderedGroup_Opordered__ab__group__add__abs' [112, 1] (w:1, o:
% 11.60/11.98 81, a:1, s:1, b:0),
% 11.60/11.98 'class_OrderedGroup_Oordered__ab__group__add' [113, 1] (w:1, o:80, a:
% 11.60/11.98 1, s:1, b:0),
% 11.60/11.98 'class_OrderedGroup_Olordered__ab__group__add' [115, 1] (w:1, o:82
% 11.60/11.98 , a:1, s:1, b:0),
% 11.60/11.98 'class_OrderedGroup_Omonoid__mult' [117, 1] (w:1, o:83, a:1, s:1, b:0
% 11.60/11.98 ),
% 11.60/11.98 'class_OrderedGroup_Oab__semigroup__add' [118, 1] (w:1, o:84, a:1, s:
% 11.60/11.98 1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Osemiring' [121, 1] (w:1, o:97, a:1, s:1, b:0
% 11.60/11.98 ),
% 11.60/11.98 'class_OrderedGroup_Omonoid__add' [124, 1] (w:1, o:85, a:1, s:1, b:0)
% 11.60/11.98 ,
% 11.60/11.98 'class_OrderedGroup_Ocancel__ab__semigroup__add' [125, 1] (w:1, o:86
% 11.60/11.98 , a:1, s:1, b:0),
% 11.60/11.98 'class_OrderedGroup_Ocancel__semigroup__add' [126, 1] (w:1, o:87, a:1
% 11.60/11.98 , s:1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Oring__1' [128, 1] (w:1, o:96, a:1, s:1, b:0)
% 11.60/11.98 ,
% 11.60/11.98 'class_Ring__and__Field_Ocomm__ring__1' [130, 1] (w:1, o:56, a:1, s:1
% 11.60/11.98 , b:0),
% 11.60/11.98 'v_p' [131, 0] (w:1, o:45, a:1, s:1, b:0),
% 11.60/11.98 'v_q' [132, 0] (w:1, o:46, a:1, s:1, b:0),
% 11.60/11.98 'tc_Complex_Ocomplex' [133, 0] (w:1, o:47, a:1, s:1, b:0),
% 11.60/11.98 'v_a' [134, 0] (w:1, o:48, a:1, s:1, b:0),
% 11.60/11.98 'class_OrderedGroup_Ocancel__comm__monoid__add' [136, 1] (w:1, o:88
% 11.60/11.98 , a:1, s:1, b:0).
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Starting Search:
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Intermediate Status:
% 11.60/11.98 Generated: 4023
% 11.60/11.98 Kept: 2001
% 11.60/11.98 Inuse: 123
% 11.60/11.98 Deleted: 1
% 11.60/11.98 Deletedinuse: 0
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Intermediate Status:
% 11.60/11.98 Generated: 12436
% 11.60/11.98 Kept: 4182
% 11.60/11.98 Inuse: 167
% 11.60/11.98 Deleted: 4
% 11.60/11.98 Deletedinuse: 0
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Intermediate Status:
% 11.60/11.98 Generated: 21944
% 11.60/11.98 Kept: 6429
% 11.60/11.98 Inuse: 227
% 11.60/11.98 Deleted: 4
% 11.60/11.98 Deletedinuse: 0
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Intermediate Status:
% 11.60/11.98 Generated: 34616
% 11.60/11.98 Kept: 8714
% 11.60/11.98 Inuse: 267
% 11.60/11.98 Deleted: 4
% 11.60/11.98 Deletedinuse: 0
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Intermediate Status:
% 11.60/11.98 Generated: 44570
% 11.60/11.98 Kept: 10781
% 11.60/11.98 Inuse: 297
% 11.60/11.98 Deleted: 4
% 11.60/11.98 Deletedinuse: 0
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Intermediate Status:
% 11.60/11.98 Generated: 63001
% 11.60/11.98 Kept: 12841
% 11.60/11.98 Inuse: 397
% 11.60/11.98 Deleted: 4
% 11.60/11.98 Deletedinuse: 0
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Intermediate Status:
% 11.60/11.98 Generated: 77321
% 11.60/11.98 Kept: 15293
% 11.60/11.98 Inuse: 427
% 11.60/11.98 Deleted: 4
% 11.60/11.98 Deletedinuse: 0
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Intermediate Status:
% 11.60/11.98 Generated: 96393
% 11.60/11.98 Kept: 17494
% 11.60/11.98 Inuse: 471
% 11.60/11.98 Deleted: 4
% 11.60/11.98 Deletedinuse: 0
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Intermediate Status:
% 11.60/11.98 Generated: 105321
% 11.60/11.98 Kept: 20204
% 11.60/11.98 Inuse: 481
% 11.60/11.98 Deleted: 36
% 11.60/11.98 Deletedinuse: 2
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98 Resimplifying clauses:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Intermediate Status:
% 12.07/12.43 Generated: 120301
% 12.07/12.43 Kept: 22279
% 12.07/12.43 Inuse: 502
% 12.07/12.43 Deleted: 317
% 12.07/12.43 Deletedinuse: 7
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 131862
% 12.07/12.43 Kept: 24313
% 12.07/12.43 Inuse: 557
% 12.07/12.43 Deleted: 327
% 12.07/12.43 Deletedinuse: 17
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 153258
% 12.07/12.43 Kept: 27514
% 12.07/12.43 Inuse: 644
% 12.07/12.43 Deleted: 346
% 12.07/12.43 Deletedinuse: 33
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 161974
% 12.07/12.43 Kept: 29577
% 12.07/12.43 Inuse: 661
% 12.07/12.43 Deleted: 349
% 12.07/12.43 Deletedinuse: 33
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 169301
% 12.07/12.43 Kept: 31701
% 12.07/12.43 Inuse: 671
% 12.07/12.43 Deleted: 349
% 12.07/12.43 Deletedinuse: 33
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 182798
% 12.07/12.43 Kept: 33749
% 12.07/12.43 Inuse: 704
% 12.07/12.43 Deleted: 351
% 12.07/12.43 Deletedinuse: 33
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 197447
% 12.07/12.43 Kept: 36183
% 12.07/12.43 Inuse: 738
% 12.07/12.43 Deleted: 371
% 12.07/12.43 Deletedinuse: 47
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 210485
% 12.07/12.43 Kept: 38185
% 12.07/12.43 Inuse: 778
% 12.07/12.43 Deleted: 393
% 12.07/12.43 Deletedinuse: 59
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 232682
% 12.07/12.43 Kept: 40488
% 12.07/12.43 Inuse: 824
% 12.07/12.43 Deleted: 443
% 12.07/12.43 Deletedinuse: 95
% 12.07/12.43
% 12.07/12.43 Resimplifying clauses:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 254974
% 12.07/12.43 Kept: 42609
% 12.07/12.43 Inuse: 859
% 12.07/12.43 Deleted: 1588
% 12.07/12.43 Deletedinuse: 95
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 277293
% 12.07/12.43 Kept: 44940
% 12.07/12.43 Inuse: 874
% 12.07/12.43 Deleted: 1590
% 12.07/12.43 Deletedinuse: 97
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 295839
% 12.07/12.43 Kept: 46940
% 12.07/12.43 Inuse: 902
% 12.07/12.43 Deleted: 1593
% 12.07/12.43 Deletedinuse: 99
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 314326
% 12.07/12.43 Kept: 49751
% 12.07/12.43 Inuse: 913
% 12.07/12.43 Deleted: 1593
% 12.07/12.43 Deletedinuse: 99
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 323338
% 12.07/12.43 Kept: 51772
% 12.07/12.43 Inuse: 923
% 12.07/12.43 Deleted: 1629
% 12.07/12.43 Deletedinuse: 100
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 335863
% 12.07/12.43 Kept: 53805
% 12.07/12.43 Inuse: 929
% 12.07/12.43 Deleted: 1639
% 12.07/12.43 Deletedinuse: 101
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 345588
% 12.07/12.43 Kept: 56037
% 12.07/12.43 Inuse: 933
% 12.07/12.43 Deleted: 1655
% 12.07/12.43 Deletedinuse: 101
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 376529
% 12.07/12.43 Kept: 58379
% 12.07/12.43 Inuse: 937
% 12.07/12.43 Deleted: 1671
% 12.07/12.43 Deletedinuse: 101
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 384256
% 12.07/12.43 Kept: 60394
% 12.07/12.43 Inuse: 951
% 12.07/12.43 Deleted: 1717
% 12.07/12.43 Deletedinuse: 101
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying clauses:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 400840
% 12.07/12.43 Kept: 62432
% 12.07/12.43 Inuse: 990
% 12.07/12.43 Deleted: 2324
% 12.07/12.43 Deletedinuse: 103
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 422544
% 12.07/12.43 Kept: 65888
% 12.07/12.43 Inuse: 1024
% 12.07/12.43 Deleted: 2326
% 12.07/12.43 Deletedinuse: 104
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 450221
% 12.07/12.43 Kept: 68048
% 12.07/12.43 Inuse: 1083
% 12.07/12.43 Deleted: 2327
% 12.07/12.43 Deletedinuse: 104
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 472324
% 12.07/12.43 Kept: 70071
% 12.07/12.43 Inuse: 1128
% 12.07/12.43 Deleted: 2352
% 12.07/12.43 Deletedinuse: 129
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 495611
% 12.07/12.43 Kept: 73859
% 12.07/12.43 Inuse: 1173
% 12.07/12.43 Deleted: 2369
% 12.07/12.43 Deletedinuse: 146
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 506108
% 12.07/12.43 Kept: 76513
% 12.07/12.43 Inuse: 1186
% 12.07/12.43 Deleted: 2375
% 12.07/12.43 Deletedinuse: 152
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 526525
% 12.07/12.43 Kept: 79379
% 12.07/12.43 Inuse: 1216
% 12.07/12.43 Deleted: 2377
% 12.07/12.43 Deletedinuse: 152
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 Intermediate Status:
% 12.07/12.43 Generated: 542881
% 12.07/12.43 Kept: 81561
