TSTP Solution File: LCL774-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL774-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:57:48 EDT 2022
% Result : Unsatisfiable 0.85s 1.23s
% Output : Refutation 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL774-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n025.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 : Sun Jul 3 20:09:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.80/1.22 *** allocated 10000 integers for termspace/termends
% 0.80/1.22 *** allocated 10000 integers for clauses
% 0.80/1.22 *** allocated 10000 integers for justifications
% 0.80/1.22 Bliksem 1.12
% 0.80/1.22
% 0.80/1.22
% 0.80/1.22 Automatic Strategy Selection
% 0.80/1.22
% 0.80/1.22 Clauses:
% 0.80/1.22 [
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.80/1.22 , Y, X ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.80/1.22 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.80/1.22 ,
% 0.80/1.22 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.80/1.22 , Y, X ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.80/1.22 ), Y ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.22 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.80/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.22 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.80/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.80/1.22 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.80/1.22 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.80/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.80/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.80/1.22 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.80/1.22 , X ), W, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.80/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.80/1.22 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.80/1.22 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.80/1.22 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.80/1.22 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.80/1.22 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.80/1.22 ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.80/1.22 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.80/1.22 ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.80/1.22 Y, 'tc_nat' ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.80/1.22 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.80/1.22 ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.80/1.22 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.80/1.22 ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.80/1.22 X ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.80/1.22 X ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 X, T, 'tc_nat' ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.80/1.22 X ) ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.80/1.22 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.80/1.22 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.22 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.22 ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.22 ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.80/1.22 ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.22 ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.22 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.80/1.22 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.80/1.22 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.80/1.22 , X ), W, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.80/1.22 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.80/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.80/1.22 W, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.80/1.22 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.80/1.22 , X ), T, X ), W, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.80/1.22 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.80/1.22 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.80/1.22 W, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.22 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.22 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.80/1.22 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.80/1.22 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.80/1.22 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.80/1.22 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.80/1.22 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.80/1.22 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.80/1.22 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.80/1.22 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.80/1.22 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.80/1.22 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.80/1.22 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 0.80/1.22 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.80/1.22 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.80/1.22 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.22 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.80/1.22 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.22 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.80/1.22 , T, X ) ) ), =( Y, Z ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.80/1.22 , T, X ) ) ), =( Z, T ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.22 'tc_nat' ) ), =( Y, Z ) ],
% 0.80/1.22 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.22 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.80/1.22 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.22 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.80/1.22 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.22 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 0.80/1.22 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.80/1.22 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.80/1.22 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.80/1.22 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.22 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 0.80/1.22 ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.22 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.80/1.22 ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.22 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.22 ) ), =( Y, Z ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.22 ) ), =( Y, Z ) ],
% 0.80/1.22 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.80/1.22 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.22 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.22 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 0.80/1.22 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 0.80/1.22 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.80/1.22 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.80/1.22 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.22 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.80/1.22 X ) ) ), =( Z, T ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.80/1.22 X ) ) ), =( Z, T ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.80/1.22 X ) ) ), =( Y, T ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.80/1.22 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.22 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.80/1.22 X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.80/1.22 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.80/1.22 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.80/1.22 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.80/1.22 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.80/1.22 'tc_nat' ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.22 'tc_nat' ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.22 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.80/1.22 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.80/1.22 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.80/1.22 'tc_nat' ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.22 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.80/1.22 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.80/1.22 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 X ), T, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.80/1.22 ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.80/1.22 ],
% 0.80/1.22 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.80/1.22 , X, 'tc_nat' ), X ) ],
% 0.80/1.22 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.22 ), 'tc_nat' ), X ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.22 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.80/1.22 ), X ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.80/1.22 ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.80/1.22 ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.80/1.22 ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.80/1.22 ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.80/1.22 ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.80/1.22 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 0.80/1.22 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.80/1.22 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.80/1.22 ), Y ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.80/1.22 'tc_nat' ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.22 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.22 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.22 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.80/1.22 ,
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.80/1.22 ,
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.80/1.22 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.22 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.22 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.80/1.22 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.80/1.22 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.80/1.22 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.80/1.22 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.80/1.22 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.22 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.80/1.22 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.80/1.22 ,
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.22 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.80/1.22 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.80/1.22 ,
% 0.80/1.22 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.80/1.22 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.80/1.22 , T ), =( X, Z ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.22 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.80/1.22 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.80/1.22 , T ), =( X, Z ) ],
% 0.80/1.22 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.80/1.22 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 0.80/1.22 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.22 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.22 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.80/1.22 ) ],
% 0.80/1.22 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.22 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.80/1.22 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.22 , X ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.22 , X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.80/1.22 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.80/1.22 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.80/1.22 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.80/1.22 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.80/1.22 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.80/1.22 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.22 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.80/1.22 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.80/1.22 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.22 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.80/1.22 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.80/1.22 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 0.80/1.22 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.80/1.22 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.80/1.22 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.80/1.22 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.80/1.22 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 Y, T, X ) ) ],
% 0.80/1.22 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.80/1.22 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.80/1.23 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 Y, T, X ) ) ],
% 0.80/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.80/1.23 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.80/1.23 X ), X ) ) ],
% 0.80/1.23 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.80/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 Z, T, X ) ) ],
% 0.80/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.80/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.80/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 Z, T, X ) ) ],
