TSTP Solution File: LCL855-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL855-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n008.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 07:58:49 EDT 2022
% Result : Unsatisfiable 32.08s 32.50s
% Output : Refutation 32.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL855-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Jul 3 07:22:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.83/1.18 *** allocated 10000 integers for termspace/termends
% 0.83/1.18 *** allocated 10000 integers for clauses
% 0.83/1.18 *** allocated 10000 integers for justifications
% 0.83/1.18 Bliksem 1.12
% 0.83/1.18
% 0.83/1.18
% 0.83/1.18 Automatic Strategy Selection
% 0.83/1.18
% 0.83/1.18 Clauses:
% 0.83/1.18 [
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.83/1.18 , Y, X ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.83/1.18 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.83/1.18 ,
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.83/1.18 , Y, X ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.83/1.18 ), Y ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.83/1.18 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.83/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.83/1.18 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.83/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.83/1.18 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 0.83/1.18 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.83/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.83/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.83/1.18 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.83/1.18 , X ), W, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.83/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.83/1.18 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.83/1.18 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.83/1.18 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.83/1.18 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.83/1.18 ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.83/1.18 ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.83/1.18 Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.83/1.18 ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.83/1.18 ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.83/1.18 X ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.83/1.18 X ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 X, T, 'tc_nat' ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.83/1.18 X ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.83/1.18 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.83/1.18 ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.83/1.18 ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.83/1.18 ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.83/1.18 ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.83/1.18 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.83/1.18 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.83/1.18 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.83/1.18 , X ), W, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.83/1.18 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.83/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.83/1.18 W, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.83/1.18 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.83/1.18 , X ), T, X ), W, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.83/1.18 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.83/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.83/1.18 W, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.83/1.18 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.83/1.18 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.83/1.18 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.83/1.18 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.83/1.18 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.83/1.18 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.83/1.18 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.83/1.18 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.83/1.18 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.83/1.18 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.83/1.18 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.83/1.18 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 0.83/1.18 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.83/1.18 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.83/1.18 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.83/1.18 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.83/1.18 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.83/1.18 , T, X ) ) ), =( Y, Z ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.83/1.18 , T, X ) ) ), =( Z, T ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.83/1.18 'tc_nat' ) ), =( Y, Z ) ],
% 0.83/1.18 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.83/1.18 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.83/1.18 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.83/1.18 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.83/1.18 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.83/1.18 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 0.83/1.18 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.83/1.18 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.83/1.18 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.83/1.18 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 0.83/1.18 ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.83/1.18 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.83/1.18 ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.83/1.18 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.83/1.18 ) ), =( Y, Z ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.83/1.18 ) ), =( Y, Z ) ],
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.83/1.18 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.83/1.18 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.83/1.18 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 0.83/1.18 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 0.83/1.18 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.83/1.18 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.83/1.18 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.83/1.18 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.83/1.18 X ) ) ), =( Z, T ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.83/1.18 X ) ) ), =( Z, T ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.83/1.18 X ) ) ), =( Y, T ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.83/1.18 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.83/1.18 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.83/1.18 X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.83/1.18 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.83/1.18 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.83/1.18 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.83/1.18 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.83/1.18 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.83/1.18 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.83/1.18 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.83/1.18 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.83/1.18 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.83/1.18 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.83/1.18 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.83/1.18 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.83/1.18 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 X ), T, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.83/1.18 ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.83/1.18 ],
% 0.83/1.18 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.83/1.18 , X, 'tc_nat' ), X ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.83/1.18 ), 'tc_nat' ), X ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.83/1.18 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.83/1.18 ), X ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.83/1.18 ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.83/1.18 ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.83/1.18 ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.83/1.18 ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.83/1.18 ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.83/1.18 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 0.83/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.83/1.18 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.83/1.18 ), Y ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.83/1.18 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.83/1.18 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.83/1.18 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.83/1.18 ,
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.83/1.18 ,
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.83/1.18 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.83/1.18 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.83/1.18 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.83/1.18 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.83/1.18 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.83/1.18 ,
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.83/1.18 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.83/1.18 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.83/1.18 ,
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.83/1.18 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.83/1.18 , T ), =( X, Z ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 0.83/1.18 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 0.83/1.18 , T ), =( X, Z ) ],
% 0.83/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.83/1.18 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 0.83/1.18 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.83/1.18 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.83/1.18 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.83/1.18 ) ],