% 12.07/12.43 Inuse: 1226
% 12.07/12.43 Deleted: 2377
% 12.07/12.43 Deletedinuse: 152
% 12.07/12.43
% 12.07/12.43 Resimplifying inuse:
% 12.07/12.43 Done
% 12.07/12.43
% 12.07/12.43 Resimplifying clauses:
% 12.07/12.43
% 12.07/12.43 Bliksems!, er is een bewijs:
% 12.07/12.43 % SZS status Unsatisfiable
% 12.07/12.43 % SZS output start Refutation
% 12.07/12.43
% 12.07/12.43 clause( 27, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 12.07/12.43 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 29, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 12.07/12.43 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 41, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 12.07/12.43 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.43 X ), X ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 42, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 12.07/12.43 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.43 X ), X ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 91, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 99, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 104, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.43 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.43 ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 116, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 12.07/12.43 ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 174, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 12.07/12.43 ), Y ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 218, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 12.07/12.43 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_Osmult'( Y, T, X ),
% 12.07/12.43 'c_Polynomial_Osmult'( Z, T, X ), 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.43 'c_Polynomial_Osmult'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ) )
% 12.07/12.43 ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 277, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.43 , X ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 284, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y
% 12.07/12.43 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 12.07/12.43 , X ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 296, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( Z, T, X
% 12.07/12.43 ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.43 ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 321, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p', 'v_q',
% 12.07/12.43 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 324, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p',
% 12.07/12.43 'c_Polynomial_Osmult'( 'v_a', 'v_q', 'tc_Complex_Ocomplex' ),
% 12.07/12.43 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 332, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 12.07/12.43 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 342, [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex'
% 12.07/12.43 ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 344, [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex'
% 12.07/12.43 ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 345, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' )
% 12.07/12.43 ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 348, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ]
% 12.07/12.43 )
% 12.07/12.43 .
% 12.07/12.43 clause( 350, [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ]
% 12.07/12.43 )
% 12.07/12.43 .
% 12.07/12.43 clause( 351, [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 365, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.43 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 381, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Polynomial_Opoly'( X )
% 12.07/12.43 ), ~( 'class_OrderedGroup_Oab__group__add'( X ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 383, [ 'class_Divides_Osemiring__div'( 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.43 , ~( 'class_Ring__and__Field_Ofield'( X ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 556, [ 'class_Divides_Osemiring__div'( 'tc_Polynomial_Opoly'(
% 12.07/12.43 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 638, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Polynomial_Opoly'(
% 12.07/12.43 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 1979, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 12.07/12.43 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 3324, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y ) ), =( Z, Y ), ~( =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 12.07/12.43 ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 3664, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ), ~( =( Y,
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 9549, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex'
% 12.07/12.43 ) ), 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 16749, [ =( 'c_HOL_Ominus__class_Ominus'( X, X,
% 12.07/12.43 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex'
% 12.07/12.43 ) ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 16751, [ =( 'c_HOL_Ominus__class_Ominus'( X, X,
% 12.07/12.43 'tc_Complex_Ocomplex' ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 18261, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( Z, Y, X ), Y ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Y
% 12.07/12.43 , X ), T ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 18282, [ ~( =( X, Y ) ), ~( 'class_Divides_Osemiring__div'( Z ) ),
% 12.07/12.43 =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y, Z )
% 12.07/12.43 , X, Z ), Y ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 18283, [ ~( =( X, Y ) ), ~( 'class_Divides_Osemiring__div'( Z ) ),
% 12.07/12.43 =( X, Y ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 20177, [ 'class_Ring__and__Field_Ocomm__semiring__1'( X ), ~( =(
% 12.07/12.43 'tc_Complex_Ocomplex', X ) ), ~( 'class_Divides_Osemiring__div'( Y ) ) ]
% 12.07/12.43 )
% 12.07/12.43 .
% 12.07/12.43 clause( 21629, [ 'class_Ring__and__Field_Ocomm__semiring__1'( X ), ~( =(
% 12.07/12.43 'tc_Complex_Ocomplex', X ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 22294, [ ~( =( 'tc_Complex_Ocomplex', X ) ),
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.43 , X ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 23748, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'(
% 12.07/12.43 'tc_Complex_Ocomplex' ), X, 'tc_Complex_Ocomplex' ), X ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 25260, [ =( 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_Complex_Ocomplex' ),
% 12.07/12.43 'tc_Complex_Ocomplex' ), X ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 25344, [ ~( =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex'
% 12.07/12.43 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 28068, [ 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X,
% 12.07/12.43 'tc_Complex_Ocomplex' ), ~( =( X, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Complex_Ocomplex' ) ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 62639, [ =( 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Complex_Ocomplex' ), Y, 'tc_Complex_Ocomplex' ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex'
% 12.07/12.43 ) ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 71963, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ), X,
% 12.07/12.43 'tc_Complex_Ocomplex' ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 75940, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ), 'v_a',
% 12.07/12.43 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 76519, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' )
% 12.07/12.43 , 'v_a' ) ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 80598, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p', 'v_q',
% 12.07/12.43 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ), =(
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ), 'v_a' ) ] )
% 12.07/12.43 .
% 12.07/12.43 clause( 81561, [] )
% 12.07/12.43 .
% 12.07/12.43
% 12.07/12.43
% 12.07/12.43 % SZS output end Refutation
% 12.07/12.43 found a proof!