% 0.80/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.80/1.23 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.80/1.23 X ), X ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.80/1.23 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.80/1.23 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.80/1.23 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.80/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.80/1.23 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.23 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.23 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.23 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 0.80/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.80/1.23 ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.80/1.23 , Y, X ), X ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.80/1.23 , T, X ), X ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.80/1.23 , T, X ), X ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.80/1.23 , Y, X ), X ) ) ],
% 0.80/1.23 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 0.80/1.23 ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.80/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.80/1.23 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.80/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.23 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.80/1.23 'tc_nat' ) ) ],
% 0.80/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.80/1.23 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.80/1.23 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.80/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.80/1.23 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.80/1.23 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.80/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.80/1.23 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 0.80/1.23 ],
% 0.80/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.23 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.80/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.80/1.23 T, X ), X ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.80/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.80/1.23 X ), Z, X ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.80/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.80/1.23 T, X ), X ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.80/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.80/1.23 X ), T, X ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.80/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.80/1.23 T, X ), X ) ) ],
% 0.80/1.23 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.23 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.80/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.80/1.23 X ), T, X ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.80/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.80/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.80/1.23 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.80/1.23 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.23 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.80/1.23 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.80/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.80/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.23 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.23 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.23 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.23 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.80/1.23 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.80/1.23 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.23 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.80/1.23 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.80/1.23 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.80/1.23 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.23 ) ), X, 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.80/1.23 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.23 ) ), X, 'tc_nat' ) ) ],
% 0.80/1.23 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.23 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 0.80/1.23 X ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.23 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.80/1.23 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.23 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.80/1.23 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.80/1.23 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.23 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.80/1.23 ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.23 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.23 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.80/1.23 ) ],
% 0.80/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.80/1.23 ), =( Z, Y ) ],
% 0.80/1.23 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.80/1.23 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.23 , Y, X ) ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.23 , Y, X ) ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.80/1.23 , X ) ) ],
% 0.80/1.23 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.80/1.23 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.80/1.23 [ =( X, 'c_Suc'(
% 0.80/1.23 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1'( X, Y ) ) ), =(
% 0.80/1.23 X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.80/1.23 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.80/1.23 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.80/1.23 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.80/1.23 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.80/1.23 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.23 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.80/1.23 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.80/1.23 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.80/1.23 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.80/1.23 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.80/1.23 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1'( X
% 0.80/1.23 ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.23 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.80/1.23 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.23 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.80/1.23 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1'( X ) )
% 0.80/1.23 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.80/1.23 , X, 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1'( X, Y ), Y,
% 0.80/1.23 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.23 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.80/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.80/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.80/1.23 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.23 ), 'tc_nat' ) ) ],
% 0.80/1.23 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.23 ), 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.23 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.80/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.23 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.23 'c_Suc'( X ), 'tc_nat' ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.23 'c_Suc'( X ), 'tc_nat' ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.80/1.23 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.80/1.23 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.80/1.23 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.80/1.23 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.80/1.23 ,
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.80/1.23 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.80/1.23 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.80/1.23 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 0.80/1.23 [ =( X, 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'(
% 0.80/1.23 Y, X ) ) ), ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( Y ), X ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubstn'(
% 0.80/1.23 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'( X, Y,
% 0.80/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.23 [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ), 'c_Lambda_Olift'( Z, Y ) )
% 0.80/1.23 , ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.80/1.23 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.80/1.23 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.80/1.23 ) ) ],
% 0.80/1.23 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X ) ],
% 0.80/1.23 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.80/1.23 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.80/1.23 ) ) ],
% 0.80/1.23 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubst'(
% 0.80/1.23 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.80/1.23 [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 0.80/1.23 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 0.80/1.23 ],
% 0.80/1.23 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.23 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.80/1.23 'tc_nat' ) ],
% 0.80/1.23 [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ), 'c_Lambda_Osubst'( T,
% 0.80/1.23 Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ],
% 0.80/1.23 [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ), 'c_Lambda_Olift'(
% 0.80/1.23 'c_Lambda_Oliftn'( X, Y, Z ), Z ) ) ],
% 0.80/1.23 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.23 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.80/1.23 'tc_nat' ) ],
% 0.80/1.23 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.80/1.23 ) ],
% 0.80/1.23 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 0.80/1.23 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.80/1.23 ,
% 0.80/1.23 [ 'c_Lambda_Obeta'( X, 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'( X, Y
% 0.80/1.23 ) ), ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), Y ) ) ],
% 0.80/1.23 [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.80/1.23 , 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.80/1.23 ,
% 0.80/1.23 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.23 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.80/1.23 ) ) ],
% 0.80/1.23 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T ),
% 0.80/1.23 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubst'( X, Z, T ), 'c_Lambda_Osubst'( Y,
% 0.80/1.23 Z, T ) ) ) ],
% 0.80/1.23 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.80/1.23 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OAbs'( Z ) ) ) ],
% 0.80/1.23 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.80/1.23 ) ],
% 0.80/1.23 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OApp'( Y, Z ) ) ) ],
% 0.80/1.23 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.80/1.23 [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( X, 'c_Lambda_OdB_OVar'( Y ), Z
% 0.80/1.23 ) ), ~( 'c_InductTermi_OIT'( X ) ) ],
% 0.80/1.23 [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ],
% 0.80/1.23 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z, T ) ) ),
% 0.80/1.23 =( X, Z ) ],
% 0.80/1.23 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z, T ) ) ),
% 0.80/1.23 =( Y, T ) ],
% 0.80/1.23 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OApp'( Y, Z ) ) ) ],
% 0.80/1.23 [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 0.80/1.23 'c_InductTermi_OIT'( X ) ) ],
% 0.80/1.23 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.80/1.23 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( X ) ) ],
% 0.80/1.23 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OApp'( X, Y ), Z ),
% 0.80/1.23 'c_Lambda_OdB_OApp'( 'c_Lambda_Olift'( X, Z ), 'c_Lambda_Olift'( Y, Z ) )
% 0.80/1.23 ) ],
% 0.80/1.23 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 0.80/1.23 'c_InductTermi_OIT'( X ) ) ],
% 0.80/1.23 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( X
% 0.80/1.23 , Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ],
% 0.80/1.23 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z
% 0.80/1.23 , Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.80/1.23 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OApp'( Y, Z ), T ),
% 0.80/1.23 'c_Lambda_OdB_OApp'( 'c_Lambda_Oliftn'( X, Y, T ), 'c_Lambda_Oliftn'( X,
% 0.80/1.23 Z, T ) ) ) ],
% 0.80/1.23 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T ),
% 0.80/1.23 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ), 'c_Lambda_Osubstn'( Y
% 0.80/1.23 , Z, T ) ) ) ],
% 0.80/1.23 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OVar'( Z ) ) ) ],
% 0.80/1.23 [ 'c_InductTermi_OIT'( 'v_r' ) ],
% 0.85/1.23 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( 'v_r', 'c_Lambda_OdB_OVar'(
% 0.85/1.23 'v_i' ) ) ) ],
% 0.85/1.23 [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( 'v_i' ) ) ) ],
% 0.85/1.23 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.85/1.23 ],
% 0.85/1.23 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.85/1.23 ) ],
% 0.85/1.23 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.85/1.23 ],
% 0.85/1.23 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.85/1.23 [ 'class_Orderings_Oorder'( 'tc_nat' ) ]
% 0.85/1.23 ] .