% 0.83/1.18 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.83/1.18 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.83/1.18 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.83/1.18 , X ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.83/1.18 , X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.83/1.18 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.83/1.18 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.83/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.83/1.18 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.83/1.18 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.83/1.18 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.83/1.18 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.83/1.18 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.83/1.18 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.83/1.18 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 0.83/1.18 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.83/1.18 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 Y, T, X ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.83/1.18 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 Y, T, X ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.83/1.18 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.83/1.18 X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 Z, T, X ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.83/1.18 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 Z, T, X ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.83/1.18 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.83/1.18 X ), X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.83/1.18 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.83/1.18 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.83/1.18 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 0.83/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.83/1.18 , Y, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.83/1.18 , T, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.83/1.18 , T, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.83/1.18 , Y, X ), X ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 0.83/1.18 ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.83/1.18 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.83/1.18 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.83/1.18 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.83/1.18 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.83/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.83/1.18 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 0.83/1.18 ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.83/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.83/1.18 T, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.83/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.83/1.18 X ), Z, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.83/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.83/1.18 T, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.83/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.83/1.18 X ), T, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.83/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.83/1.18 T, X ), X ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.83/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.83/1.18 X ), T, X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.83/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.83/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.83/1.18 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.83/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.83/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.83/1.18 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.83/1.18 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.83/1.18 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.83/1.18 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.83/1.18 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.83/1.18 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.83/1.18 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.83/1.18 ) ), X, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.83/1.18 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.83/1.18 ) ), X, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 0.83/1.18 X ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.83/1.18 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.83/1.18 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.83/1.18 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.83/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.83/1.18 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.83/1.18 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.83/1.18 ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.83/1.18 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.83/1.18 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.83/1.18 ) ],
% 0.83/1.18 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.83/1.18 ), =( Z, Y ) ],
% 0.83/1.18 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.83/1.18 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.83/1.18 , Y, X ) ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.83/1.18 , Y, X ) ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.83/1.18 , X ) ) ],
% 0.83/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.83/1.18 [ =( X, 'c_Suc'(
% 0.83/1.18 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1'( X, Y ) ) ), =(
% 0.83/1.18 X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.83/1.18 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.83/1.18 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.83/1.18 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.83/1.18 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.83/1.18 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.83/1.18 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.83/1.18 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.83/1.18 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.83/1.18 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1'( X
% 0.83/1.18 ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.83/1.18 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.83/1.18 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1'( X ) )
% 0.83/1.18 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.83/1.18 , X, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1'( X, Y ), Y,
% 0.83/1.18 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.83/1.18 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.83/1.18 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.83/1.18 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.83/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.83/1.18 ), 'tc_nat' ) ) ],
% 0.83/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.83/1.18 ), 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.83/1.18 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.83/1.18 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.83/1.18 'c_Suc'( X ), 'tc_nat' ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.83/1.18 'c_Suc'( X ), 'tc_nat' ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.83/1.18 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.83/1.18 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.83/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.83/1.18 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.83/1.18 ,
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.83/1.18 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.83/1.18 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.83/1.18 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 0.83/1.18 [ =( X, 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'(
% 0.83/1.18 Y, X ) ) ), ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( Y ), X ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubstn'(
% 0.83/1.18 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'( X, Y,
% 0.83/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ), 'c_Lambda_Olift'( Z, Y ) )
% 0.83/1.18 , ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.83/1.18 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.83/1.18 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X ) ],
% 0.83/1.18 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.83/1.18 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubst'(
% 0.83/1.18 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.83/1.18 [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 0.83/1.18 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 0.83/1.18 ],
% 0.83/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.83/1.18 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.83/1.18 'tc_nat' ) ],
% 0.83/1.18 [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ), 'c_Lambda_Osubst'( T,
% 0.83/1.18 Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ],
% 0.83/1.18 [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ), 'c_Lambda_Olift'(
% 0.83/1.18 'c_Lambda_Oliftn'( X, Y, Z ), Z ) ) ],
% 0.83/1.18 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.83/1.18 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.83/1.18 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.83/1.18 'tc_nat' ) ],
% 0.83/1.18 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.83/1.18 ) ],
% 0.83/1.18 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 0.83/1.18 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.83/1.18 ,
% 0.83/1.18 [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ],
% 0.83/1.18 [ 'c_Lambda_Obeta'( X, 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'( X, Y
% 0.83/1.18 ) ), ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), Y ) ) ],
% 0.83/1.18 [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.83/1.18 , 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.83/1.18 ,