% 12.07/12.43
% 12.07/12.43 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 12.07/12.43
% 12.07/12.43 initialclauses(
% 12.07/12.43 [ clause( 81563, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.43 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_Polynomial_Osmult'( Z, T, X ),
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'( U, T, X ) ) ), =( U
% 12.07/12.43 , 'c_Polynomial_Opoly'( Y, Z, X ) ) ] )
% 12.07/12.43 , clause( 81564, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.43 =( 'c_Polynomial_Opoly'( 'c_Polynomial_OpCons'( Y, Z, X ), T, X ),
% 12.07/12.43 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 12.07/12.43 'c_Polynomial_Opoly'( Z, T, X ), X ), X ) ) ] )
% 12.07/12.43 , clause( 81565, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 12.07/12.43 'c_Polynomial_Opoly'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 12.07/12.43 X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 , clause( 81566, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.43 =( 'c_Polynomial_Opoly'( 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 12.07/12.43 )
% 12.07/12.43 , clause( 81567, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.43 =( 'c_Polynomial_Opoly'( 'c_Polynomial_Osmult'( Y, Z, X ), T, X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 12.07/12.43 )
% 12.07/12.43 , clause( 81568, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.43 =( 'c_Polynomial_Opoly'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.43 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 12.07/12.43 )
% 12.07/12.43 , clause( 81569, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.43 =( 'c_Polynomial_Opoly'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.43 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 12.07/12.43 )
% 12.07/12.43 , clause( 81570, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 12.07/12.43 'c_Polynomial_Opoly'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), Z, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.43 'c_Polynomial_Opoly'( Y, Z, X ), X ) ) ] )
% 12.07/12.43 , clause( 81571, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 12.07/12.43 'c_Polynomial_Opoly'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Ominus__class_Ominus'(
% 12.07/12.43 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 12.07/12.43 )
% 12.07/12.43 , clause( 81572, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.43 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 12.07/12.43 'c_Polynomial_OpCons'( T, U, X ), 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.43 'c_Polynomial_OpCons'( 'c_HOL_Ominus__class_Ominus'( Y, T, X ),
% 12.07/12.43 'c_HOL_Ominus__class_Ominus'( Z, U, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 12.07/12.43 )
% 12.07/12.43 , clause( 81573, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 12.07/12.43 , 'tc_Polynomial_Opoly'( X ) ), X ) ) ] )
% 12.07/12.43 , clause( 81574, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.43 ~( =( 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_OpCons'( T, Z, X )
% 12.07/12.43 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ]
% 12.07/12.43 )
% 12.07/12.43 , clause( 81575, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 12.07/12.43 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 12.07/12.43 'c_Polynomial_OpCons'( T, U, X ), 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.43 'c_Polynomial_OpCons'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ),
% 12.07/12.43 'c_HOL_Oplus__class_Oplus'( Z, U, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 12.07/12.43 )
% 12.07/12.43 , clause( 81576, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.43 =( 'c_Polynomial_Osmult'( Y, 'c_Polynomial_OpCons'( Z, T, X ), X ),
% 12.07/12.43 'c_Polynomial_OpCons'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.43 'c_Polynomial_Osmult'( Y, T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81577, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 12.07/12.43 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 12.07/12.43 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 , clause( 81578, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_OpCons'(
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.43 , clause( 81579, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 12.07/12.43 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 12.07/12.43 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.43 , clause( 81580, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 12.07/12.43 Y, Z, X ), 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Y, T ) ] )
% 12.07/12.43 , clause( 81581, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 12.07/12.43 Y, Z, X ), 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Z, U ) ] )
% 12.07/12.43 , clause( 81582, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 12.07/12.43 'c_Polynomial_Opoly'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_Polynomial_OpCons'(
% 12.07/12.43 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y, 'tc_Polynomial_Opoly'( X ) ) )
% 12.07/12.43 ] )
% 12.07/12.43 , clause( 81583, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 12.07/12.43 'c_Polynomial_Opoly'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_Polynomial_OpCons'(
% 12.07/12.43 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y, 'tc_Polynomial_Opoly'( X ) ) ]
% 12.07/12.43 )
% 12.07/12.43 , clause( 81584, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 12.07/12.43 'c_Polynomial_Opoly'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'( Z,
% 12.07/12.43 'c_Polynomial_OpCons'( 'c_HOL_Oone__class_Oone'( X ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y,
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ) ] )
% 12.07/12.43 , clause( 81585, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 12.07/12.43 'c_Polynomial_Opoly'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'( Z,
% 12.07/12.43 'c_Polynomial_OpCons'( 'c_HOL_Oone__class_Oone'( X ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y,
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.43 , clause( 81586, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.43 ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 12.07/12.43 'c_Polynomial_OpCons'( T, Z, X ), 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z,
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.43 , clause( 81587, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 12.07/12.43 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 , clause( 81588, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 12.07/12.43 ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 12.07/12.43 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 , clause( 81589, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 12.07/12.43 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 12.07/12.43 )
% 12.07/12.43 , clause( 81590, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 12.07/12.43 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 , clause( 81591, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 12.07/12.43 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 , clause( 81592, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 12.07/12.43 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 , clause( 81593, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 12.07/12.43 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 12.07/12.43 , clause( 81594, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 12.07/12.43 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 12.07/12.43 , clause( 81595, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 12.07/12.43 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 12.07/12.43 , clause( 81596, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 12.07/12.43 , X ) ) ), =( Y, Z ) ] )
% 12.07/12.43 , clause( 81597, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 12.07/12.43 , X ) ) ), =( Y, Z ) ] )
% 12.07/12.43 , clause( 81598, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, Z ),
% 12.07/12.43 ~( 'c_Polynomial_Opdivmod__rel'( T, U, Z, W, X ) ), ~(
% 12.07/12.43 'c_Polynomial_Opdivmod__rel'( T, U, Y, V0, X ) ) ] )
% 12.07/12.43 , clause( 81599, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, Z ),
% 12.07/12.43 ~( 'c_Polynomial_Opdivmod__rel'( T, U, W, Z, X ) ), ~(
% 12.07/12.43 'c_Polynomial_Opdivmod__rel'( T, U, V0, Y, X ) ) ] )
% 12.07/12.43 , clause( 81600, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ] )
% 12.07/12.43 , clause( 81601, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ] )
% 12.07/12.43 , clause( 81602, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.43 'c_Polynomial_Opoly__gcd'( 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.43 , clause( 81603, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 12.07/12.43 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 12.07/12.43 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 12.07/12.43 , clause( 81604, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.43 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 12.07/12.43 , Z, X ) ) ] )
% 12.07/12.43 , clause( 81605, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.43 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 12.07/12.43 X ), X ) ) ] )
% 12.07/12.43 , clause( 81606, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 12.07/12.43 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 12.07/12.43 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 12.07/12.43 , clause( 81607, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 12.07/12.43 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 12.07/12.43 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 12.07/12.43 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 12.07/12.43 ) ) ] )
% 12.07/12.43 , clause( 81608, [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 12.07/12.43 X ) ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 12.07/12.43 ) ) ] )
% 12.07/12.43 , clause( 81609, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( T, U, X ), X ),
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), ~(
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 12.07/12.43 , clause( 81610, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, Z ),
% 12.07/12.43 ~( 'c_Polynomial_Opdivmod__rel'( Z, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), T, Y, X ) ) ] )
% 12.07/12.43 , clause( 81611, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 X ) ) ] )
% 12.07/12.43 , clause( 81612, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 12.07/12.43 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 12.07/12.43 , clause( 81613, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 12.07/12.43 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 12.07/12.43 , clause( 81614, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.43 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ] )
% 12.07/12.43 , clause( 81615, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), T, 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), 'c_Divides_Odiv__class_Omod'( Y, Z,
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.43 , clause( 81616, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 12.07/12.43 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.43 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 , clause( 81617, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 12.07/12.43 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 12.07/12.43 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 12.07/12.43 ) ) ] )
% 12.07/12.43 , clause( 81618, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 12.07/12.43 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 12.07/12.43 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 12.07/12.43 ) ) ] )
% 12.07/12.43 , clause( 81619, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 12.07/12.43 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 12.07/12.43 , clause( 81620, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 12.07/12.43 'c_Polynomial_Opdivmod__rel'( Y, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), Z, T, X ) ), =( Z,
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.43 , clause( 81621, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 12.07/12.43 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), Z, Y, T, X ) ) ] )
% 12.07/12.43 , clause( 81622, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 12.07/12.43 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), Z, T, Y, X ) ) ] )
% 12.07/12.43 , clause( 81623, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 12.07/12.43 'c_Polynomial_Opdivmod__rel'( Z, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), Y, T, X ) ) ] )
% 12.07/12.43 , clause( 81624, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 =( 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 12.07/12.43 ), T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 12.07/12.43 Y, T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81625, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 12.07/12.43 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.43 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 12.07/12.43 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81626, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 12.07/12.43 ) ) ] )