% 0.85/1.23
% 0.85/1.23
% 0.85/1.23 percentage equality = 0.354533, percentage horn = 0.869436
% 0.85/1.23 This is a problem with some equality
% 0.85/1.23
% 0.85/1.23
% 0.85/1.23
% 0.85/1.23 Options Used:
% 0.85/1.23
% 0.85/1.23 useres = 1
% 0.85/1.23 useparamod = 1
% 0.85/1.23 useeqrefl = 1
% 0.85/1.23 useeqfact = 1
% 0.85/1.23 usefactor = 1
% 0.85/1.23 usesimpsplitting = 0
% 0.85/1.23 usesimpdemod = 5
% 0.85/1.23 usesimpres = 3
% 0.85/1.23
% 0.85/1.23 resimpinuse = 1000
% 0.85/1.23 resimpclauses = 20000
% 0.85/1.23 substype = eqrewr
% 0.85/1.23 backwardsubs = 1
% 0.85/1.23 selectoldest = 5
% 0.85/1.23
% 0.85/1.23 litorderings [0] = split
% 0.85/1.23 litorderings [1] = extend the termordering, first sorting on arguments
% 0.85/1.23
% 0.85/1.23 termordering = kbo
% 0.85/1.23
% 0.85/1.23 litapriori = 0
% 0.85/1.23 termapriori = 1
% 0.85/1.23 litaposteriori = 0
% 0.85/1.23 termaposteriori = 0
% 0.85/1.23 demodaposteriori = 0
% 0.85/1.23 ordereqreflfact = 0
% 0.85/1.23
% 0.85/1.23 litselect = negord
% 0.85/1.23
% 0.85/1.23 maxweight = 15
% 0.85/1.23 maxdepth = 30000
% 0.85/1.23 maxlength = 115
% 0.85/1.23 maxnrvars = 195
% 0.85/1.23 excuselevel = 1
% 0.85/1.23 increasemaxweight = 1
% 0.85/1.23
% 0.85/1.23 maxselected = 10000000
% 0.85/1.23 maxnrclauses = 10000000
% 0.85/1.23
% 0.85/1.23 showgenerated = 0
% 0.85/1.23 showkept = 0
% 0.85/1.23 showselected = 0
% 0.85/1.23 showdeleted = 0
% 0.85/1.23 showresimp = 1
% 0.85/1.23 showstatus = 2000
% 0.85/1.23
% 0.85/1.23 prologoutput = 1
% 0.85/1.23 nrgoals = 5000000
% 0.85/1.23 totalproof = 1
% 0.85/1.23
% 0.85/1.23 Symbols occurring in the translation:
% 0.85/1.23
% 0.85/1.23 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.85/1.23 . [1, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.85/1.23 ! [4, 1] (w:0, o:47, a:1, s:1, b:0),
% 0.85/1.23 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.85/1.23 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.85/1.23 'class_Ring__and__Field_Ocomm__semiring__1' [40, 1] (w:1, o:52, a:1
% 0.85/1.23 , s:1, b:0),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes' [43, 3] (w:1, o:124, a:1, s:1, b:0),
% 0.85/1.23 'tc_nat' [44, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero' [45, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus' [46, 3] (w:1, o:126, a:1, s:1, b:0),
% 0.85/1.23 'class_OrderedGroup_Olordered__ab__group__add' [47, 1] (w:1, o:55, a:
% 0.85/1.23 1, s:1, b:0),
% 0.85/1.23 'class_OrderedGroup_Ogroup__add' [52, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.85/1.23
% 0.85/1.23 'c_HOL_Ominus__class_Ominus' [53, 3] (w:1, o:127, a:1, s:1, b:0),
% 0.85/1.23 'class_Ring__and__Field_Oidom' [54, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.85/1.23 'class_Int_Onumber__ring' [55, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.85/1.23 'c_Suc' [59, 1] (w:1, o:59, a:1, s:1, b:0),
% 0.85/1.23 'class_Ring__and__Field_Oring' [60, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.85/1.23 'c_HOL_Oord__class_Oless' [63, 3] (w:1, o:125, a:1, s:1, b:0),
% 0.85/1.23 'class_OrderedGroup_Ocomm__monoid__add' [66, 1] (w:1, o:61, a:1, s:1
% 0.85/1.23 , b:0),
% 0.85/1.23 'class_Nat_Osemiring__char__0' [68, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat' [69, 2] (w:1, o:118, a:1, s:1
% 0.85/1.23 , b:0),
% 0.85/1.23 'class_OrderedGroup_Oab__group__add' [70, 1] (w:1, o:62, a:1, s:1, b:
% 0.85/1.23 0),
% 0.85/1.23 'class_Ring__and__Field_Opordered__ring' [71, 1] (w:1, o:68, a:1, s:1
% 0.85/1.23 , b:0),
% 0.85/1.23 'class_Ring__and__Field_Oring__no__zero__divisors' [72, 1] (w:1, o:69
% 0.85/1.23 , a:1, s:1, b:0),
% 0.85/1.23 'class_Ring__and__Field_Ono__zero__divisors' [73, 1] (w:1, o:71, a:1
% 0.85/1.23 , s:1, b:0),
% 0.85/1.23 'class_OrderedGroup_Oab__semigroup__add' [74, 1] (w:1, o:72, a:1, s:1
% 0.85/1.23 , b:0),