% 0.83/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.83/1.18 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.83/1.18 ) ) ],
% 0.83/1.18 [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( X, 'c_Lambda_OdB_OVar'( Y ), Z
% 0.83/1.18 ) ), ~( 'c_InductTermi_OIT'( X ) ) ],
% 0.83/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.83/1.18 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.83/1.18 ) ],
% 0.83/1.18 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.83/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T ),
% 0.83/1.18 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubst'( X, Z, T ), 'c_Lambda_Osubst'( Y,
% 0.83/1.18 Z, T ) ) ) ],
% 0.83/1.18 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OAbs'( Z ) ) ) ],
% 0.83/1.18 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OApp'( Y, Z ) ) ) ],
% 0.83/1.18 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z, T ) ) ),
% 0.83/1.18 =( X, Z ) ],
% 0.83/1.18 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z, T ) ) ),
% 0.83/1.18 =( Y, T ) ],
% 0.83/1.18 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OApp'( Y, Z ) ) ) ],
% 0.83/1.18 [ 'c_InductTermi_OIT'( 'v_s____' ) ],
% 0.83/1.18 [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 0.83/1.18 'c_InductTermi_OIT'( X ) ) ],
% 0.83/1.18 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( X ) ) ],
% 0.83/1.18 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OApp'( X, Y ), Z ),
% 0.83/1.18 'c_Lambda_OdB_OApp'( 'c_Lambda_Olift'( X, Z ), 'c_Lambda_Olift'( Y, Z ) )
% 0.83/1.18 ) ],
% 0.83/1.18 [ 'c_InductTermi_OIT'( 'v_ta____' ) ],
% 0.83/1.18 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 0.83/1.18 'c_InductTermi_OIT'( X ) ) ],
% 0.83/1.18 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( X
% 0.83/1.18 , Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ],
% 0.83/1.18 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z
% 0.83/1.18 , Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.83/1.18 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OApp'( Y, Z ), T ),
% 0.83/1.18 'c_Lambda_OdB_OApp'( 'c_Lambda_Oliftn'( X, Y, T ), 'c_Lambda_Oliftn'( X,
% 0.83/1.18 Z, T ) ) ) ],
% 0.83/1.18 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( X, 'c_Lambda_OdB_OVar'( Y )
% 0.83/1.18 ) ), ~( 'c_InductTermi_OIT'( X ) ) ],
% 0.83/1.18 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T ),
% 0.83/1.18 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ), 'c_Lambda_Osubstn'( Y
% 0.83/1.18 , Z, T ) ) ) ],
% 0.83/1.18 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OVar'( Z ) ) ) ],
% 0.83/1.18 [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'(
% 0.83/1.18 'c_Lambda_OdB_OVar'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.83/1.18 'c_Lambda_Olift'( 'v_ta____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )
% 0.83/1.18 , 'v_s____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.83/1.18 [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( 'v_s____', 'v_ta____' ) )
% 0.83/1.18 ) ],
% 0.83/1.18 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.83/1.18 ],
% 0.83/1.18 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.83/1.18 ) ],
% 0.83/1.18 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.83/1.18 ],
% 0.83/1.18 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.83/1.18 [ 'class_Orderings_Oorder'( 'tc_nat' ) ]
% 0.83/1.18 ] .
% 0.83/1.18
% 0.83/1.18
% 0.83/1.18 percentage equality = 0.353100, percentage horn = 0.870206
% 0.83/1.18 This is a problem with some equality
% 0.83/1.18
% 0.83/1.18
% 0.83/1.18
% 0.83/1.18 Options Used:
% 0.83/1.18
% 0.83/1.18 useres = 1
% 0.83/1.18 useparamod = 1
% 0.83/1.18 useeqrefl = 1
% 0.83/1.18 useeqfact = 1
% 0.83/1.18 usefactor = 1
% 0.83/1.18 usesimpsplitting = 0
% 0.83/1.18 usesimpdemod = 5
% 0.83/1.18 usesimpres = 3
% 0.83/1.18
% 0.83/1.18 resimpinuse = 1000
% 0.83/1.18 resimpclauses = 20000
% 0.83/1.18 substype = eqrewr
% 0.83/1.18 backwardsubs = 1
% 0.83/1.18 selectoldest = 5
% 0.83/1.18
% 0.83/1.18 litorderings [0] = split
% 0.83/1.18 litorderings [1] = extend the termordering, first sorting on arguments
% 0.83/1.18
% 0.83/1.18 termordering = kbo
% 0.83/1.18
% 0.83/1.18 litapriori = 0
% 0.83/1.18 termapriori = 1
% 0.83/1.18 litaposteriori = 0
% 0.83/1.18 termaposteriori = 0
% 0.83/1.18 demodaposteriori = 0
% 0.83/1.18 ordereqreflfact = 0
% 0.83/1.18
% 0.83/1.18 litselect = negord
% 0.83/1.18
% 0.83/1.18 maxweight = 15
% 0.83/1.18 maxdepth = 30000
% 0.83/1.18 maxlength = 115
% 0.83/1.18 maxnrvars = 195
% 0.83/1.18 excuselevel = 1
% 0.83/1.18 increasemaxweight = 1
% 0.83/1.18
% 0.83/1.18 maxselected = 10000000
% 0.83/1.18 maxnrclauses = 10000000
% 0.83/1.18
% 0.83/1.18 showgenerated = 0
% 0.83/1.18 showkept = 0
% 0.83/1.18 showselected = 0
% 0.83/1.18 showdeleted = 0
% 0.83/1.18 showresimp = 1
% 0.83/1.18 showstatus = 2000
% 0.83/1.18
% 0.83/1.18 prologoutput = 1
% 0.83/1.18 nrgoals = 5000000
% 0.83/1.18 totalproof = 1
% 0.83/1.18
% 0.83/1.18 Symbols occurring in the translation:
% 0.83/1.18
% 0.83/1.18 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 11.48/11.91 . [1, 2] (w:1, o:93, a:1, s:1, b:0),
% 11.48/11.91 ! [4, 1] (w:0, o:47, a:1, s:1, b:0),
% 11.48/11.91 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 11.48/11.91 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 11.48/11.91 'class_Ring__and__Field_Ocomm__semiring__1' [40, 1] (w:1, o:52, a:1
% 11.48/11.91 , s:1, b:0),
% 11.48/11.91 'c_HOL_Otimes__class_Otimes' [43, 3] (w:1, o:124, a:1, s:1, b:0),
% 11.48/11.91 'tc_nat' [44, 0] (w:1, o:12, a:1, s:1, b:0),
% 11.48/11.91 'c_HOL_Ozero__class_Ozero' [45, 1] (w:1, o:53, a:1, s:1, b:0),
% 11.48/11.91 'c_HOL_Oplus__class_Oplus' [46, 3] (w:1, o:126, a:1, s:1, b:0),
% 11.48/11.91 'class_OrderedGroup_Olordered__ab__group__add' [47, 1] (w:1, o:55, a:
% 11.48/11.91 1, s:1, b:0),
% 11.48/11.91 'class_OrderedGroup_Ogroup__add' [52, 1] (w:1, o:56, a:1, s:1, b:0),
% 11.48/11.91
% 11.48/11.91 'c_HOL_Ominus__class_Ominus' [53, 3] (w:1, o:127, a:1, s:1, b:0),
% 11.48/11.91 'class_Ring__and__Field_Oidom' [54, 1] (w:1, o:57, a:1, s:1, b:0),
% 11.48/11.91 'class_Int_Onumber__ring' [55, 1] (w:1, o:58, a:1, s:1, b:0),
% 11.48/11.91 'c_Suc' [59, 1] (w:1, o:59, a:1, s:1, b:0),
% 11.48/11.91 'class_Ring__and__Field_Oring' [60, 1] (w:1, o:60, a:1, s:1, b:0),
% 11.48/11.91 'c_HOL_Oord__class_Oless' [63, 3] (w:1, o:125, a:1, s:1, b:0),
% 11.48/11.91 'class_OrderedGroup_Ocomm__monoid__add' [66, 1] (w:1, o:61, a:1, s:1
% 11.48/11.91 , b:0),
% 11.48/11.91 'class_Nat_Osemiring__char__0' [68, 1] (w:1, o:54, a:1, s:1, b:0),
% 11.48/11.91 'c_Nat_Osemiring__1__class_Oof__nat' [69, 2] (w:1, o:118, a:1, s:1
% 11.48/11.91 , b:0),
% 11.48/11.91 'class_OrderedGroup_Oab__group__add' [70, 1] (w:1, o:62, a:1, s:1, b:
% 11.48/11.91 0),
% 11.48/11.91 'class_Ring__and__Field_Opordered__ring' [71, 1] (w:1, o:68, a:1, s:1
% 11.48/11.91 , b:0),
% 11.48/11.91 'class_Ring__and__Field_Oring__no__zero__divisors' [72, 1] (w:1, o:69
% 11.48/11.91 , a:1, s:1, b:0),
% 11.48/11.91 'class_Ring__and__Field_Ono__zero__divisors' [73, 1] (w:1, o:71, a:1
% 11.48/11.91 , s:1, b:0),
% 11.48/11.91 'class_OrderedGroup_Oab__semigroup__add' [74, 1] (w:1, o:72, a:1, s:1
% 11.48/11.91 , b:0),
% 11.48/11.91 'class_Ring__and__Field_Osemiring' [79, 1] (w:1, o:73, a:1, s:1, b:0)
% 11.48/11.91 ,
% 11.48/11.91 'class_Ring__and__Field_Osemiring__1' [80, 1] (w:1, o:74, a:1, s:1
% 11.48/11.91 , b:0),
% 11.48/11.91 'class_OrderedGroup_Opordered__comm__monoid__add' [81, 1] (w:1, o:75
% 11.48/11.91 , a:1, s:1, b:0),
% 11.48/11.91 'class_Ring__and__Field_Oordered__ring__strict' [82, 1] (w:1, o:63
% 11.48/11.91 , a:1, s:1, b:0),
% 11.48/11.91 'class_OrderedGroup_Ocancel__ab__semigroup__add' [83, 1] (w:1, o:76
% 11.48/11.91 , a:1, s:1, b:0),
% 11.48/11.91 'class_OrderedGroup_Ocancel__semigroup__add' [84, 1] (w:1, o:77, a:1
% 11.48/11.91 , s:1, b:0),
% 11.48/11.91 'class_Ring__and__Field_Oordered__semidom' [85, 1] (w:1, o:64, a:1
% 11.48/11.91 , s:1, b:0),
% 11.48/11.91 'class_Ring__and__Field_Oordered__semiring__strict' [86, 1] (w:1, o:
% 11.48/11.91 65, a:1, s:1, b:0),
% 11.48/11.91 'class_Ring__and__Field_Oordered__comm__semiring__strict' [87, 1] (w:
% 11.48/11.91 1, o:66, a:1, s:1, b:0),
% 11.48/11.91 'class_OrderedGroup_Omonoid__add' [88, 1] (w:1, o:78, a:1, s:1, b:0)
% 11.48/11.91 ,
% 11.48/11.91 'class_Ring__and__Field_Oordered__idom' [89, 1] (w:1, o:67, a:1, s:1
% 11.48/11.91 , b:0),
% 11.48/11.91 'class_Ring__and__Field_Omult__zero' [95, 1] (w:1, o:70, a:1, s:1, b:
% 11.48/11.91 0),
% 11.48/11.91 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [96, 1]
% 11.48/11.91 (w:1, o:79, a:1, s:1, b:0),
% 11.48/11.91 'class_OrderedGroup_Opordered__ab__group__add' [97, 1] (w:1, o:80, a:
% 11.48/11.91 1, s:1, b:0),
% 11.48/11.91 'class_OrderedGroup_Oab__semigroup__idem__mult' [98, 1] (w:1, o:81
% 11.48/11.91 , a:1, s:1, b:0),
% 11.48/11.91 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [100, 1]
% 11.48/11.91 (w:1, o:82, a:1, s:1, b:0),
% 11.48/11.91 'class_OrderedGroup_Oab__semigroup__mult' [101, 1] (w:1, o:83, a:1
% 11.48/11.91 , s:1, b:0),
% 11.48/11.91 'class_Ring__and__Field_Ocomm__semiring' [102, 1] (w:1, o:84, a:1, s:
% 11.48/11.91 1, b:0),
% 11.48/11.91 'class_Orderings_Opreorder' [103, 1] (w:1, o:86, a:1, s:1, b:0),
% 11.48/11.91 'class_Orderings_Olinorder' [104, 1] (w:1, o:87, a:1, s:1, b:0),
% 11.48/11.91 'class_Orderings_Oorder' [105, 1] (w:1, o:85, a:1, s:1, b:0),
% 11.48/11.91 'c_Lambda_Oliftn' [107, 3] (w:1, o:128, a:1, s:1, b:0),
% 11.48/11.91 'c_Lambda_OdB_OVar' [109, 1] (w:1, o:88, a:1, s:1, b:0),
% 11.48/11.91 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1' [110, 2] (w:
% 11.48/11.91 1, o:119, a:1, s:1, b:0),
% 11.48/11.91 'c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1' [112, 1] (w:1, o:
% 11.48/11.91 89, a:1, s:1, b:0),
% 11.48/11.91 'c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1' [113, 1] (w:1, o:90
% 32.08/32.50 , a:1, s:1, b:0),
% 32.08/32.50 'c_Lambda_OdB_OAbs' [115, 1] (w:1, o:91, a:1, s:1, b:0),
% 32.08/32.50 'c_Lambda_Obeta' [116, 2] (w:1, o:120, a:1, s:1, b:0),
% 32.08/32.50 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1' [117, 2] (w:1, o:121, a:1