% 12.07/12.43 , clause( 81627, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 12.07/12.43 ) ) ] )
% 12.07/12.43 , clause( 81628, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 12.07/12.43 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.43 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 12.07/12.43 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 12.07/12.43 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ] )
% 12.07/12.43 , clause( 81629, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 12.07/12.43 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 12.07/12.43 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 12.07/12.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 12.07/12.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ] )
% 12.07/12.43 , clause( 81630, [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y,
% 12.07/12.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ) ) ] )
% 12.07/12.43 , clause( 81631, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Y ) ] )
% 12.07/12.43 , clause( 81632, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( Z, Y, X ), X ),
% 12.07/12.43 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), Z ) ] )
% 12.07/12.43 , clause( 81633, [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Y, X
% 12.07/12.43 ) ) ] )
% 12.07/12.43 , clause( 81634, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 12.07/12.43 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 12.07/12.43 X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 12.07/12.43 , clause( 81635, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 12.07/12.43 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 12.07/12.43 X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 12.07/12.43 , clause( 81636, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 12.07/12.43 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 12.07/12.43 T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81637, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 12.07/12.43 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 12.07/12.43 T, X ), Z, X ) ) ] )
% 12.07/12.43 , clause( 81638, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 12.07/12.43 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.43 Z, T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81639, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 12.07/12.43 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 12.07/12.43 , X ), T, X ) ) ] )
% 12.07/12.43 , clause( 81640, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 12.07/12.43 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 12.07/12.43 , T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81641, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 12.07/12.43 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 12.07/12.43 , X ), T, X ) ) ] )
% 12.07/12.43 , clause( 81642, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 12.07/12.43 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 12.07/12.43 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81643, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 12.07/12.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81644, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 12.07/12.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81645, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 12.07/12.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81646, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 12.07/12.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81647, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.43 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), T, 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Otimes__class_Otimes'( Z, T,
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.43 , clause( 81648, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 12.07/12.43 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 12.07/12.43 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81649, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 12.07/12.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 12.07/12.43 , clause( 81650, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 12.07/12.43 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 12.07/12.43 ), X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X
% 12.07/12.43 ), X ) ) ] )
% 12.07/12.43 , clause( 81651, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 12.07/12.43 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.43 , clause( 81652, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 12.07/12.43 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.43 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.43 , clause( 81653, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 12.07/12.43 , ~( =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 12.07/12.43 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.43 , clause( 81654, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 12.07/12.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Z, Y, X ),
% 12.07/12.43 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 12.07/12.43 ) ) ] )
% 12.07/12.43 , clause( 81655, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.43 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 12.07/12.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 12.07/12.43 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 12.07/12.43 ) ) ] )
% 12.07/12.43 , clause( 81656, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 12.07/12.43 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 12.07/12.43 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 12.07/12.43 , clause( 81657, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.43 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 12.07/12.43 ) ) ] )
% 12.07/12.43 , clause( 81658, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 12.07/12.43 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.43 X ), X ) ) ] )
% 12.07/12.43 , clause( 81659, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 12.07/12.44 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.44 X ), X ) ) ] )
% 12.07/12.44 , clause( 81660, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 12.07/12.44 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.44 X ), X ) ) ] )
% 12.07/12.44 , clause( 81661, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 12.07/12.44 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.44 X ), X ) ) ] )
% 12.07/12.44 , clause( 81662, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 Y, Y, X ) ) ] )
% 12.07/12.44 , clause( 81663, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81664, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81665, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81666, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 12.07/12.44 X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ] )
% 12.07/12.44 , clause( 81667, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ] )
% 12.07/12.44 , clause( 81668, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81669, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( 'c_Polynomial_OpCons'( Y, Z, X ), T,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_Polynomial_Osmult'( Y, T, X ), 'c_Polynomial_OpCons'(
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, T,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81670, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_OpCons'( Z, T, X ),
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_Polynomial_Osmult'( Z, Y, X ), 'c_Polynomial_OpCons'(
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, T,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81671, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 12.07/12.44 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81672, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81673, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81674, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 12.07/12.44 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81675, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y ) ] )
% 12.07/12.44 , clause( 81676, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81677, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81678, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81679, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81680, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 12.07/12.44 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 12.07/12.44 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81681, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 12.07/12.44 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81682, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 12.07/12.44 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 12.07/12.44 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81683, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 12.07/12.44 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81684, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), U, 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 12.07/12.44 'c_Polynomial_Opdivmod__rel'( Y, T, Z, U, X ) ) ] )
% 12.07/12.44 , clause( 81685, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.44 =( 'c_Polynomial_Osmult'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_Osmult'( Y, T, X ),
% 12.07/12.44 'c_Polynomial_Osmult'( Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81686, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81687, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 12.07/12.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, T, X ),
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ] )
% 12.07/12.44 , clause( 81688, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 12.07/12.44 , X ) ) ] )
% 12.07/12.44 , clause( 81689, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81690, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81691, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81692, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81693, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81694, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81695, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Polynomial_Opdivmod__rel'( Y, Z, 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_Divides_Odiv__class_Omod'( Y, Z,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ) ] )
% 12.07/12.44 , clause( 81696, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81697, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 12.07/12.44 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 12.07/12.44 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 12.07/12.44 , clause( 81698, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 12.07/12.44 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 12.07/12.44 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 12.07/12.44 , clause( 81699, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Opoly__gcd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T, X ), X ),
% 12.07/12.44 'c_Polynomial_Opoly__gcd'( Z, 'c_Polynomial_Opoly__gcd'( Y, T, X ), X ) )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81700, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Opoly__gcd'( 'c_Polynomial_Opoly__gcd'( Y, Z, X ), T, X ),
% 12.07/12.44 'c_Polynomial_Opoly__gcd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T, X ), X ) )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81701, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 12.07/12.44 ), Y ) ] )
% 12.07/12.44 , clause( 81702, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Opoly__gcd'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Polynomial_Opoly__gcd'( Y, Z, X ) )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81703, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Opoly__gcd'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), Z, X ), 'c_Polynomial_Opoly__gcd'( Y, Z, X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81704, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 Z, Y, X ) ) ] )
% 12.07/12.44 , clause( 81705, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 12.07/12.44 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81706, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 Z, Y, X ) ) ] )
% 12.07/12.44 , clause( 81707, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 12.07/12.44 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 12.07/12.44 , T, X ), X ), T, X ) ) ] )
% 12.07/12.44 , clause( 81708, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 12.07/12.44 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 12.07/12.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81709, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 12.07/12.44 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81710, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 12.07/12.44 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81711, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 12.07/12.44 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 12.07/12.44 , X ) ) ] )