% 0.85/1.23 'class_Ring__and__Field_Osemiring' [79, 1] (w:1, o:73, a:1, s:1, b:0)
% 0.85/1.23 ,
% 0.85/1.23 'class_Ring__and__Field_Osemiring__1' [80, 1] (w:1, o:74, a:1, s:1
% 0.85/1.23 , b:0),
% 0.85/1.23 'class_OrderedGroup_Opordered__comm__monoid__add' [81, 1] (w:1, o:75
% 0.85/1.23 , a:1, s:1, b:0),
% 0.85/1.23 'class_Ring__and__Field_Oordered__ring__strict' [82, 1] (w:1, o:63
% 0.85/1.23 , a:1, s:1, b:0),
% 0.85/1.23 'class_OrderedGroup_Ocancel__ab__semigroup__add' [83, 1] (w:1, o:76
% 0.85/1.23 , a:1, s:1, b:0),
% 0.85/1.23 'class_OrderedGroup_Ocancel__semigroup__add' [84, 1] (w:1, o:77, a:1
% 0.85/1.23 , s:1, b:0),
% 0.85/1.23 'class_Ring__and__Field_Oordered__semidom' [85, 1] (w:1, o:64, a:1
% 0.85/1.23 , s:1, b:0),
% 0.85/1.23 'class_Ring__and__Field_Oordered__semiring__strict' [86, 1] (w:1, o:
% 0.85/1.23 65, a:1, s:1, b:0),
% 0.85/1.23 'class_Ring__and__Field_Oordered__comm__semiring__strict' [87, 1] (w:
% 0.85/1.23 1, o:66, a:1, s:1, b:0),
% 0.85/1.23 'class_OrderedGroup_Omonoid__add' [88, 1] (w:1, o:78, a:1, s:1, b:0)
% 0.85/1.23 ,
% 0.85/1.23 'class_Ring__and__Field_Oordered__idom' [89, 1] (w:1, o:67, a:1, s:1
% 0.85/1.23 , b:0),
% 0.85/1.23 'class_Ring__and__Field_Omult__zero' [95, 1] (w:1, o:70, a:1, s:1, b:
% 0.85/1.23 0),
% 0.85/1.23 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [96, 1]
% 0.85/1.23 (w:1, o:79, a:1, s:1, b:0),
% 0.85/1.23 'class_OrderedGroup_Opordered__ab__group__add' [97, 1] (w:1, o:80, a:
% 0.85/1.23 1, s:1, b:0),
% 0.85/1.23 'class_OrderedGroup_Oab__semigroup__idem__mult' [98, 1] (w:1, o:81
% 0.85/1.23 , a:1, s:1, b:0),
% 0.85/1.23 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [100, 1]
% 0.85/1.23 (w:1, o:82, a:1, s:1, b:0),
% 0.85/1.23 'class_OrderedGroup_Oab__semigroup__mult' [101, 1] (w:1, o:83, a:1
% 0.85/1.23 , s:1, b:0),
% 0.85/1.23 'class_Ring__and__Field_Ocomm__semiring' [102, 1] (w:1, o:84, a:1, s:
% 0.85/1.23 1, b:0),
% 0.85/1.23 'class_Orderings_Opreorder' [103, 1] (w:1, o:86, a:1, s:1, b:0),
% 0.85/1.23 'class_Orderings_Olinorder' [104, 1] (w:1, o:87, a:1, s:1, b:0),
% 0.85/1.23 'class_Orderings_Oorder' [105, 1] (w:1, o:85, a:1, s:1, b:0),
% 0.85/1.23 'c_Lambda_Oliftn' [107, 3] (w:1, o:128, a:1, s:1, b:0),
% 0.85/1.23 'c_Lambda_OdB_OVar' [109, 1] (w:1, o:88, a:1, s:1, b:0),
% 0.85/1.23 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1' [110, 2] (w:
% 0.85/1.23 1, o:119, a:1, s:1, b:0),
% 0.85/1.23 'c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1' [112, 1] (w:1, o:
% 0.85/1.23 89, a:1, s:1, b:0),
% 0.85/1.23 'c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1' [113, 1] (w:1, o:90
% 0.85/1.23 , a:1, s:1, b:0),
% 0.85/1.23 'c_Lambda_OdB_OAbs' [115, 1] (w:1, o:91, a:1, s:1, b:0),
% 0.85/1.23 'c_Lambda_Obeta' [116, 2] (w:1, o:120, a:1, s:1, b:0),
% 0.85/1.23 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1' [117, 2] (w:1, o:121, a:1
% 0.85/1.23 , s:1, b:0),
% 0.85/1.23 'c_Lambda_Osubstn' [118, 3] (w:1, o:129, a:1, s:1, b:0),
% 0.85/1.23 'c_Lambda_Olift' [119, 2] (w:1, o:122, a:1, s:1, b:0),
% 0.85/1.23 'c_Lambda_Osubst' [120, 3] (w:1, o:130, a:1, s:1, b:0),
% 0.85/1.23 'c_Lambda_OdB_OApp' [123, 2] (w:1, o:123, a:1, s:1, b:0),
% 0.85/1.23 'c_InductTermi_OIT' [126, 1] (w:1, o:92, a:1, s:1, b:0),
% 0.85/1.23 'v_r' [129, 0] (w:1, o:45, a:1, s:1, b:0),
% 0.85/1.23 'v_i' [130, 0] (w:1, o:46, a:1, s:1, b:0).
% 0.85/1.23
% 0.85/1.23
% 0.85/1.23 Starting Search:
% 0.85/1.23
% 0.85/1.23
% 0.85/1.23 Bliksems!, er is een bewijs:
% 0.85/1.23 % SZS status Unsatisfiable
% 0.85/1.23 % SZS output start Refutation
% 0.85/1.23
% 0.85/1.23 clause( 280, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( X ) ) ] )
% 0.85/1.23 .
% 0.85/1.23 clause( 289, [] )
% 0.85/1.23 .
% 0.85/1.23
% 0.85/1.23
% 0.85/1.23 % SZS output end Refutation
% 0.85/1.23 found a proof!