% 32.08/32.50 , s:1, b:0),
% 32.08/32.50 'c_Lambda_Osubstn' [118, 3] (w:1, o:129, a:1, s:1, b:0),
% 32.08/32.50 'c_Lambda_Olift' [119, 2] (w:1, o:122, a:1, s:1, b:0),
% 32.08/32.50 'c_Lambda_Osubst' [120, 3] (w:1, o:130, a:1, s:1, b:0),
% 32.08/32.50 'c_Lambda_OdB_OApp' [123, 2] (w:1, o:123, a:1, s:1, b:0),
% 32.08/32.50 'c_InductTermi_OIT' [124, 1] (w:1, o:92, a:1, s:1, b:0),
% 32.08/32.50 'v_s____' [129, 0] (w:1, o:45, a:1, s:1, b:0),
% 32.08/32.50 'v_ta____' [130, 0] (w:1, o:46, a:1, s:1, b:0).
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Starting Search:
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 5346
% 32.08/32.50 Kept: 2002
% 32.08/32.50 Inuse: 142
% 32.08/32.50 Deleted: 4
% 32.08/32.50 Deletedinuse: 0
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 15040
% 32.08/32.50 Kept: 4010
% 32.08/32.50 Inuse: 182
% 32.08/32.50 Deleted: 6
% 32.08/32.50 Deletedinuse: 1
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 25035
% 32.08/32.50 Kept: 6024
% 32.08/32.50 Inuse: 217
% 32.08/32.50 Deleted: 6
% 32.08/32.50 Deletedinuse: 1
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 35537
% 32.08/32.50 Kept: 8075
% 32.08/32.50 Inuse: 271
% 32.08/32.50 Deleted: 7
% 32.08/32.50 Deletedinuse: 1
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 48632
% 32.08/32.50 Kept: 10127
% 32.08/32.50 Inuse: 308
% 32.08/32.50 Deleted: 10
% 32.08/32.50 Deletedinuse: 2
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 60070
% 32.08/32.50 Kept: 12175
% 32.08/32.50 Inuse: 355
% 32.08/32.50 Deleted: 17
% 32.08/32.50 Deletedinuse: 7
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 70018
% 32.08/32.50 Kept: 14734
% 32.08/32.50 Inuse: 361
% 32.08/32.50 Deleted: 17
% 32.08/32.50 Deletedinuse: 7
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 84865
% 32.08/32.50 Kept: 17230
% 32.08/32.50 Inuse: 400
% 32.08/32.50 Deleted: 18
% 32.08/32.50 Deletedinuse: 7
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 104354
% 32.08/32.50 Kept: 19320
% 32.08/32.50 Inuse: 424
% 32.08/32.50 Deleted: 20
% 32.08/32.50 Deletedinuse: 8
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying clauses:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 115359
% 32.08/32.50 Kept: 21409
% 32.08/32.50 Inuse: 454
% 32.08/32.50 Deleted: 428
% 32.08/32.50 Deletedinuse: 8
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 125681
% 32.08/32.50 Kept: 23527
% 32.08/32.50 Inuse: 494
% 32.08/32.50 Deleted: 430
% 32.08/32.50 Deletedinuse: 10
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 138367
% 32.08/32.50 Kept: 25537
% 32.08/32.50 Inuse: 538
% 32.08/32.50 Deleted: 430
% 32.08/32.50 Deletedinuse: 10
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 150824
% 32.08/32.50 Kept: 27649
% 32.08/32.50 Inuse: 584
% 32.08/32.50 Deleted: 430
% 32.08/32.50 Deletedinuse: 10
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 174716
% 32.08/32.50 Kept: 30253
% 32.08/32.50 Inuse: 614
% 32.08/32.50 Deleted: 430
% 32.08/32.50 Deletedinuse: 10
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 192820
% 32.08/32.50 Kept: 32377
% 32.08/32.50 Inuse: 639
% 32.08/32.50 Deleted: 430
% 32.08/32.50 Deletedinuse: 10
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 220612
% 32.08/32.50 Kept: 34841
% 32.08/32.50 Inuse: 667
% 32.08/32.50 Deleted: 434
% 32.08/32.50 Deletedinuse: 12
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 246722
% 32.08/32.50 Kept: 36861
% 32.08/32.50 Inuse: 691
% 32.08/32.50 Deleted: 441
% 32.08/32.50 Deletedinuse: 12
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 264199
% 32.08/32.50 Kept: 38933
% 32.08/32.50 Inuse: 725
% 32.08/32.50 Deleted: 443
% 32.08/32.50 Deletedinuse: 14
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying clauses:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 273883
% 32.08/32.50 Kept: 40967
% 32.08/32.50 Inuse: 752
% 32.08/32.50 Deleted: 978
% 32.08/32.50 Deletedinuse: 14
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 302682
% 32.08/32.50 Kept: 43525
% 32.08/32.50 Inuse: 782
% 32.08/32.50 Deleted: 978
% 32.08/32.50 Deletedinuse: 14
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 328669
% 32.08/32.50 Kept: 45550
% 32.08/32.50 Inuse: 792
% 32.08/32.50 Deleted: 978
% 32.08/32.50 Deletedinuse: 14
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 344953
% 32.08/32.50 Kept: 47593
% 32.08/32.50 Inuse: 817
% 32.08/32.50 Deleted: 978
% 32.08/32.50 Deletedinuse: 14
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 364092
% 32.08/32.50 Kept: 51615
% 32.08/32.50 Inuse: 848
% 32.08/32.50 Deleted: 978
% 32.08/32.50 Deletedinuse: 14
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 385148
% 32.08/32.50 Kept: 53730
% 32.08/32.50 Inuse: 881
% 32.08/32.50 Deleted: 979
% 32.08/32.50 Deletedinuse: 14
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 401575
% 32.08/32.50 Kept: 55886
% 32.08/32.50 Inuse: 895
% 32.08/32.50 Deleted: 979
% 32.08/32.50 Deletedinuse: 14
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 417206
% 32.08/32.50 Kept: 57928
% 32.08/32.50 Inuse: 926
% 32.08/32.50 Deleted: 980
% 32.08/32.50 Deletedinuse: 15
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 434669
% 32.08/32.50 Kept: 59935
% 32.08/32.50 Inuse: 963
% 32.08/32.50 Deleted: 980
% 32.08/32.50 Deletedinuse: 15
% 32.08/32.50
% 32.08/32.50 Resimplifying clauses:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 445784
% 32.08/32.50 Kept: 62090
% 32.08/32.50 Inuse: 982
% 32.08/32.50 Deleted: 1592
% 32.08/32.50 Deletedinuse: 22
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 466409
% 32.08/32.50 Kept: 64208
% 32.08/32.50 Inuse: 989
% 32.08/32.50 Deleted: 1601
% 32.08/32.50 Deletedinuse: 23
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 489872
% 32.08/32.50 Kept: 66724
% 32.08/32.50 Inuse: 1004
% 32.08/32.50 Deleted: 1605
% 32.08/32.50 Deletedinuse: 27
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 502898
% 32.08/32.50 Kept: 68725
% 32.08/32.50 Inuse: 1011
% 32.08/32.50 Deleted: 1605
% 32.08/32.50 Deletedinuse: 27
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 512504
% 32.08/32.50 Kept: 71718
% 32.08/32.50 Inuse: 1016
% 32.08/32.50 Deleted: 1606
% 32.08/32.50 Deletedinuse: 27
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 518551
% 32.08/32.50 Kept: 73788
% 32.08/32.50 Inuse: 1018
% 32.08/32.50 Deleted: 1608
% 32.08/32.50 Deletedinuse: 29
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 537134
% 32.08/32.50 Kept: 76498
% 32.08/32.50 Inuse: 1047
% 32.08/32.50 Deleted: 1610
% 32.08/32.50 Deletedinuse: 30
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 549086
% 32.08/32.50 Kept: 79954
% 32.08/32.50 Inuse: 1058
% 32.08/32.50 Deleted: 1611
% 32.08/32.50 Deletedinuse: 31
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying clauses:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 561129
% 32.08/32.50 Kept: 82033
% 32.08/32.50 Inuse: 1087
% 32.08/32.50 Deleted: 2340
% 32.08/32.50 Deletedinuse: 32
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 577199
% 32.08/32.50 Kept: 84044
% 32.08/32.50 Inuse: 1103
% 32.08/32.50 Deleted: 2340
% 32.08/32.50 Deletedinuse: 32
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 593675
% 32.08/32.50 Kept: 86126
% 32.08/32.50 Inuse: 1116
% 32.08/32.50 Deleted: 2341
% 32.08/32.50 Deletedinuse: 32
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 611685
% 32.08/32.50 Kept: 89668
% 32.08/32.50 Inuse: 1126
% 32.08/32.50 Deleted: 2341
% 32.08/32.50 Deletedinuse: 32
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Intermediate Status:
% 32.08/32.50 Generated: 627071
% 32.08/32.50 Kept: 92995
% 32.08/32.50 Inuse: 1131
% 32.08/32.50 Deleted: 2341
% 32.08/32.50 Deletedinuse: 32
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50 Resimplifying inuse:
% 32.08/32.50 Done
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 Bliksems!, er is een bewijs:
% 32.08/32.50 % SZS status Unsatisfiable
% 32.08/32.50 % SZS output start Refutation
% 32.08/32.50
% 32.08/32.50 clause( 220, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 32.08/32.50 , X, Y ), X ) ] )
% 32.08/32.50 .
% 32.08/32.50 clause( 234, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 32.08/32.50 .
% 32.08/32.50 clause( 254, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ),
% 32.08/32.50 'c_Lambda_Oliftn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.50 .
% 32.08/32.50 clause( 257, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X )
% 32.08/32.50 ] )
% 32.08/32.50 .
% 32.08/32.50 clause( 260, [ =( 'c_Lambda_Osubst'( X, 'c_Lambda_Oliftn'( Z, Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ), 'c_Lambda_Osubstn'( X, Y,
% 32.08/32.50 Z ) ) ] )
% 32.08/32.50 .
% 32.08/32.50 clause( 270, [ =( 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ) ) ) ] )
% 32.08/32.50 .
% 32.08/32.50 clause( 289, [ =( 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ),
% 32.08/32.50 'c_Lambda_Osubstn'( Y, Z, T ) ), 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'(
% 32.08/32.50 X, Y ), Z, T ) ) ] )
% 32.08/32.50 .
% 32.08/32.50 clause( 290, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'(
% 32.08/32.50 'c_Lambda_OdB_OVar'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 32.08/32.50 'c_Lambda_Olift'( 'v_ta____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )
% 32.08/32.50 , 'v_s____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.50 .
% 32.08/32.50 clause( 291, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( 'v_s____',
% 32.08/32.50 'v_ta____' ) ) ) ] )
% 32.08/32.50 .
% 32.08/32.50 clause( 80558, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ) ), X ) ] )
% 32.08/32.50 .
% 32.08/32.50 clause( 81935, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X
% 32.08/32.50 ) ] )
% 32.08/32.50 .
% 32.08/32.50 clause( 94494, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( T,
% 32.08/32.50 'c_Lambda_Olift'( X, Y ) ), Z, Y ), 'c_Lambda_OdB_OApp'(
% 32.08/32.50 'c_Lambda_Osubstn'( T, Z, Y ), X ) ) ] )
% 32.08/32.50 .
% 32.08/32.50 clause( 94862, [] )
% 32.08/32.50 .
% 32.08/32.50
% 32.08/32.50
% 32.08/32.50 % SZS output end Refutation
% 32.08/32.50 found a proof!