% 12.07/12.44 , clause( 81712, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 12.07/12.44 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81713, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 12.07/12.44 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81714, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 12.07/12.44 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 12.07/12.44 , X ) ) ] )
% 12.07/12.44 , clause( 81715, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 12.07/12.44 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 12.07/12.44 , X ) ) ] )
% 12.07/12.44 , clause( 81716, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 12.07/12.44 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 12.07/12.44 , X ) ) ] )
% 12.07/12.44 , clause( 81717, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 12.07/12.44 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 12.07/12.44 , X ) ) ] )
% 12.07/12.44 , clause( 81718, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 12.07/12.44 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ] )
% 12.07/12.44 , clause( 81719, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81720, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), Z, 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81721, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 12.07/12.44 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 12.07/12.44 , clause( 81722, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 12.07/12.44 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 12.07/12.44 , clause( 81723, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 12.07/12.44 , T, X ) ) ), =( Z, T ) ] )
% 12.07/12.44 , clause( 81724, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 12.07/12.44 , T, X ) ) ), =( Y, Z ) ] )
% 12.07/12.44 , clause( 81725, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_Polynomial_Opoly'( X ) ), T ),
% 12.07/12.44 ~( 'c_Polynomial_Opdivmod__rel'( Y, Z, U, T, X ) ) ] )
% 12.07/12.44 , clause( 81726, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 12.07/12.44 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 12.07/12.44 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ] )
% 12.07/12.44 , clause( 81727, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 12.07/12.44 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 12.07/12.44 , clause( 81728, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 12.07/12.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81729, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 12.07/12.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81730, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 12.07/12.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81731, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 12.07/12.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81732, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.44 ) ), =( Y, Z ) ] )
% 12.07/12.44 , clause( 81733, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.44 ) ), =( Y, Z ) ] )
% 12.07/12.44 , clause( 81734, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 12.07/12.44 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 12.07/12.44 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 12.07/12.44 , clause( 81735, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 12.07/12.44 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.44 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 12.07/12.44 , clause( 81736, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 12.07/12.44 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.44 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 12.07/12.44 , clause( 81737, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 12.07/12.44 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 12.07/12.44 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 12.07/12.44 , clause( 81738, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 12.07/12.44 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 12.07/12.44 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 12.07/12.44 , clause( 81739, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 12.07/12.44 , U, X ), X ) ) ] )
% 12.07/12.44 , clause( 81740, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), T
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 12.07/12.44 X ), Z, X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 12.07/12.44 , clause( 81741, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 12.07/12.44 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 12.07/12.44 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81742, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 12.07/12.44 , clause( 81743, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 12.07/12.44 , clause( 81744, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Polynomial_Opdivmod__rel'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), U, 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Z, W, 'tc_Polynomial_Opoly'( X ) ), V0,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ), ~( 'c_Polynomial_Opdivmod__rel'( V1, T
% 12.07/12.44 , U, W, X ) ), ~( 'c_Polynomial_Opdivmod__rel'( Y, Z, V1, V0, X ) ) ] )
% 12.07/12.44 , clause( 81745, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 12.07/12.44 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ] )
% 12.07/12.44 , clause( 81746, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 12.07/12.44 , X ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81747, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 12.07/12.44 , X ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 12.07/12.44 , clause( 81748, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 12.07/12.44 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81749, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81750, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ] )
% 12.07/12.44 , clause( 81751, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 12.07/12.44 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 12.07/12.44 , clause( 81752, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 12.07/12.44 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 12.07/12.44 , clause( 81753, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ), Y ) ] )
% 12.07/12.44 , clause( 81754, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y ) ] )
% 12.07/12.44 , clause( 81755, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81756, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81757, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81758, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 12.07/12.44 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 12.07/12.44 , clause( 81759, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81760, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81761, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81762, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81763, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 12.07/12.44 ), Y ) ] )
% 12.07/12.44 , clause( 81764, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 12.07/12.44 ), Y ) ] )
% 12.07/12.44 , clause( 81765, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81766, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81767, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 12.07/12.44 ), Y ) ] )
% 12.07/12.44 , clause( 81768, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 12.07/12.44 ), Y ) ] )
% 12.07/12.44 , clause( 81769, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81770, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 12.07/12.44 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ] )
% 12.07/12.44 , clause( 81771, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 12.07/12.44 X ), X ) ) ] )
% 12.07/12.44 , clause( 81772, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 12.07/12.44 , clause( 81773, [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 12.07/12.44 , clause( 81774, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 12.07/12.44 , clause( 81775, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 12.07/12.44 , clause( 81776, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 12.07/12.44 , T, X ), X ), T, X ) ) ] )
% 12.07/12.44 , clause( 81777, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 12.07/12.44 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 12.07/12.44 ), X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 12.07/12.44 , clause( 81778, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 12.07/12.44 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 12.07/12.44 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 12.07/12.44 , clause( 81779, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 12.07/12.44 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 12.07/12.44 , clause( 81780, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 12.07/12.44 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 Y, T, X ) ) ), =( Z, T ) ] )
% 12.07/12.44 , clause( 81781, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 12.07/12.44 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 T, Z, X ) ) ), =( Y, T ) ] )
% 12.07/12.44 , clause( 81782, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), Y, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ) ] )
% 12.07/12.44 , clause( 81783, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.44 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 12.07/12.44 , clause( 81784, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.44 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ] )
% 12.07/12.44 , clause( 81785, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 12.07/12.44 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81786, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 12.07/12.44 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 12.07/12.44 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 12.07/12.44 , clause( 81787, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 12.07/12.44 , clause( 81788, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 12.07/12.44 , clause( 81789, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 12.07/12.44 'c_Polynomial_Osmult'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81790, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 12.07/12.44 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 12.07/12.44 , clause( 81791, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, 'c_Polynomial_Osmult'( Z, T, X ),
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_Divides_Odiv__class_Omod'( Y, T,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81792, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), Y, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ) ] )
% 12.07/12.44 , clause( 81793, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), Y, X ) ] )
% 12.07/12.44 , clause( 81794, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81795, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 12.07/12.44 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81796, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Osmult'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81797, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 12.07/12.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 12.07/12.44 , clause( 81798, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 12.07/12.44 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X )
% 12.07/12.44 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 12.07/12.44 , clause( 81799, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 12.07/12.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 12.07/12.44 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 12.07/12.44 , clause( 81800, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 12.07/12.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 12.07/12.44 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 12.07/12.44 , X ), W, X ) ) ] )
% 12.07/12.44 , clause( 81801, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), T, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ] )
% 12.07/12.44 , clause( 81802, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), T, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Z, T, X ) ) ] )
% 12.07/12.44 , clause( 81803, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Polynomial_Opdivmod__rel'( Y, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), Y, X ) ] )
% 12.07/12.44 , clause( 81804, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81805, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81806, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 12.07/12.44 Y, X ) ) ] )
% 12.07/12.44 , clause( 81807, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 12.07/12.44 Y, X ) ) ] )
% 12.07/12.44 , clause( 81808, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 12.07/12.44 X ) ) ] )
% 12.07/12.44 , clause( 81809, [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 12.07/12.44 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 12.07/12.44 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Z, X
% 12.07/12.44 ), 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ] )