% 0.85/1.23
% 0.85/1.23 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.85/1.23
% 0.85/1.23 initialclauses(
% 0.85/1.23 [ clause( 291, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.85/1.23 , Y, X ) ) ] )
% 0.85/1.23 , clause( 292, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 293, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.85/1.23 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.85/1.23 )
% 0.85/1.23 , clause( 294, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 295, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.85/1.23 , Y, X ) ) ] )
% 0.85/1.23 , clause( 296, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.85/1.23 ), Y ) ] )
% 0.85/1.23 , clause( 297, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.85/1.23 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.85/1.23 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 0.85/1.23 , clause( 298, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.85/1.23 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.85/1.23 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 0.85/1.23 , clause( 299, [ =( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.85/1.23 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 300, [ =( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.85/1.23 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 301, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.85/1.23 ) ] )
% 0.85/1.23 , clause( 302, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.85/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 0.85/1.23 , clause( 303, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' )
% 0.85/1.23 , 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 0.85/1.23 , clause( 304, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' )
% 0.85/1.23 , 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 0.85/1.23 , clause( 305, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 306, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.85/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.85/1.23 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.85/1.23 , X ), W, X ) ) ] )
% 0.85/1.23 , clause( 307, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.85/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.85/1.23 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 0.85/1.23 , clause( 308, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 0.85/1.23 , clause( 309, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 0.85/1.23 , clause( 310, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 0.85/1.23 , clause( 311, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 312, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 313, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.85/1.23 Y, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 314, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 315, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 316, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.85/1.23 X ) ) ] )
% 0.85/1.23 , clause( 317, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.85/1.23 X ) ) ] )
% 0.85/1.23 , clause( 318, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 319, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 X, T, 'tc_nat' ) ] )
% 0.85/1.23 , clause( 320, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.85/1.23 X ) ) ] )
% 0.85/1.23 , clause( 321, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.85/1.23 , clause( 322, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.85/1.23 , clause( 323, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 0.85/1.23 , Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.85/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 324, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 0.85/1.23 , clause( 325, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.85/1.23 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 0.85/1.23 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 326, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) )
% 0.85/1.23 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 327, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) )
% 0.85/1.23 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 328, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.85/1.23 ) ] )
% 0.85/1.23 , clause( 329, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.85/1.23 ) ] )
% 0.85/1.23 , clause( 330, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.85/1.23 ) ] )
% 0.85/1.23 , clause( 331, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.85/1.23 ) ] )
% 0.85/1.23 , clause( 332, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.85/1.23 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 0.85/1.23 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 333, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 334, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 0.85/1.23 , clause( 335, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 336, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 0.85/1.23 , clause( 337, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 0.85/1.23 , clause( 338, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 339, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 340, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.85/1.23 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 341, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.85/1.23 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.85/1.23 , X ), W, X ), X ) ) ] )
% 0.85/1.23 , clause( 342, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.85/1.23 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.85/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.85/1.23 W, X ), X ) ) ] )
% 0.85/1.23 , clause( 343, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.85/1.23 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.85/1.23 , X ), T, X ), W, X ) ) ] )
% 0.85/1.23 , clause( 344, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.85/1.23 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.85/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.85/1.23 W, X ), X ) ) ] )
% 0.85/1.23 , clause( 345, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.85/1.23 ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.85/1.23 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 346, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 0.85/1.23 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 347, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 0.85/1.23 , Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.85/1.23 , clause( 348, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.85/1.23 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 349, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.85/1.23 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 350, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.85/1.23 ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 351, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 X, Y, 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 352, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.85/1.23 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 353, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.85/1.23 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 354, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.85/1.23 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 355, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.85/1.23 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 356, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.85/1.23 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 357, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.85/1.23 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 358, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.85/1.23 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 359, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 360, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.85/1.23 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 0.85/1.23 , clause( 361, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.85/1.23 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 362, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 363, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.85/1.23 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 364, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.85/1.23 , T, X ) ) ), =( Y, Z ) ] )
% 0.85/1.23 , clause( 365, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.85/1.23 , T, X ) ) ), =( Z, T ) ] )
% 0.85/1.23 , clause( 366, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.85/1.23 'tc_nat' ) ), =( Y, Z ) ] )
% 0.85/1.23 , clause( 367, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 368, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.85/1.23 , clause( 369, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 370, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 371, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' )
% 0.85/1.23 , 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 372, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 373, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 Z, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 374, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 X, Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 375, [ =( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 0.85/1.23 ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.85/1.23 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 376, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.85/1.23 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 0.85/1.23 , clause( 377, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 378, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.85/1.23 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 379, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.85/1.23 Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 380, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.85/1.23 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 381, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.85/1.23 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.85/1.23 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 0.85/1.23 , clause( 382, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.85/1.23 ) ), =( Y, Z ) ] )
% 0.85/1.23 , clause( 383, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.85/1.23 ) ), =( Y, Z ) ] )
% 0.85/1.23 , clause( 384, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.85/1.23 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 0.85/1.23 ] )
% 0.85/1.23 , clause( 385, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 0.85/1.23 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 0.85/1.23 ] )
% 0.85/1.23 , clause( 386, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 0.85/1.23 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 387, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 388, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_Suc'( X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 0.85/1.23 Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 0.85/1.23 ) ] )