% 32.08/32.50
% 32.08/32.50 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 32.08/32.50
% 32.08/32.50 initialclauses(
% 32.08/32.50 [ clause( 94864, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 Z, Y, X ) ) ] )
% 32.08/32.50 , clause( 94865, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94866, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.08/32.50 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 32.08/32.50 )
% 32.08/32.50 , clause( 94867, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94868, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 Z, Y, X ) ) ] )
% 32.08/32.50 , clause( 94869, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 32.08/32.50 ), Y ) ] )
% 32.08/32.50 , clause( 94870, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.08/32.50 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 32.08/32.50 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 32.08/32.50 , clause( 94871, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.08/32.50 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 32.08/32.50 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 32.08/32.50 , clause( 94872, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 32.08/32.50 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94873, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 32.08/32.50 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94874, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.08/32.50 ) ] )
% 32.08/32.50 , clause( 94875, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 32.08/32.50 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 32.08/32.50 , clause( 94876, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat'
% 32.08/32.50 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 94877, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 32.08/32.50 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 94878, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 94879, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 32.08/32.50 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 32.08/32.50 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 32.08/32.50 , X ), W, X ) ) ] )
% 32.08/32.50 , clause( 94880, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 32.08/32.50 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 32.08/32.50 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 32.08/32.50 , clause( 94881, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 32.08/32.50 , clause( 94882, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 32.08/32.50 , clause( 94883, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 32.08/32.50 , clause( 94884, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94885, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94886, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 32.08/32.50 Y, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94887, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94888, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94889, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 32.08/32.50 Y, X ) ) ] )
% 32.08/32.50 , clause( 94890, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 32.08/32.50 X ) ) ] )
% 32.08/32.50 , clause( 94891, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94892, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 X, T, 'tc_nat' ) ] )
% 32.08/32.50 , clause( 94893, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 32.08/32.50 Y, X ) ) ] )
% 32.08/32.50 , clause( 94894, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 94895, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 94896, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 32.08/32.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94897, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 32.08/32.50 , clause( 94898, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.08/32.50 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 32.08/32.50 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 94899, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X )
% 32.08/32.50 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94900, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) )
% 32.08/32.50 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94901, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.08/32.50 ) ] )
% 32.08/32.50 , clause( 94902, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.08/32.50 ) ] )
% 32.08/32.50 , clause( 94903, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 32.08/32.50 ) ] )
% 32.08/32.50 , clause( 94904, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.08/32.50 ) ] )
% 32.08/32.50 , clause( 94905, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.08/32.50 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 32.08/32.50 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 94906, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94907, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 32.08/32.50 , clause( 94908, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94909, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 32.08/32.50 , clause( 94910, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 32.08/32.50 , clause( 94911, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94912, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94913, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.08/32.50 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 94914, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 32.08/32.50 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 32.08/32.50 , X ), W, X ), X ) ) ] )
% 32.08/32.50 , clause( 94915, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 32.08/32.50 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 32.08/32.50 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 32.08/32.50 W, X ), X ) ) ] )
% 32.08/32.50 , clause( 94916, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 32.08/32.50 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 32.08/32.50 , X ), T, X ), W, X ) ) ] )
% 32.08/32.50 , clause( 94917, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 32.08/32.50 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 32.08/32.50 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 32.08/32.50 W, X ), X ) ) ] )
% 32.08/32.50 , clause( 94918, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 32.08/32.50 ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 32.08/32.50 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 94919, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 32.08/32.50 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 94920, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 X, Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 32.08/32.50 , clause( 94921, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 32.08/32.50 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 32.08/32.50 , X ) ) ] )
% 32.08/32.50 , clause( 94922, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 32.08/32.50 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 94923, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 32.08/32.50 ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94924, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat'
% 32.08/32.50 ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94925, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 32.08/32.50 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 94926, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 32.08/32.50 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 94927, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 32.08/32.50 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 94928, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 32.08/32.50 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 32.08/32.50 , X ) ) ] )
% 32.08/32.50 , clause( 94929, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 32.08/32.50 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 32.08/32.50 , X ) ) ] )
% 32.08/32.50 , clause( 94930, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 32.08/32.50 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 32.08/32.50 , X ) ) ] )
% 32.08/32.50 , clause( 94931, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 32.08/32.50 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 32.08/32.50 , X ) ) ] )
% 32.08/32.50 , clause( 94932, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94933, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 32.08/32.50 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 32.08/32.50 , clause( 94934, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 32.08/32.50 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94935, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94936, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 32.08/32.50 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94937, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 32.08/32.50 , T, X ) ) ), =( Y, Z ) ] )
% 32.08/32.50 , clause( 94938, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 32.08/32.50 , T, X ) ) ), =( Z, T ) ] )
% 32.08/32.50 , clause( 94939, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.08/32.50 'tc_nat' ) ), =( Y, Z ) ] )
% 32.08/32.50 , clause( 94940, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.08/32.50 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94941, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.08/32.50 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 94942, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94943, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94944, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 32.08/32.50 ), 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94945, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94946, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 Z, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94947, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 X, Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94948, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 32.08/32.50 ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 32.08/32.50 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94949, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 32.08/32.50 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 32.08/32.50 , clause( 94950, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 94951, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 32.08/32.50 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94952, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 32.08/32.50 Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94953, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.08/32.50 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 94954, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.08/32.50 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 32.08/32.50 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 32.08/32.50 , clause( 94955, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.08/32.50 ) ), =( Y, Z ) ] )
% 32.08/32.50 , clause( 94956, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.08/32.50 ) ), =( Y, Z ) ] )
% 32.08/32.50 , clause( 94957, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 32.08/32.50 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 32.08/32.50 ] )
% 32.08/32.50 , clause( 94958, [ =( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 32.08/32.50 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 32.08/32.50 ] )
% 32.08/32.50 , clause( 94959, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 32.08/32.50 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94960, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 32.08/32.50 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 94961, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_Suc'( X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 32.08/32.50 Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 32.08/32.50 ) ] )
% 32.08/32.50 , clause( 94962, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 32.08/32.50 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94963, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 32.08/32.50 , clause( 94964, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 32.08/32.50 , clause( 94965, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 32.08/32.50 , clause( 94966, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.08/32.50 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 32.08/32.50 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 32.08/32.50 , clause( 94967, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 32.08/32.50 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 32.08/32.50 , clause( 94968, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 32.08/32.50 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 Y, T, X ) ) ), =( Z, T ) ] )
% 32.08/32.50 , clause( 94969, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 32.08/32.50 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 T, Z, X ) ) ), =( Y, T ) ] )
% 32.08/32.50 , clause( 94970, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94971, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 94972, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 32.08/32.50 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 32.08/32.50 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94973, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 94974, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 94975, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 32.08/32.50 X ), X ) ) ] )
% 32.08/32.50 , clause( 94976, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.08/32.50 ~( 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X
% 32.08/32.50 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 94977, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 32.08/32.50 , clause( 94978, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 32.08/32.50 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 32.08/32.50 X ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 32.08/32.50 , clause( 94979, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 32.08/32.50 , clause( 94980, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 32.08/32.50 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 32.08/32.50 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 32.08/32.50 , clause( 94981, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 32.08/32.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94982, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 32.08/32.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94983, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 32.08/32.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 94984, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 32.08/32.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 94985, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 32.08/32.50 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94986, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 32.08/32.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 94987, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.08/32.50 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 94988, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 94989, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.08/32.50 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 X ), T, X ) ) ] )
% 32.08/32.50 , clause( 94990, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.08/32.50 , clause( 94991, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 32.08/32.50 , clause( 94992, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.08/32.50 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.08/32.50 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 32.08/32.50 , clause( 94993, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.08/32.50 , clause( 94994, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 94995, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 32.08/32.50 , clause( 94996, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.08/32.50 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.08/32.50 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 32.08/32.50 , clause( 94997, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 32.08/32.50 , clause( 94998, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 94999, [ ~(