% 12.07/12.44 , clause( 81810, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 12.07/12.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81811, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 12.07/12.44 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 12.07/12.44 X ) ) ] )
% 12.07/12.44 , clause( 81812, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 12.07/12.44 , T, X ), X ), T, X ) ) ] )
% 12.07/12.44 , clause( 81813, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 12.07/12.44 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 12.07/12.44 Y, Z, X ), X ) ) ] )
% 12.07/12.44 , clause( 81814, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Z, 'c_Divides_Odiv__class_Odiv'( Y, T, X ), X
% 12.07/12.44 ) ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81815, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( T, 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), X
% 12.07/12.44 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81816, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 12.07/12.44 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 12.07/12.44 , clause( 81817, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_Polynomial_Opoly'( X ) ), T ),
% 12.07/12.44 ~( 'c_Polynomial_Opdivmod__rel'( Y, Z, T, U, X ) ) ] )
% 12.07/12.44 , clause( 81818, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 12.07/12.44 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 12.07/12.44 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 12.07/12.44 Z, X ) ) ] )
% 12.07/12.44 , clause( 81819, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Osmult'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_Osmult'( Y, T, X ),
% 12.07/12.44 'c_Polynomial_Osmult'( Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81820, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 12.07/12.44 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ] )
% 12.07/12.44 , clause( 81821, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 12.07/12.44 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ] )
% 12.07/12.44 , clause( 81822, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 12.07/12.44 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 12.07/12.44 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 12.07/12.44 , clause( 81823, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 12.07/12.44 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 12.07/12.44 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 12.07/12.44 =( Y, T ) ] )
% 12.07/12.44 , clause( 81824, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 12.07/12.44 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 12.07/12.44 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 12.07/12.44 =( Y, T ) ] )
% 12.07/12.44 , clause( 81825, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 12.07/12.44 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 12.07/12.44 , X ) ) ] )
% 12.07/12.44 , clause( 81826, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 12.07/12.44 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 12.07/12.44 X ), Z, X ) ) ] )
% 12.07/12.44 , clause( 81827, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 12.07/12.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81828, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 12.07/12.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81829, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81830, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81831, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81832, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81833, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81834, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81835, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 12.07/12.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81836, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81837, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81838, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 12.07/12.44 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 12.07/12.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81839, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 12.07/12.44 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81840, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 12.07/12.44 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ),
% 12.07/12.44 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81841, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 12.07/12.44 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 12.07/12.44 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ] )
% 12.07/12.44 , clause( 81842, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 12.07/12.44 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 12.07/12.44 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 12.07/12.44 , clause( 81843, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81844, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 12.07/12.44 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 12.07/12.44 X ), Z, X ) ) ] )
% 12.07/12.44 , clause( 81845, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ] )
% 12.07/12.44 , clause( 81846, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ] )
% 12.07/12.44 , clause( 81847, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81848, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 12.07/12.44 , clause( 81849, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_Polynomial_Opoly__gcd'( Z, Y, X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81850, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 12.07/12.44 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 12.07/12.44 X ), X ) ) ] )
% 12.07/12.44 , clause( 81851, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81852, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 12.07/12.44 , =( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 12.07/12.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81853, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81854, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_Polynomial_Opoly__gcd'( Z,
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_Polynomial_Opoly'( X ) ), X ) ),
% 12.07/12.44 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81855, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81856, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.44 =( 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81857, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 12.07/12.44 X ) ) ] )
% 12.07/12.44 , clause( 81858, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( Y, Z,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), T, 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81859, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 12.07/12.44 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 12.07/12.44 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 12.07/12.44 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 12.07/12.44 , clause( 81860, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 12.07/12.44 X ) ), ~( =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81861, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 12.07/12.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81862, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 12.07/12.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81863, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ),
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 12.07/12.44 , X ), X ), Y ) ] )
% 12.07/12.44 , clause( 81864, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 12.07/12.44 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81865, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ),
% 12.07/12.44 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), Y, Z, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ) ] )
% 12.07/12.44 , clause( 81866, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), Z, 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_Divides_Odiv__class_Omod'( Y, Z,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81867, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 12.07/12.44 , X ) ) ] )
% 12.07/12.44 , clause( 81868, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 12.07/12.44 , X ) ) ] )
% 12.07/12.44 , clause( 81869, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 12.07/12.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 12.07/12.44 , clause( 81870, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 12.07/12.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 12.07/12.44 , clause( 81871, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 12.07/12.44 =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 12.07/12.44 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ] )
% 12.07/12.44 , clause( 81872, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 12.07/12.44 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 12.07/12.44 , clause( 81873, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.44 =( 'c_Polynomial_Osmult'( Y, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81874, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Osmult'( Y, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81875, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ] )
% 12.07/12.44 , clause( 81876, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T
% 12.07/12.44 , X ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'(
% 12.07/12.44 X ) ) ) ] )
% 12.07/12.44 , clause( 81877, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T
% 12.07/12.44 , X ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'(
% 12.07/12.44 X ) ) ) ] )
% 12.07/12.44 , clause( 81878, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Opoly__gcd'( Y, Z, X
% 12.07/12.44 ), Y, 'tc_Polynomial_Opoly'( X ) ) ] )
% 12.07/12.44 , clause( 81879, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Opoly__gcd'( Y, Z, X
% 12.07/12.44 ), Z, 'tc_Polynomial_Opoly'( X ) ) ] )
% 12.07/12.44 , clause( 81880, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'(
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Z, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81881, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 12.07/12.44 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81882, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 12.07/12.44 ), X ) ) ] )
% 12.07/12.44 , clause( 81883, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 12.07/12.44 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81884, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 12.07/12.44 Z, X ) ) ] )
% 12.07/12.44 , clause( 81885, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.44 , X ) ] )
% 12.07/12.44 , clause( 81886, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Osmult'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ominus__class_Ominus'(
% 12.07/12.44 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_Osmult'( Y, T, X ),
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81887, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'(
% 12.07/12.44 T, Z, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81888, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'(
% 12.07/12.44 Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81889, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 12.07/12.44 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 12.07/12.44 , clause( 81890, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 12.07/12.44 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ] )
% 12.07/12.44 , clause( 81891, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Osmult'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 'c_Polynomial_Osmult'( Y, Z, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81892, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 12.07/12.44 , X ) ) ] )
% 12.07/12.44 , clause( 81893, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 12.07/12.44 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81894, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 12.07/12.44 , X ), Z, X ) ) ] )
% 12.07/12.44 , clause( 81895, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81896, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 Z, X ), X ) ) ] )
% 12.07/12.44 , clause( 81897, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 12.07/12.44 , clause( 81898, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 12.07/12.44 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ] )
% 12.07/12.44 , clause( 81899, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 12.07/12.44 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81900, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 =( 'c_Polynomial_Osmult'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y ) ] )
% 12.07/12.44 , clause( 81901, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( 'c_Polynomial_Osmult'( Y, Z, X ), T,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Y,
% 12.07/12.44 'c_Divides_Odiv__class_Omod'( Z, T, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81902, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 , =( T, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( T, Z, X