% 0.85/1.23 , clause( 389, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.85/1.23 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 390, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 0.85/1.23 , clause( 391, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 0.85/1.23 , clause( 392, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 0.85/1.23 , clause( 393, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.85/1.23 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 0.85/1.23 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 0.85/1.23 , clause( 394, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) )
% 0.85/1.23 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 Y, T, X ) ) ), =( Z, T ) ] )
% 0.85/1.23 , clause( 395, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.85/1.23 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 Y, T, X ) ) ), =( Z, T ) ] )
% 0.85/1.23 , clause( 396, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.85/1.23 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 T, Z, X ) ) ), =( Y, T ) ] )
% 0.85/1.23 , clause( 397, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 398, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.85/1.23 , clause( 399, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 0.85/1.23 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 0.85/1.23 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 400, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 401, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 402, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.85/1.23 X ), X ) ) ] )
% 0.85/1.23 , clause( 403, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 404, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 0.85/1.23 , clause( 405, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y,
% 0.85/1.23 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 0.85/1.23 ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 0.85/1.23 , clause( 406, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 0.85/1.23 , clause( 407, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y,
% 0.85/1.23 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 0.85/1.23 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 0.85/1.23 , clause( 408, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.85/1.23 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat'
% 0.85/1.23 ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 409, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.85/1.23 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.85/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 410, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.85/1.23 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.85/1.23 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.85/1.23 , X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 411, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.85/1.23 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat'
% 0.85/1.23 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.85/1.23 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 412, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.85/1.23 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 413, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.85/1.23 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.85/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 414, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.85/1.23 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 415, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 416, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.85/1.23 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 X ), T, X ) ) ] )
% 0.85/1.23 , clause( 417, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.85/1.23 , clause( 418, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.85/1.23 , clause( 419, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.85/1.23 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.85/1.23 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.85/1.23 , clause( 420, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.85/1.23 , clause( 421, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 422, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 0.85/1.23 , clause( 423, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.85/1.23 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.85/1.23 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.85/1.23 , clause( 424, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.85/1.23 , clause( 425, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 426, [ ~(
% 0.85/1.23 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.85/1.23 , clause( 427, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 428, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.85/1.23 ] )
% 0.85/1.23 , clause( 429, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.85/1.23 ] )
% 0.85/1.23 , clause( 430, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 431, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 0.85/1.23 , clause( 432, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 0.85/1.23 , clause( 433, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.85/1.23 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 434, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.85/1.23 ] )
% 0.85/1.23 , clause( 435, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.85/1.23 ] )
% 0.85/1.23 , clause( 436, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.85/1.23 ] )
% 0.85/1.23 , clause( 437, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.85/1.23 ] )
% 0.85/1.23 , clause( 438, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.85/1.23 ] )
% 0.85/1.23 , clause( 439, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 0.85/1.23 , clause( 440, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ) ] )
% 0.85/1.23 , clause( 441, [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 0.85/1.23 , clause( 442, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.85/1.23 ), Y ) ] )
% 0.85/1.23 , clause( 443, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 444, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 445, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 0.85/1.23 , clause( 446, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.85/1.23 , clause( 447, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 0.85/1.23 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 448, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 449, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 450, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 451, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 452, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 453, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.85/1.23 , clause( 454, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 455, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.85/1.23 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.85/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.85/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 0.85/1.23 , clause( 456, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.85/1.23 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.85/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.85/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 0.85/1.23 , clause( 457, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.85/1.23 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.85/1.23 , clause( 458, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 459, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.85/1.23 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 460, [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat'
% 0.85/1.23 ), 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.85/1.23 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 461, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat'
% 0.85/1.23 ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.85/1.23 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 462, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.85/1.23 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 463, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.85/1.23 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 0.85/1.23 , clause( 464, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.85/1.23 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.85/1.23 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 0.85/1.23 =( Y, T ) ] )
% 0.85/1.23 , clause( 465, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.85/1.23 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.85/1.23 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 0.85/1.23 =( Y, T ) ] )
% 0.85/1.23 , clause( 466, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.85/1.23 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.85/1.23 , T ), =( X, Z ) ] )
% 0.85/1.23 , clause( 467, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.85/1.23 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.85/1.23 , T ), =( X, Z ) ] )
% 0.85/1.23 , clause( 468, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y
% 0.85/1.23 ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 469, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.85/1.23 , clause( 470, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 0.85/1.23 , clause( 471, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 0.85/1.23 , clause( 472, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 0.85/1.23 , clause( 473, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 474, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 475, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.85/1.23 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 476, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.85/1.23 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y,
% 0.85/1.23 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 477, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 478, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 479, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 480, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 481, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 482, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 0.85/1.23 , Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 483, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.85/1.23 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 484, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.85/1.23 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.85/1.23 , clause( 485, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 0.85/1.23 , clause( 486, [ ~(
% 0.85/1.23 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.85/1.23 , clause( 487, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.85/1.23 Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 488, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.85/1.23 , X ) ) ] )
% 0.85/1.23 , clause( 489, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.85/1.23 , X ) ) ] )