% 32.08/32.50 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 32.08/32.50 , clause( 95000, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 95001, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 32.08/32.50 ) ] )
% 32.08/32.50 , clause( 95002, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 32.08/32.50 ] )
% 32.08/32.50 , clause( 95003, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95004, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 32.08/32.50 , clause( 95005, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 32.08/32.50 , clause( 95006, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.08/32.50 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 95007, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 32.08/32.50 ] )
% 32.08/32.50 , clause( 95008, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 32.08/32.50 ] )
% 32.08/32.50 , clause( 95009, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 32.08/32.50 ] )
% 32.08/32.50 , clause( 95010, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 32.08/32.50 ) ] )
% 32.08/32.50 , clause( 95011, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 32.08/32.50 ) ] )
% 32.08/32.50 , clause( 95012, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 32.08/32.50 , clause( 95013, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ) ] )
% 32.08/32.50 , clause( 95014, [ =( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 32.08/32.50 , clause( 95015, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 32.08/32.50 ), Y ) ] )
% 32.08/32.50 , clause( 95016, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95017, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95018, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.08/32.50 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 32.08/32.50 , clause( 95019, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.08/32.50 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.08/32.50 , clause( 95020, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 32.08/32.50 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 95021, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95022, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.08/32.50 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 95023, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 32.08/32.50 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 95024, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 95025, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 95026, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.08/32.50 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 95027, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.08/32.50 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95028, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.08/32.50 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 32.08/32.50 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 32.08/32.50 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 32.08/32.50 , clause( 95029, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.08/32.50 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 32.08/32.50 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 32.08/32.50 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 32.08/32.50 , clause( 95030, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.08/32.50 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.08/32.50 , clause( 95031, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 95032, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.08/32.50 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95033, [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ),
% 32.08/32.50 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95034, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 32.08/32.50 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95035, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 32.08/32.50 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 95036, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 32.08/32.50 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 32.08/32.50 , clause( 95037, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.08/32.50 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.08/32.50 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 32.08/32.50 =( Y, T ) ] )
% 32.08/32.50 , clause( 95038, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.08/32.50 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.08/32.50 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 32.08/32.50 =( Y, T ) ] )
% 32.08/32.50 , clause( 95039, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 32.08/32.50 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 32.08/32.50 , T ), =( X, Z ) ] )
% 32.08/32.50 , clause( 95040, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 32.08/32.50 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 32.08/32.50 , T ), =( X, Z ) ] )
% 32.08/32.50 , clause( 95041, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'(
% 32.08/32.50 Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95042, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 95043, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.08/32.50 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 32.08/32.50 , clause( 95044, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.08/32.50 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 32.08/32.50 , clause( 95045, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.08/32.50 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 32.08/32.50 , clause( 95046, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 32.08/32.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 95047, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 32.08/32.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 95048, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 32.08/32.50 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 32.08/32.50 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 95049, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 32.08/32.50 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 32.08/32.50 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 95050, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 95051, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 95052, [ =( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95053, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95054, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 32.08/32.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 95055, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95056, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.08/32.50 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95057, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 32.08/32.50 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.08/32.50 , clause( 95058, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 32.08/32.50 , clause( 95059, [ ~(
% 32.08/32.50 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 32.08/32.50 , clause( 95060, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 32.08/32.50 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' )
% 32.08/32.50 , ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95061, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.08/32.50 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 32.08/32.50 , X ) ) ] )
% 32.08/32.50 , clause( 95062, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.08/32.50 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 32.08/32.50 , X ) ) ] )
% 32.08/32.50 , clause( 95063, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95064, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 32.08/32.50 , clause( 95065, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 32.08/32.50 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95066, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 32.08/32.50 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95067, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 32.08/32.50 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 32.08/32.50 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 32.08/32.50 , clause( 95068, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.08/32.50 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.08/32.50 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 32.08/32.50 , clause( 95069, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.08/32.50 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.08/32.50 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 32.08/32.50 , clause( 95070, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.08/32.50 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.08/32.50 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 32.08/32.50 , clause( 95071, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 32.08/32.50 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 32.08/32.50 , clause( 95072, [ =( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95073, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95074, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95075, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95076, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 32.08/32.50 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 32.08/32.50 , clause( 95077, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y, T,
% 32.08/32.50 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95078, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 32.08/32.50 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 95079, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 32.08/32.50 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 95080, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 32.08/32.50 , Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95081, [ 'c_HOL_Oord__class_Oless'( X,
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 32.08/32.50 Y, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95082, [ ~(
% 32.08/32.50 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 Y, T, X ) ) ] )
% 32.08/32.50 , clause( 95083, [ ~(
% 32.08/32.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 Y, T, X ) ) ] )
% 32.08/32.50 , clause( 95084, [ ~(
% 32.08/32.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 32.08/32.50 X ), X ) ) ] )
% 32.08/32.50 , clause( 95085, [ ~(
% 32.08/32.50 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 Z, T, X ) ) ] )
% 32.08/32.50 , clause( 95086, [ ~(
% 32.08/32.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 Z, T, X ) ) ] )
% 32.08/32.50 , clause( 95087, [ ~(
% 32.08/32.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 32.08/32.50 X ), X ) ) ] )
% 32.08/32.50 , clause( 95088, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 32.08/32.50 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 32.08/32.50 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95089, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95090, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 32.08/32.50 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 32.08/32.50 , ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95091, [ =( 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 95092, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 32.08/32.50 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 32.08/32.50 , clause( 95093, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95094, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95095, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 95096, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.08/32.50 , Y, X ), X ) ) ] )
% 32.08/32.50 , clause( 95097, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 32.08/32.50 , T, X ), X ) ) ] )
% 32.08/32.50 , clause( 95098, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 32.08/32.50 , T, X ), X ) ) ] )
% 32.08/32.50 , clause( 95099, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 32.08/32.50 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 32.08/32.50 , Y, X ), X ) ) ] )
% 32.08/32.50 , clause( 95100, [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 32.08/32.50 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) )
% 32.08/32.50 , =( Y, Z ) ] )
% 32.08/32.50 , clause( 95101, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 32.08/32.50 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 32.08/32.50 , clause( 95102, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95103, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.08/32.50 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 32.08/32.50 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 32.08/32.50 , clause( 95104, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 32.08/32.50 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 32.08/32.50 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 32.08/32.50 , clause( 95105, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 32.08/32.50 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 32.08/32.50 , clause( 95106, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 95107, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95108, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 32.08/32.50 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 32.08/32.50 T, X ), X ) ) ] )
% 32.08/32.50 , clause( 95109, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.08/32.50 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 32.08/32.50 T, X ), Z, X ) ) ] )
% 32.08/32.50 , clause( 95110, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 32.08/32.50 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 Z, T, X ), X ) ) ] )
% 32.08/32.50 , clause( 95111, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 32.08/32.50 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 32.08/32.50 , X ), T, X ) ) ] )
% 32.08/32.50 , clause( 95112, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 32.08/32.50 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 32.08/32.50 , T, X ), X ) ) ] )
% 32.08/32.50 , clause( 95113, [ =( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 32.08/32.50 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95114, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 32.08/32.50 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 32.08/32.50 , X ), T, X ) ) ] )
% 32.08/32.50 , clause( 95115, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 32.08/32.50 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 32.08/32.50 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 32.08/32.50 , clause( 95116, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 32.08/32.50 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 32.08/32.50 , clause( 95117, [ =( 'c_HOL_Otimes__class_Otimes'(
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 32.08/32.50 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95118, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 32.08/32.50 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95119, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 32.08/32.50 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 32.08/32.50 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 32.08/32.50 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 32.08/32.50 , clause( 95120, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.08/32.50 Y, X ) ) ] )
% 32.08/32.50 , clause( 95121, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.08/32.50 Y, X ) ) ] )
% 32.08/32.50 , clause( 95122, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.08/32.50 Y, X ) ) ] )
% 32.08/32.50 , clause( 95123, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 32.08/32.50 Y, X ) ) ] )
% 32.08/32.50 , clause( 95124, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 32.08/32.50 X, 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95125, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95126, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 32.08/32.50 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95127, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95128, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 32.08/32.50 , clause( 95129, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 32.08/32.50 , clause( 95130, [ 'c_HOL_Oord__class_Oless'( X,