% 12.07/12.44 ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81903, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 12.07/12.44 T, 'tc_Polynomial_Opoly'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) )
% 12.07/12.44 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, 'tc_Polynomial_Opoly'(
% 12.07/12.44 X ) ) ) ] )
% 12.07/12.44 , clause( 81904, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( T,
% 12.07/12.44 Z, X ), 'tc_Polynomial_Opoly'( X ) ) ), =( T, 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 X ) ) ] )
% 12.07/12.44 , clause( 81905, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( Z, T, X
% 12.07/12.44 ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81906, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 , =( T, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( T, Y, X ),
% 12.07/12.44 Z, 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81907, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 12.07/12.44 T, 'tc_Polynomial_Opoly'( X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 12.07/12.44 Z, T, 'tc_Polynomial_Opoly'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81908, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z
% 12.07/12.44 , 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81909, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 12.07/12.44 , X ), Z, X ) ) ] )
% 12.07/12.44 , clause( 81910, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 12.07/12.44 , X ), Z, X ) ) ] )
% 12.07/12.44 , clause( 81911, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 12.07/12.44 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81912, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 12.07/12.44 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 12.07/12.44 , clause( 81913, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 12.07/12.44 X ) ] )
% 12.07/12.44 , clause( 81914, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 12.07/12.44 , clause( 81915, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ] )
% 12.07/12.44 , clause( 81916, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'(
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ] )
% 12.07/12.44 , clause( 81917, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.44 'c_Polynomial_Opdivmod__rel'( 'c_Polynomial_Osmult'( Y, Z, X ), T,
% 12.07/12.44 'c_Polynomial_Osmult'( Y, U, X ), 'c_Polynomial_Osmult'( Y, W, X ), X ),
% 12.07/12.44 ~( 'c_Polynomial_Opdivmod__rel'( Z, T, U, W, X ) ) ] )
% 12.07/12.44 , clause( 81918, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 12.07/12.44 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81919, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.44 =( 'c_Polynomial_Osmult'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Oplus__class_Oplus'(
% 12.07/12.44 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_Osmult'( Y, T, X ),
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81920, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 12.07/12.44 , T, X ), X ) ) ] )
% 12.07/12.44 , clause( 81921, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 12.07/12.44 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 12.07/12.44 , clause( 81922, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 12.07/12.44 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81923, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 12.07/12.44 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 81924, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( 'c_Polynomial_Osmult'( Y, Z, X ), T,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Y,
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( Z, T, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81925, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 12.07/12.44 , Y, X ), X ) ] )
% 12.07/12.44 , clause( 81926, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 12.07/12.44 , Z, X ), X ) ] )
% 12.07/12.44 , clause( 81927, [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 12.07/12.44 , Z, X ), X ) ] )
% 12.07/12.44 , clause( 81928, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( T, Y,
% 12.07/12.44 X ), Z, 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , clause( 81929, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( Z, T, X
% 12.07/12.44 ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81930, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 12.07/12.44 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 12.07/12.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 12.07/12.44 , clause( 81931, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_Osmult'( Z, T, X ),
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Z,
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81932, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.44 =( 'c_HOL_Otimes__class_Otimes'( 'c_Polynomial_Osmult'( Y, Z, X ), T,
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Y,
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81933, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p', 'v_q',
% 12.07/12.44 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.44 , clause( 81934, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 12.07/12.44 =( 'c_Polynomial_Osmult'( Y, 'c_Polynomial_Osmult'( Z, T, X ), X ),
% 12.07/12.44 'c_Polynomial_Osmult'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ) )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81935, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_q',
% 12.07/12.44 'c_Polynomial_Osmult'( 'v_a', 'v_q', 'tc_Complex_Ocomplex' ),
% 12.07/12.44 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.44 , clause( 81936, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p', 'v_q',
% 12.07/12.44 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.44 , clause( 81937, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p',
% 12.07/12.44 'c_Polynomial_Osmult'( 'v_a', 'v_q', 'tc_Complex_Ocomplex' ),
% 12.07/12.44 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ) ] )
% 12.07/12.44 , clause( 81938, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 12.07/12.44 , clause( 81939, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81940, [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81941, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81942, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81943, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81944, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81945, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81946, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81947, [ 'class_RealVector_Oreal__normed__algebra'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81948, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81949, [ 'class_OrderedGroup_Ocomm__monoid__mult'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81950, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81951, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81952, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81953, [ 'class_Ring__and__Field_Ozero__neq__one'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81954, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81955, [ 'class_OrderedGroup_Oab__group__add'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81956, [ 'class_Ring__and__Field_Omult__zero'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81957, [ 'class_Ring__and__Field_Ocomm__ring'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81958, [ 'class_OrderedGroup_Omonoid__mult'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81959, [ 'class_Ring__and__Field_Osemiring'(
% 12.07/12.44 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81960, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex'
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81961, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex'
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81962, [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex'
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81963, [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81964, [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81965, [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81966, [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81967, [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81968, [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81969, [ 'class_HOL_Ozero'( 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.44 , clause( 81970, [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81971, [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 12.07/12.44 X ) ) ] )
% 12.07/12.44 , clause( 81972, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81973, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 12.07/12.44 , clause( 81974, [ 'class_Ring__and__Field_Oordered__ring__strict'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 12.07/12.44 X ) ) ] )
% 12.07/12.44 , clause( 81975, [ 'class_OrderedGroup_Oordered__ab__group__add'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 12.07/12.44 X ) ) ] )
% 12.07/12.44 , clause( 81976, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 12.07/12.44 , clause( 81977, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 12.07/12.44 )
% 12.07/12.44 , clause( 81978, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 12.07/12.44 , clause( 81979, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 12.07/12.44 , clause( 81980, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 12.07/12.44 , clause( 81981, [ 'class_OrderedGroup_Ocomm__monoid__mult'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 12.07/12.44 , clause( 81982, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 12.07/12.44 X ) ) ] )
% 12.07/12.44 , clause( 81983, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 12.07/12.44 , clause( 81984, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 12.07/12.44 X ) ) ] )
% 12.07/12.44 , clause( 81985, [ 'class_Ring__and__Field_Ozero__neq__one'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 12.07/12.44 , clause( 81986, [ 'class_Ring__and__Field_Oordered__idom'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 12.07/12.44 X ) ) ] )
% 12.07/12.44 , clause( 81987, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Ocomm__ring__1'(
% 12.07/12.44 X ) ) ] )
% 12.07/12.44 , clause( 81988, [ 'class_OrderedGroup_Oab__group__add'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Oab__group__add'( X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81989, [ 'class_Ring__and__Field_Omult__zero'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 12.07/12.44 , clause( 81990, [ 'class_Ring__and__Field_Ocomm__ring'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Ocomm__ring'( X
% 12.07/12.44 ) ) ] )
% 12.07/12.44 , clause( 81991, [ 'class_OrderedGroup_Omonoid__mult'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 12.07/12.44 , clause( 81992, [ 'class_Ring__and__Field_Osemiring'(
% 12.07/12.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 12.07/12.44 , clause( 81993, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Polynomial_Opoly'(
% 12.07/12.44 X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ] )
% 12.07/12.44 , clause( 81994, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Polynomial_Opoly'(
% 12.07/12.44 X ) ), ~( 'class_OrderedGroup_Oab__group__add'( X ) ) ] )
% 12.07/12.44 , clause( 81995, [ 'class_Ring__and__Field_Oring__1'( 'tc_Polynomial_Opoly'(
% 12.07/12.44 X ) ), ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ] )
% 12.07/12.44 , clause( 81996, [ 'class_Divides_Osemiring__div'( 'tc_Polynomial_Opoly'( X
% 12.07/12.44 ) ), ~( 'class_Ring__and__Field_Ofield'( X ) ) ] )
% 12.07/12.44 , clause( 81997, [ 'class_Ring__and__Field_Oring'( 'tc_Polynomial_Opoly'( X
% 12.07/12.44 ) ), ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ) ] )
% 12.07/12.44 , clause( 81998, [ 'class_Ring__and__Field_Oidom'( 'tc_Polynomial_Opoly'( X
% 12.07/12.44 ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ] )
% 12.07/12.44 , clause( 81999, [ 'class_Ring__and__Field_Odvd'( 'tc_Polynomial_Opoly'( X
% 12.07/12.44 ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 12.07/12.44 , clause( 82000, [ 'class_Divides_Oring__div'( 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 , ~( 'class_Ring__and__Field_Ofield'( X ) ) ] )
% 12.07/12.44 , clause( 82001, [ 'class_Int_Onumber__ring'( 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.44 , ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ] )
% 12.07/12.44 , clause( 82002, [ 'class_Power_Opower'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 12.07/12.44 , clause( 82003, [ 'class_HOL_Ozero'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.44 'class_HOL_Ozero'( X ) ) ] )
% 12.07/12.44 ] ).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 subsumption(
% 12.07/12.44 clause( 27, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 12.07/12.44 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81590, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 12.07/12.44 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 12.07/12.44 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 subsumption(
% 12.07/12.44 clause( 29, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 12.07/12.44 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81592, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 12.07/12.44 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 12.07/12.44 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 eqswap(