% 0.85/1.23 , clause( 490, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 491, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 0.85/1.23 , clause( 492, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.85/1.23 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 493, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.85/1.23 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 494, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 0.85/1.23 , =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.85/1.23 , X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 0.85/1.23 , clause( 495, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.85/1.23 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.85/1.23 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.85/1.23 , clause( 496, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.85/1.23 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.85/1.23 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.85/1.23 , clause( 497, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.85/1.23 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.85/1.23 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.85/1.23 , clause( 498, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.85/1.23 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.85/1.23 , clause( 499, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 500, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 501, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 502, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 503, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.85/1.23 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.85/1.23 , clause( 504, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.85/1.23 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 505, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X
% 0.85/1.23 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 506, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X
% 0.85/1.23 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 507, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.85/1.23 Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 508, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'(
% 0.85/1.23 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 509, [ ~(
% 0.85/1.23 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 Y, T, X ) ) ] )
% 0.85/1.23 , clause( 510, [ ~(
% 0.85/1.23 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 Y, T, X ) ) ] )
% 0.85/1.23 , clause( 511, [ ~(
% 0.85/1.23 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.85/1.23 X ), X ) ) ] )
% 0.85/1.23 , clause( 512, [ ~(
% 0.85/1.23 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 Z, T, X ) ) ] )
% 0.85/1.23 , clause( 513, [ ~(
% 0.85/1.23 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 Z, T, X ) ) ] )
% 0.85/1.23 , clause( 514, [ ~(
% 0.85/1.23 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.85/1.23 X ), X ) ) ] )
% 0.85/1.23 , clause( 515, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.85/1.23 Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 516, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 517, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.85/1.23 Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 518, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 0.85/1.23 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.85/1.23 , clause( 519, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 0.85/1.23 , =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 0.85/1.23 , clause( 520, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 521, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 522, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 523, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.85/1.23 , Y, X ), X ) ) ] )
% 0.85/1.23 , clause( 524, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.85/1.23 , T, X ), X ) ) ] )
% 0.85/1.23 , clause( 525, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.85/1.23 , T, X ), X ) ) ] )
% 0.85/1.23 , clause( 526, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.85/1.23 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.85/1.23 , Y, X ), X ) ) ] )
% 0.85/1.23 , clause( 527, [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 0.85/1.23 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) )
% 0.85/1.23 , =( Y, Z ) ] )
% 0.85/1.23 , clause( 528, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.85/1.23 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 0.85/1.23 , clause( 529, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 0.85/1.23 , Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 530, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.85/1.23 ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 0.85/1.23 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.85/1.23 , clause( 531, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.85/1.23 ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 0.85/1.23 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 0.85/1.23 , clause( 532, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 0.85/1.23 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 0.85/1.23 , clause( 533, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.85/1.23 , clause( 534, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 535, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.85/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.85/1.23 T, X ), X ) ) ] )
% 0.85/1.23 , clause( 536, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.85/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.85/1.23 X ), Z, X ) ) ] )
% 0.85/1.23 , clause( 537, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.85/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.85/1.23 T, X ), X ) ) ] )
% 0.85/1.23 , clause( 538, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.85/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.85/1.23 X ), T, X ) ) ] )
% 0.85/1.23 , clause( 539, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.85/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.85/1.23 T, X ), X ) ) ] )
% 0.85/1.23 , clause( 540, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.85/1.23 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 541, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.85/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.85/1.23 X ), T, X ) ) ] )
% 0.85/1.23 , clause( 542, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.85/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 0.85/1.23 , clause( 543, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.85/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 0.85/1.23 , clause( 544, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.85/1.23 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 545, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 0.85/1.23 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 546, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.85/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.85/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 0.85/1.23 , clause( 547, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.85/1.23 Y, X ) ) ] )
% 0.85/1.23 , clause( 548, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.85/1.23 Y, X ) ) ] )
% 0.85/1.23 , clause( 549, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.85/1.23 Y, X ) ) ] )
% 0.85/1.23 , clause( 550, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.85/1.23 Y, X ) ) ] )
% 0.85/1.23 , clause( 551, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 0.85/1.23 , 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 552, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 553, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.85/1.23 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 554, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 555, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 0.85/1.23 , clause( 556, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 0.85/1.23 , clause( 557, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 X, Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.85/1.23 ) ), X, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 558, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'(
% 0.85/1.23 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.85/1.23 ) ), X, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 559, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 560, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.85/1.23 ), X, Y ), X ) ] )
% 0.85/1.23 , clause( 561, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.85/1.23 ] )
% 0.85/1.23 , clause( 562, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.85/1.23 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.85/1.23 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 0.85/1.23 , clause( 563, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.85/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 564, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.85/1.23 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 565, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 0.85/1.23 )
% 0.85/1.23 , clause( 566, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 0.85/1.23 )
% 0.85/1.23 , clause( 567, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 568, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 569, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.85/1.23 ) ] )
% 0.85/1.23 , clause( 570, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 0.85/1.23 , clause( 571, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.85/1.23 ), =( Z, Y ) ] )
% 0.85/1.23 , clause( 572, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 0.85/1.23 , clause( 573, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 0.85/1.23 , clause( 574, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.85/1.23 ) ] )
% 0.85/1.23 , clause( 575, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.85/1.23 ), =( Z, Y ) ] )
% 0.85/1.23 , clause( 576, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.85/1.23 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ] )
% 0.85/1.23 , clause( 577, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.85/1.23 , clause( 578, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.85/1.23 , clause( 579, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.85/1.23 , clause( 580, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 581, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 582, [ =( X, 'c_Suc'(
% 0.85/1.23 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1'( X, Y ) ) ), =(
% 0.85/1.23 X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 583, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ),
% 0.85/1.23 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 0.85/1.23 , clause( 584, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ),
% 0.85/1.23 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 0.85/1.23 , clause( 585, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.85/1.23 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 586, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 0.85/1.23 ] )
% 0.85/1.23 , clause( 587, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 0.85/1.23 , clause( 588, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 0.85/1.23 , clause( 589, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X )
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 590, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X )
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 591, [ =( X, 'c_Suc'(
% 0.85/1.23 'c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1'( X ) ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 592, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 593, [ =( X, 'c_Suc'(