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.08/32.50 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95131, [ 'c_HOL_Oord__class_Oless'( X,
% 32.08/32.50 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.08/32.50 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95132, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95133, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), X, Y ), X ) ] )
% 32.08/32.50 , clause( 95134, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.08/32.50 ] )
% 32.08/32.50 , clause( 95135, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.08/32.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 32.08/32.50 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 32.08/32.50 , clause( 95136, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 32.08/32.50 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95137, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 32.08/32.50 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95138, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 32.08/32.50 )
% 32.08/32.50 , clause( 95139, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 32.08/32.50 )
% 32.08/32.50 , clause( 95140, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.08/32.50 ) ) ) ] )
% 32.08/32.50 , clause( 95141, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.08/32.50 ) ) ) ] )
% 32.08/32.50 , clause( 95142, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 32.08/32.50 ) ] )
% 32.08/32.50 , clause( 95143, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 32.08/32.50 , clause( 95144, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 32.08/32.50 ), =( Z, Y ) ] )
% 32.08/32.50 , clause( 95145, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 32.08/32.50 , clause( 95146, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 32.08/32.50 , clause( 95147, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 32.08/32.50 ) ] )
% 32.08/32.50 , clause( 95148, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 32.08/32.50 ), =( Z, Y ) ] )
% 32.08/32.50 , clause( 95149, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 32.08/32.50 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ] )
% 32.08/32.50 , clause( 95150, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 32.08/32.50 , clause( 95151, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 32.08/32.50 , clause( 95152, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 32.08/32.50 , clause( 95153, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95154, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95155, [ =( X, 'c_Suc'(
% 32.08/32.50 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1'( X, Y ) ) ), =(
% 32.08/32.50 X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95156, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 32.08/32.50 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 32.08/32.50 , clause( 95157, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X )
% 32.08/32.50 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 32.08/32.50 , clause( 95158, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 32.08/32.50 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95159, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 32.08/32.50 ] )
% 32.08/32.50 , clause( 95160, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 32.08/32.50 , clause( 95161, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 32.08/32.50 , clause( 95162, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 32.08/32.50 ) ) ) ] )
% 32.08/32.50 , clause( 95163, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 32.08/32.50 ) ) ) ] )
% 32.08/32.50 , clause( 95164, [ =( X, 'c_Suc'(
% 32.08/32.50 'c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1'( X ) ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95165, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95166, [ =( X, 'c_Suc'(
% 32.08/32.50 'c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1'( X ) ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 32.08/32.50 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95167, [ 'c_HOL_Oord__class_Oless'(
% 32.08/32.50 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1'( X, Y ), Y,
% 32.08/32.50 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95168, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 32.08/32.50 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 32.08/32.50 , clause( 95169, [ ~( 'class_Orderings_Oorder'( X ) ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 32.08/32.50 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 32.08/32.50 , clause( 95170, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95171, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95172, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 32.08/32.50 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.08/32.50 ) ), Y, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95173, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 32.08/32.50 , clause( 95174, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 32.08/32.50 , clause( 95175, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 32.08/32.50 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 32.08/32.50 )
% 32.08/32.50 , clause( 95176, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 32.08/32.50 , clause( 95177, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95178, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 32.08/32.50 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 32.08/32.50 , clause( 95179, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 32.08/32.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95180, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 32.08/32.50 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95181, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 32.08/32.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 32.08/32.50 , clause( 95182, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ),
% 32.08/32.50 'c_Lambda_OdB_OAbs'( Y ) ), ~( 'c_Lambda_Obeta'( X, Y ) ) ] )
% 32.08/32.50 , clause( 95183, [ =( X, 'c_Lambda_OdB_OAbs'(
% 32.08/32.50 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'( Y, X ) ) ), ~(
% 32.08/32.50 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( Y ), X ) ) ] )
% 32.08/32.50 , clause( 95184, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 32.08/32.50 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'(
% 32.08/32.50 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 95185, [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ),
% 32.08/32.50 'c_Lambda_Olift'( Z, Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ] )
% 32.08/32.50 , clause( 95186, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 32.08/32.50 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 95187, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ),
% 32.08/32.50 X ) ] )
% 32.08/32.50 , clause( 95188, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 32.08/32.50 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 95189, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 32.08/32.50 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ] )
% 32.08/32.50 , clause( 95190, [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 32.08/32.50 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 32.08/32.50 ] )
% 32.08/32.50 , clause( 95191, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 32.08/32.50 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 32.08/32.50 'tc_nat' ) ] )
% 32.08/32.50 , clause( 95192, [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ),
% 32.08/32.50 'c_Lambda_Osubst'( T, Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ] )
% 32.08/32.50 , clause( 95193, [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ),
% 32.08/32.50 'c_Lambda_Olift'( 'c_Lambda_Oliftn'( X, Y, Z ), Z ) ) ] )
% 32.08/32.50 , clause( 95194, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 95195, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z )
% 32.08/32.50 , 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X
% 32.08/32.50 , 'tc_nat' ) ] )
% 32.08/32.50 , clause( 95196, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 32.08/32.50 ) ), =( X, Y ) ] )
% 32.08/32.50 , clause( 95197, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'(
% 32.08/32.50 'c_Lambda_OdB_OAbs'( X ), Y ), 'c_Lambda_Osubst'( X, Y,
% 32.08/32.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 95198, [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ]
% 32.08/32.50 )
% 32.08/32.50 , clause( 95199, [ 'c_Lambda_Obeta'( X,
% 32.08/32.50 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'( X, Y ) ), ~(
% 32.08/32.50 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), Y ) ) ] )
% 32.08/32.50 , clause( 95200, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ) ), 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ) ) ) ] )
% 32.08/32.50 , clause( 95201, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 32.08/32.50 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 95202, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( X,
% 32.08/32.50 'c_Lambda_OdB_OVar'( Y ), Z ) ), ~( 'c_InductTermi_OIT'( X ) ) ] )
% 32.08/32.50 , clause( 95203, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ),
% 32.08/32.50 Y ) ] )
% 32.08/32.50 , clause( 95204, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y )
% 32.08/32.50 ) ), =( X, Y ) ] )
% 32.08/32.50 , clause( 95205, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y )
% 32.08/32.50 ) ) ] )
% 32.08/32.50 , clause( 95206, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T
% 32.08/32.50 ), 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubst'( X, Z, T ), 'c_Lambda_Osubst'(
% 32.08/32.50 Y, Z, T ) ) ) ] )
% 32.08/32.50 , clause( 95207, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OAbs'(
% 32.08/32.50 Z ) ) ) ] )
% 32.08/32.50 , clause( 95208, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OApp'( Y,
% 32.08/32.50 Z ) ) ) ] )
% 32.08/32.50 , clause( 95209, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'(
% 32.08/32.50 Z, T ) ) ), =( X, Z ) ] )
% 32.08/32.50 , clause( 95210, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'(
% 32.08/32.50 Z, T ) ) ), =( Y, T ) ] )
% 32.08/32.50 , clause( 95211, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OApp'( Y,
% 32.08/32.50 Z ) ) ) ] )
% 32.08/32.50 , clause( 95212, [ 'c_InductTermi_OIT'( 'v_s____' ) ] )
% 32.08/32.50 , clause( 95213, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 32.08/32.50 'c_InductTermi_OIT'( X ) ) ] )
% 32.08/32.50 , clause( 95214, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( X ) ) ] )
% 32.08/32.50 , clause( 95215, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OApp'( X, Y ), Z ),
% 32.08/32.50 'c_Lambda_OdB_OApp'( 'c_Lambda_Olift'( X, Z ), 'c_Lambda_Olift'( Y, Z ) )
% 32.08/32.50 ) ] )
% 32.08/32.50 , clause( 95216, [ 'c_InductTermi_OIT'( 'v_ta____' ) ] )
% 32.08/32.50 , clause( 95217, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 32.08/32.50 'c_InductTermi_OIT'( X ) ) ] )
% 32.08/32.50 , clause( 95218, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ),
% 32.08/32.50 'c_Lambda_OdB_OApp'( X, Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ] )
% 32.08/32.50 , clause( 95219, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ),
% 32.08/32.50 'c_Lambda_OdB_OApp'( Z, Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ] )
% 32.08/32.50 , clause( 95220, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OApp'( Y, Z ), T
% 32.08/32.50 ), 'c_Lambda_OdB_OApp'( 'c_Lambda_Oliftn'( X, Y, T ), 'c_Lambda_Oliftn'(
% 32.08/32.50 X, Z, T ) ) ) ] )
% 32.08/32.50 , clause( 95221, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( X,
% 32.08/32.50 'c_Lambda_OdB_OVar'( Y ) ) ), ~( 'c_InductTermi_OIT'( X ) ) ] )
% 32.08/32.50 , clause( 95222, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T
% 32.08/32.50 ), 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ),
% 32.08/32.50 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ] )
% 32.08/32.50 , clause( 95223, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OVar'(
% 32.08/32.50 Z ) ) ) ] )
% 32.08/32.50 , clause( 95224, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'(
% 32.08/32.50 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OVar'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ) ), 'c_Lambda_Olift'( 'v_ta____', 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.50 'tc_nat' ) ) ), 'v_s____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 32.08/32.50 )
% 32.08/32.50 , clause( 95225, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( 'v_s____',
% 32.08/32.50 'v_ta____' ) ) ) ] )
% 32.08/32.50 , clause( 95226, [
% 32.08/32.50 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 32.08/32.50 )
% 32.08/32.50 , clause( 95227, [
% 32.08/32.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 32.08/32.51 )
% 32.08/32.51 , clause( 95228, [
% 32.08/32.51 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' ) ]
% 32.08/32.51 )
% 32.08/32.51 , clause( 95229, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 32.08/32.51 'tc_nat' ) ] )
% 32.08/32.51 , clause( 95230, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 32.08/32.51 'tc_nat' ) ] )
% 32.08/32.51 , clause( 95231, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 32.08/32.51 'tc_nat' ) ] )
% 32.08/32.51 , clause( 95232, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 32.08/32.51 ] )
% 32.08/32.51 , clause( 95233, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 32.08/32.51 ] )
% 32.08/32.51 , clause( 95234, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 32.08/32.51 )
% 32.08/32.51 , clause( 95235, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 32.08/32.51 ] )
% 32.08/32.51 , clause( 95236, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 32.08/32.51 )
% 32.08/32.51 , clause( 95237, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 32.08/32.51 )
% 32.08/32.51 , clause( 95238, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ]
% 32.08/32.51 )
% 32.08/32.51 , clause( 95239, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 32.08/32.51 , clause( 95240, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 32.08/32.51 , clause( 95241, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 32.08/32.51 , clause( 95242, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 32.08/32.51 , clause( 95243, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 32.08/32.51 , clause( 95244, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 32.08/32.51 , clause( 95245, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 32.08/32.51 , clause( 95246, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 32.08/32.51 , clause( 95247, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 32.08/32.51 ] ).
% 32.08/32.51
% 32.08/32.51
% 32.08/32.51
% 32.08/32.51 subsumption(
% 32.08/32.51 clause( 220, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 32.08/32.51 , X, Y ), X ) ] )
% 32.08/32.51 , clause( 95133, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.51 'tc_nat' ), X, Y ), X ) ] )
% 32.08/32.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 32.08/32.51 )] ) ).
% 32.08/32.51
% 32.08/32.51
% 32.08/32.51 subsumption(
% 32.08/32.51 clause( 234, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 32.08/32.51 , clause( 95153, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 32.08/32.51 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.08/32.51
% 32.08/32.51
% 32.08/32.51 resolution(
% 32.08/32.51 clause( 96452, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ),
% 32.08/32.51 'c_Lambda_Oliftn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.51 , clause( 234, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 32.08/32.51 , 0, clause( 95184, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 32.08/32.51 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'(
% 32.08/32.51 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.51 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ), :=( Y
% 32.08/32.51 , Y )] )).
% 32.08/32.51
% 32.08/32.51
% 32.08/32.51 subsumption(
% 32.08/32.51 clause( 254, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ),
% 32.08/32.51 'c_Lambda_Oliftn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.51 , clause( 96452, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X )
% 32.08/32.51 , 'c_Lambda_Oliftn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 32.08/32.51 )
% 32.08/32.51 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 32.08/32.51 )] ) ).