% 12.07/12.44 clause( 82204, [ =( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( X, Z ), Y, Z ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( X, Y, Z ),
% 12.07/12.44 Z ) ), ~( 'class_Ring__and__Field_Oring'( Z ) ) ] )
% 12.07/12.44 , clause( 81604, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.44 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 12.07/12.44 , Z, X ) ) ] )
% 12.07/12.44 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 subsumption(
% 12.07/12.44 clause( 41, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 12.07/12.44 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.44 X ), X ) ) ] )
% 12.07/12.44 , clause( 82204, [ =( 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( X, Z ), Y, Z ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( X, Y, Z ),
% 12.07/12.44 Z ) ), ~( 'class_Ring__and__Field_Oring'( Z ) ) ] )
% 12.07/12.44 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 12.07/12.44 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 eqswap(
% 12.07/12.44 clause( 82280, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Y, Z ), Z ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( X, Y, Z ),
% 12.07/12.44 Z ) ), ~( 'class_Ring__and__Field_Oring'( Z ) ) ] )
% 12.07/12.44 , clause( 81605, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 12.07/12.44 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 12.07/12.44 X ), X ) ) ] )
% 12.07/12.44 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 subsumption(
% 12.07/12.44 clause( 42, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 12.07/12.44 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.44 X ), X ) ) ] )
% 12.07/12.44 , clause( 82280, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Y, Z ), Z ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( X, Y, Z ),
% 12.07/12.44 Z ) ), ~( 'class_Ring__and__Field_Oring'( Z ) ) ] )
% 12.07/12.44 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 12.07/12.44 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 paramod(
% 12.07/12.44 clause( 82659, [ =( 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( X, Y ), Z,
% 12.07/12.44 Y ), Y ), 'c_HOL_Otimes__class_Otimes'( X, Z, Y ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Oring'( Y ) ), ~( 'class_Ring__and__Field_Oring'(
% 12.07/12.44 Y ) ) ] )
% 12.07/12.44 , clause( 42, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 12.07/12.44 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.44 X ), X ) ) ] )
% 12.07/12.44 , 1, clause( 81663, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 12.07/12.44 Y, Z, X ) ) ] )
% 12.07/12.44 , 1, 1, substitution( 0, [ :=( X, Y ), :=( Y,
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( X, Y ) ), :=( Z, Z )] ), substitution( 1
% 12.07/12.44 , [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] )).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 factor(
% 12.07/12.44 clause( 82660, [ =( 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( X, Y ), Z,
% 12.07/12.44 Y ), Y ), 'c_HOL_Otimes__class_Otimes'( X, Z, Y ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Oring'( Y ) ) ] )
% 12.07/12.44 , clause( 82659, [ =( 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( X, Y ), Z,
% 12.07/12.44 Y ), Y ), 'c_HOL_Otimes__class_Otimes'( X, Z, Y ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Oring'( Y ) ), ~( 'class_Ring__and__Field_Oring'(
% 12.07/12.44 Y ) ) ] )
% 12.07/12.44 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 paramod(
% 12.07/12.44 clause( 82661, [ =( 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( X, Z, Y ),
% 12.07/12.44 Y ), Y ), 'c_HOL_Otimes__class_Otimes'( X, Z, Y ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Oring'( Y ) ), ~( 'class_Ring__and__Field_Oring'(
% 12.07/12.44 Y ) ) ] )
% 12.07/12.44 , clause( 41, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 12.07/12.44 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 12.07/12.44 X ), X ) ) ] )
% 12.07/12.44 , 1, clause( 82660, [ =( 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( X, Y ), Z,
% 12.07/12.44 Y ), Y ), 'c_HOL_Otimes__class_Otimes'( X, Z, Y ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Oring'( Y ) ) ] )
% 12.07/12.44 , 0, 2, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 12.07/12.44 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 factor(
% 12.07/12.44 clause( 82664, [ =( 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( X, Y, Z ),
% 12.07/12.44 Z ), Z ), 'c_HOL_Otimes__class_Otimes'( X, Y, Z ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Oring'( Z ) ) ] )
% 12.07/12.44 , clause( 82661, [ =( 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( X, Z, Y ),
% 12.07/12.44 Y ), Y ), 'c_HOL_Otimes__class_Otimes'( X, Z, Y ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Oring'( Y ) ), ~( 'class_Ring__and__Field_Oring'(
% 12.07/12.44 Y ) ) ] )
% 12.07/12.44 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 subsumption(
% 12.07/12.44 clause( 91, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), X ),
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 12.07/12.44 , clause( 82664, [ =( 'c_HOL_Ouminus__class_Ouminus'(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( X, Y, Z ),
% 12.07/12.44 Z ), Z ), 'c_HOL_Otimes__class_Otimes'( X, Y, Z ) ), ~(
% 12.07/12.44 'class_Ring__and__Field_Oring'( Z ) ) ] )
% 12.07/12.44 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 12.07/12.44 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 subsumption(
% 12.07/12.44 clause( 99, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , clause( 81672, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 12.07/12.44 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 12.07/12.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.44 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 12.07/12.44 ), ==>( 1, 1 )] ) ).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 subsumption(
% 12.07/12.44 clause( 104, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.44 ) ] )
% 12.07/12.44 , clause( 81677, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.44 ) ] )
% 12.07/12.44 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 12.07/12.44 ), ==>( 1, 1 )] ) ).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 subsumption(
% 12.07/12.44 clause( 116, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 12.07/12.44 ] )
% 12.07/12.44 , clause( 81690, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 12.07/12.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 12.07/12.44 ] )
% 12.07/12.44 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 12.07/12.44 ), ==>( 1, 1 )] ) ).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 subsumption(
% 12.07/12.44 clause( 174, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 12.07/12.44 ), Y ) ] )
% 12.07/12.44 , clause( 81764, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 12.07/12.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 12.07/12.44 ), Y ) ] )
% 12.07/12.44 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 12.07/12.44 ), ==>( 1, 1 )] ) ).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 eqswap(
% 12.07/12.44 clause( 83886, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_Osmult'( X
% 12.07/12.44 , T, Z ), 'c_Polynomial_Osmult'( Y, T, Z ), 'tc_Polynomial_Opoly'( Z ) )
% 12.07/12.44 , 'c_Polynomial_Osmult'( 'c_HOL_Ominus__class_Ominus'( X, Y, Z ), T, Z )
% 12.07/12.44 ), ~( 'class_Ring__and__Field_Ocomm__ring'( Z ) ) ] )
% 12.07/12.44 , clause( 81819, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 12.07/12.44 'c_Polynomial_Osmult'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_Osmult'( Y, T, X ),
% 12.07/12.44 'c_Polynomial_Osmult'( Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 12.07/12.44 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] )
% 12.07/12.44 ).
% 12.07/12.44
% 12.07/12.44
% 12.07/12.44 subsumption(
% 12.07/12.44 clause( 218, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 12.07/12.44 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_Osmult'( Y, T, X ),
% 12.07/12.44 'c_Polynomial_Osmult'( Z, T, X ), 'tc_Polynomial_Opoly'( X ) ),
% 12.07/12.44 'c_Polynomial_Osmult'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ) )
% 12.07/12.47 ] )
% 12.07/12.47 , clause( 83886, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_Osmult'(
% 12.07/12.47 X, T, Z ), 'c_Polynomial_Osmult'( Y, T, Z ), 'tc_Polynomial_Opoly'( Z ) )
% 12.07/12.47 , 'c_Polynomial_Osmult'( 'c_HOL_Ominus__class_Ominus'( X, Y, Z ), T, Z )
% 12.07/12.47 ), ~( 'class_Ring__and__Field_Ocomm__ring'( Z ) ) ] )
% 12.07/12.47 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T )] ),
% 12.07/12.47 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 12.07/12.47
% 12.07/12.47
% 12.07/12.47 subsumption(
% 12.07/12.47 clause( 277, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.47 , X ) ] )
% 12.07/12.47 , clause( 81885, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 12.07/12.47 , X ) ] )
% 12.07/12.47 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 12.07/12.47 ), ==>( 1, 1 )] ) ).
% 12.07/12.47
% 12.07/12.47
% 12.07/12.47 subsumption(
% 12.07/12.47 clause( 284, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y
% 12.07/12.47 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 12.07/12.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 12.07/12.47 , X ) ) ] )
% 12.07/12.47 , clause( 81892, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 12.07/12.47 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 12.07/12.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 12.07/12.47 , X ) ) ] )
% 12.07/12.47 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 12.07/12.47 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 12.07/12.47
% 12.07/12.47
% 12.07/12.47 subsumption(
% 12.07/12.47 clause( 296, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( Z, T, X
% 12.07/12.47 ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.47 ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.47 , clause( 81905, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 12.07/12.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( Z, T, X
% 12.07/12.47 ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 12.07/12.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 12.07/12.47 ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 12.07/12.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 12.07/12.47 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 12.07/12.47 ).
% 12.07/12.47
% 12.07/12.47
% 12.07/12.47 subsumption(
% 12.07/12.47 clause( 321, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p', 'v_q',
% 12.07/12.47 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.47 , clause( 81933, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p', 'v_q',
% 12.07/12.47 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ] )
% 12.07/12.47 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 12.07/12.47
% 12.07/12.47
% 12.07/12.47 subsumption(
% 12.07/12.47 clause( 324, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p',
% 12.07/12.47 'c_Polynomial_Osmult'( 'v_a', 'v_q', 'tc_Complex_Ocomplex' ),
% 12.07/12.47 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ) ] )
% 12.07/12.47 , clause( 81937, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'v_p',
% 12.07/12.47 'c_Polynomial_Osmult'( 'v_a', 'v_q', 'tc_Complex_Ocomplex' ),
% 12.07/12.47 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ) ] )
% 12.07/12.47 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 12.07/12.47
% 12.07/12.47
% 12.07/12.47 subsumption(
% 12.07/12.47 clause( 332, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 12.07/12.47 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.47 , clause( 81945, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 12.07/12.47 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.47 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 12.07/12.47
% 12.07/12.47
% 12.07/12.47 subsumption(
% 12.07/12.47 clause( 342, [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex'
% 12.07/12.47 ) ] )
% 12.07/12.47 , clause( 81955, [ 'class_OrderedGroup_Oab__group__add'(
% 12.07/12.47 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.47 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 12.07/12.47
% 12.07/12.47
% 12.07/12.47 subsumption(
% 12.07/12.47 clause( 344, [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex'
% 12.07/12.47 ) ] )
% 12.07/12.47 , clause( 81957, [ 'class_Ring__and__Field_Ocomm__ring'(
% 12.07/12.47 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.47 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 12.07/12.47
% 12.07/12.47
% 12.07/12.47 subsumption(
% 12.07/12.47 clause( 345, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' )
% 12.07/12.47 ] )
% 12.07/12.47 , clause( 81958, [ 'class_OrderedGroup_Omonoid__mult'(
% 12.07/12.47 'tc_Complex_Ocomplex' ) ] )
% 12.07/12.47 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 12.07/12.47
% 12.07/12.47
% 12.07/12.47 subsumption(
% 12.07/12.47 clause( 348, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ]
% 12.07/12.47 )Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------