% 0.85/1.23 'c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1'( X ) ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.85/1.23 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 594, [ 'c_HOL_Oord__class_Oless'(
% 0.85/1.23 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1'( X, Y ), Y,
% 0.85/1.23 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 595, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 0.85/1.23 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.85/1.23 , clause( 596, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.85/1.23 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.85/1.23 , clause( 597, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 598, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 599, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 0.85/1.23 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.85/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.85/1.23 ) ), Y, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 600, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.85/1.23 , clause( 601, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.85/1.23 , clause( 602, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.85/1.23 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 0.85/1.23 )
% 0.85/1.23 , clause( 603, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.85/1.23 , clause( 604, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 605, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.85/1.23 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 0.85/1.23 , clause( 606, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.85/1.23 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 607, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.85/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 608, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.85/1.23 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.85/1.23 , clause( 609, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ),
% 0.85/1.23 'c_Lambda_OdB_OAbs'( Y ) ), ~( 'c_Lambda_Obeta'( X, Y ) ) ] )
% 0.85/1.23 , clause( 610, [ =( X, 'c_Lambda_OdB_OAbs'(
% 0.85/1.23 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'( Y, X ) ) ), ~(
% 0.85/1.23 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( Y ), X ) ) ] )
% 0.85/1.23 , clause( 611, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 0.85/1.23 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'(
% 0.85/1.23 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.85/1.23 , clause( 612, [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ),
% 0.85/1.23 'c_Lambda_Olift'( Z, Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ] )
% 0.85/1.23 , clause( 613, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.85/1.23 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 614, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X
% 0.85/1.23 ) ] )
% 0.85/1.23 , clause( 615, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.85/1.23 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 616, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 0.85/1.23 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ] )
% 0.85/1.23 , clause( 617, [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 0.85/1.23 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 0.85/1.23 ] )
% 0.85/1.23 , clause( 618, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.85/1.23 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.85/1.23 'tc_nat' ) ] )
% 0.85/1.23 , clause( 619, [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ),
% 0.85/1.23 'c_Lambda_Osubst'( T, Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ] )
% 0.85/1.23 , clause( 620, [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ),
% 0.85/1.23 'c_Lambda_Olift'( 'c_Lambda_Oliftn'( X, Y, Z ), Z ) ) ] )
% 0.85/1.23 , clause( 621, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.85/1.23 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.85/1.23 'tc_nat' ) ] )
% 0.85/1.23 , clause( 622, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.85/1.23 ), =( X, Y ) ] )
% 0.85/1.23 , clause( 623, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OAbs'(
% 0.85/1.23 X ), Y ), 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 624, [ 'c_Lambda_Obeta'( X,
% 0.85/1.23 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'( X, Y ) ), ~(
% 0.85/1.23 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), Y ) ) ] )
% 0.85/1.23 , clause( 625, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ) ), 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.85/1.23 'tc_nat' ) ) ) ] )
% 0.85/1.23 , clause( 626, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.85/1.23 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.85/1.23 ) ) ] )
% 0.85/1.23 , clause( 627, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T )
% 0.85/1.23 , 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubst'( X, Z, T ), 'c_Lambda_Osubst'( Y
% 0.85/1.23 , Z, T ) ) ) ] )
% 0.85/1.23 , clause( 628, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) )
% 0.85/1.24 ) ] )
% 0.85/1.24 , clause( 629, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OAbs'( Z
% 0.85/1.24 ) ) ) ] )
% 0.85/1.24 , clause( 630, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) )
% 0.85/1.24 ), =( X, Y ) ] )
% 0.85/1.24 , clause( 631, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OApp'( Y, Z
% 0.85/1.24 ) ) ) ] )
% 0.85/1.24 , clause( 632, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y
% 0.85/1.24 ) ] )
% 0.85/1.24 , clause( 633, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( X,
% 0.85/1.24 'c_Lambda_OdB_OVar'( Y ), Z ) ), ~( 'c_InductTermi_OIT'( X ) ) ] )
% 0.85/1.24 , clause( 634, [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 0.85/1.24 , clause( 635, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z
% 0.85/1.24 , T ) ) ), =( X, Z ) ] )
% 0.85/1.24 , clause( 636, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z
% 0.85/1.24 , T ) ) ), =( Y, T ) ] )
% 0.85/1.24 , clause( 637, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OApp'( Y, Z
% 0.85/1.24 ) ) ) ] )
% 0.85/1.24 , clause( 638, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 0.85/1.24 'c_InductTermi_OIT'( X ) ) ] )
% 0.85/1.24 , clause( 639, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.85/1.24 ) ] )
% 0.85/1.24 , clause( 640, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( X ) ) ] )
% 0.85/1.24 , clause( 641, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OApp'( X, Y ), Z ),
% 0.85/1.24 'c_Lambda_OdB_OApp'( 'c_Lambda_Olift'( X, Z ), 'c_Lambda_Olift'( Y, Z ) )
% 0.85/1.24 ) ] )
% 0.85/1.24 , clause( 642, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 0.85/1.24 'c_InductTermi_OIT'( X ) ) ] )
% 0.85/1.24 , clause( 643, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ),
% 0.85/1.24 'c_Lambda_OdB_OApp'( X, Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ] )
% 0.85/1.24 , clause( 644, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ),
% 0.85/1.24 'c_Lambda_OdB_OApp'( Z, Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ] )
% 0.85/1.24 , clause( 645, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OApp'( Y, Z ), T )
% 0.85/1.24 , 'c_Lambda_OdB_OApp'( 'c_Lambda_Oliftn'( X, Y, T ), 'c_Lambda_Oliftn'( X
% 0.85/1.24 , Z, T ) ) ) ] )
% 0.85/1.24 , clause( 646, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T )
% 0.85/1.24 , 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ), 'c_Lambda_Osubstn'(
% 0.85/1.24 Y, Z, T ) ) ) ] )
% 0.85/1.24 , clause( 647, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OVar'( Z
% 0.85/1.24 ) ) ) ] )
% 0.85/1.24 , clause( 648, [ 'c_InductTermi_OIT'( 'v_r' ) ] )
% 0.85/1.24 , clause( 649, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( 'v_r',
% 0.85/1.24 'c_Lambda_OdB_OVar'( 'v_i' ) ) ) ] )
% 0.85/1.24 , clause( 650, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( 'v_i' ) ) ) ]
% 0.85/1.24 )
% 0.85/1.24 , clause( 651, [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.85/1.24 'tc_nat' ) ] )
% 0.85/1.24 , clause( 652, [
% 0.85/1.24 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 0.85/1.24 )
% 0.85/1.24 , clause( 653, [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.85/1.24 'tc_nat' ) ] )
% 0.85/1.24 , clause( 654, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.85/1.24 'tc_nat' ) ] )
% 0.85/1.24 , clause( 655, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.85/1.24 'tc_nat' ) ] )
% 0.85/1.24 , clause( 656, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat'
% 0.85/1.24 ) ] )
% 0.85/1.24 , clause( 657, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ]
% 0.85/1.24 )
% 0.85/1.24 , clause( 658, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ]
% 0.85/1.24 )
% 0.85/1.24 , clause( 659, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 0.85/1.24 )
% 0.85/1.24 , clause( 660, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ]
% 0.85/1.24 )
% 0.85/1.24 , clause( 661, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ] )
% 0.85/1.24 , clause( 662, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ] )
% 0.85/1.24 , clause( 663, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ] )
% 0.85/1.24 , clause( 664, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 0.85/1.24 , clause( 665, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 0.85/1.24 , clause( 666, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 0.85/1.24 , clause( 667, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 0.85/1.24 , clause( 668, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 0.85/1.24 , clause( 669, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 0.85/1.24 , clause( 670, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 0.85/1.24 , clause( 671, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 0.85/1.24 , clause( 672, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 0.85/1.24 ] ).
% 0.85/1.24
% 0.85/1.24
% 0.85/1.24
% 0.85/1.24 subsumption(
% 0.85/1.24 clause( 280, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( X ) ) ] )
% 0.85/1.24 , clause( 640, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( X ) ) ] )
% 0.85/1.24 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.85/1.24
% 0.85/1.24
% 0.85/1.24 resolution(
% 0.85/1.24 clause( 1565, [] )
% 0.85/1.24 , clause( 650, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( 'v_i' ) ) ) ]
% 0.85/1.24 )
% 0.85/1.24 , 0, clause( 280, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( X ) ) ] )
% 0.85/1.24 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_i' )] )).
% 0.85/1.24
% 0.85/1.24
% 0.85/1.24 subsumption(
% 0.85/1.24 clause( 289, [] )
% 0.85/1.24 , clause( 1565, [] )
% 0.85/1.24 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.85/1.24
% 0.85/1.24
% 0.85/1.24 end.
% 0.85/1.24
% 0.85/1.24 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.85/1.24
% 0.85/1.24 Memory use:
% 0.85/1.24
% 0.85/1.24 space for terms: 17906
% 0.85/1.24 space for clauses: 24907
% 0.85/1.24
% 0.85/1.24
% 0.85/1.24 clauses generated: 360
% 0.85/1.24 clauses kept: 290
% 0.85/1.24 clauses selected: 0
% 0.85/1.24 clauses deleted: 0
% 0.85/1.24 clauses inuse deleted: 0
% 0.85/1.24
% 0.85/1.24 subsentry: 7706
% 0.85/1.24 literals s-matched: 3416
% 0.85/1.24 literals matched: 3328
% 0.85/1.24 full subsumption: 887
% 0.85/1.24
% 0.85/1.24 checksum: 494657667
% 0.85/1.24
% 0.85/1.24
% 0.85/1.24 Bliksem ended
%------------------------------------------------------------------------------