% 32.08/32.51
% 32.08/32.51
% 32.08/32.51 subsumption(
% 32.08/32.51 clause( 257, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X )
% 32.08/32.51 ] )
% 32.08/32.51 , clause( 95187, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ),
% 32.08/32.51 X ) ] )
% 32.08/32.51 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 32.08/32.51 permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.08/32.51
% 32.08/32.51
% 32.08/32.51 eqswap(
% 32.08/32.51 clause( 97290, [ =( 'c_Lambda_Osubst'( X, 'c_Lambda_Oliftn'( Z, Y,
% 32.08/32.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ), 'c_Lambda_Osubstn'( X, Y,
% 32.08/32.51 Z ) ) ] )
% 32.08/32.51 , clause( 95190, [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 32.08/32.51 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 32.08/32.51 ] )
% 32.08/32.51 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 32.08/32.51
% 32.08/32.51
% 32.08/32.51 subsumption(
% 32.08/32.51 clause( 260, [ =( 'c_Lambda_Osubst'( X, 'c_Lambda_Oliftn'( Z, Y,
% 32.08/32.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ), 'c_Lambda_Osubstn'( X, Y,
% 32.08/32.51 Z ) ) ] )
% 32.08/32.51 , clause( 97290, [ =( 'c_Lambda_Osubst'( X, 'c_Lambda_Oliftn'( Z, Y,
% 32.08/32.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ), 'c_Lambda_Osubstn'( X, Y,
% 32.08/32.51 Z ) ) ] )
% 32.08/32.51 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 32.08/32.52 permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 eqswap(
% 32.08/32.52 clause( 97720, [ =( 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ) ) ] )
% 32.08/32.52 , clause( 95200, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ) ) ] )
% 32.08/32.52 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 subsumption(
% 32.08/32.52 clause( 270, [ =( 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ) ) ] )
% 32.08/32.52 , clause( 97720, [ =( 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ) ) ] )
% 32.08/32.52 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 32.08/32.52 )] ) ).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 eqswap(
% 32.08/32.52 clause( 98163, [ =( 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ),
% 32.08/32.52 'c_Lambda_Osubstn'( Y, Z, T ) ), 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'(
% 32.08/32.52 X, Y ), Z, T ) ) ] )
% 32.08/32.52 , clause( 95222, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T
% 32.08/32.52 ), 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ),
% 32.08/32.52 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ] )
% 32.08/32.52 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 32.08/32.52 ).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 subsumption(
% 32.08/32.52 clause( 289, [ =( 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ),
% 32.08/32.52 'c_Lambda_Osubstn'( Y, Z, T ) ), 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'(
% 32.08/32.52 X, Y ), Z, T ) ) ] )
% 32.08/32.52 , clause( 98163, [ =( 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ),
% 32.08/32.52 'c_Lambda_Osubstn'( Y, Z, T ) ), 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'(
% 32.08/32.52 X, Y ), Z, T ) ) ] )
% 32.08/32.52 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 32.08/32.52 permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 paramod(
% 32.08/32.52 clause( 98980, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubstn'(
% 32.08/32.52 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OVar'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'c_Lambda_Olift'( 'v_ta____', 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ) ), 'v_s____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 32.08/32.52 )
% 32.08/32.52 , clause( 270, [ =( 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ) ) ] )
% 32.08/32.52 , 0, clause( 95224, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'(
% 32.08/32.52 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OVar'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'c_Lambda_Olift'( 'v_ta____', 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ) ), 'v_s____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 32.08/32.52 )
% 32.08/32.52 , 0, 1, substitution( 0, [ :=( X, 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OVar'(
% 32.08/32.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Olift'( 'v_ta____',
% 32.08/32.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), :=( Y, 'v_s____' )] ),
% 32.08/32.52 substitution( 1, [] )).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 subsumption(
% 32.08/32.52 clause( 290, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'(
% 32.08/32.52 'c_Lambda_OdB_OVar'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 32.08/32.52 'c_Lambda_Olift'( 'v_ta____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )
% 32.08/32.52 , 'v_s____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.52 , clause( 98980, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubstn'(
% 32.08/32.52 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OVar'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'c_Lambda_Olift'( 'v_ta____', 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ) ), 'v_s____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 32.08/32.52 )
% 32.08/32.52 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 subsumption(
% 32.08/32.52 clause( 291, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( 'v_s____',
% 32.08/32.52 'v_ta____' ) ) ) ] )
% 32.08/32.52 , clause( 95225, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( 'v_s____',
% 32.08/32.52 'v_ta____' ) ) ) ] )
% 32.08/32.52 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 eqswap(
% 32.08/32.52 clause( 99425, [ =( 'c_Lambda_Oliftn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ) ) ] )
% 32.08/32.52 , clause( 254, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ),
% 32.08/32.52 'c_Lambda_Oliftn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 32.08/32.52 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 eqswap(
% 32.08/32.52 clause( 99426, [ =( X, 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ), X, Y ) ) ] )
% 32.08/32.52 , clause( 220, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 32.08/32.52 ), X, Y ), X ) ] )
% 32.08/32.52 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 paramod(
% 32.08/32.52 clause( 99427, [ =( X, 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'(
% 32.08/32.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ) ) ] )
% 32.08/32.52 , clause( 99425, [ =( 'c_Lambda_Oliftn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ) ) ] )
% 32.08/32.52 , 0, clause( 99426, [ =( X, 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ), X, Y ) ) ] )
% 32.08/32.52 , 0, 2, substitution( 0, [ :=( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 32.08/32.52 , :=( Y, X )] ), substitution( 1, [ :=( X, X ), :=( Y,
% 32.08/32.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )] )).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 eqswap(
% 32.08/32.52 clause( 99428, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'(
% 32.08/32.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), X ) ] )
% 32.08/32.52 , clause( 99427, [ =( X, 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'(
% 32.08/32.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ) ) ] )
% 32.08/32.52 , 0, substitution( 0, [ :=( X, X )] )).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 subsumption(
% 32.08/32.52 clause( 80558, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'(
% 32.08/32.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), X ) ] )
% 32.08/32.52 , clause( 99428, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'(
% 32.08/32.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), X ) ] )
% 32.08/32.52 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 eqswap(
% 32.08/32.52 clause( 99429, [ =( 'c_Lambda_Osubstn'( X, Z, Y ), 'c_Lambda_Osubst'( X,
% 32.08/32.52 'c_Lambda_Oliftn'( Y, Z, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ) )
% 32.08/32.52 ] )
% 32.08/32.52 , clause( 260, [ =( 'c_Lambda_Osubst'( X, 'c_Lambda_Oliftn'( Z, Y,
% 32.08/32.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ), 'c_Lambda_Osubstn'( X, Y,
% 32.08/32.52 Z ) ) ] )
% 32.08/32.52 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 paramod(
% 32.08/32.52 clause( 99431, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X
% 32.08/32.52 ) ] )
% 32.08/32.52 , clause( 257, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X
% 32.08/32.52 ) ] )
% 32.08/32.52 , 0, clause( 99429, [ =( 'c_Lambda_Osubstn'( X, Z, Y ), 'c_Lambda_Osubst'(
% 32.08/32.52 X, 'c_Lambda_Oliftn'( Y, Z, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y )
% 32.08/32.52 ) ] )
% 32.08/32.52 , 0, 7, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, 'c_Lambda_Oliftn'(
% 32.08/32.52 Y, Z, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )] ), substitution( 1, [
% 32.08/32.52 :=( X, 'c_Lambda_Olift'( X, Y ) ), :=( Y, Y ), :=( Z, Z )] )).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 subsumption(
% 32.08/32.52 clause( 81935, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X
% 32.08/32.52 ) ] )
% 32.08/32.52 , clause( 99431, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_Olift'( X, Y ), Z, Y )
% 32.08/32.52 , X ) ] )
% 32.08/32.52 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 32.08/32.52 permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 eqswap(
% 32.08/32.52 clause( 99434, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X, T ), Y, Z )
% 32.08/32.52 , 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubstn'(
% 32.08/32.52 T, Y, Z ) ) ) ] )
% 32.08/32.52 , clause( 289, [ =( 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ),
% 32.08/32.52 'c_Lambda_Osubstn'( Y, Z, T ) ), 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'(
% 32.08/32.52 X, Y ), Z, T ) ) ] )
% 32.08/32.52 , 0, substitution( 0, [ :=( X, X ), :=( Y, T ), :=( Z, Y ), :=( T, Z )] )
% 32.08/32.52 ).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 paramod(
% 32.08/32.52 clause( 99436, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X,
% 32.08/32.52 'c_Lambda_Olift'( Y, Z ) ), T, Z ), 'c_Lambda_OdB_OApp'(
% 32.08/32.52 'c_Lambda_Osubstn'( X, T, Z ), Y ) ) ] )
% 32.08/32.52 , clause( 81935, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_Olift'( X, Y ), Z, Y )
% 32.08/32.52 , X ) ] )
% 32.08/32.52 , 0, clause( 99434, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X, T ), Y
% 32.08/32.52 , Z ), 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Y, Z ),
% 32.08/32.52 'c_Lambda_Osubstn'( T, Y, Z ) ) ) ] )
% 32.08/32.52 , 0, 14, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T )] ),
% 32.08/32.52 substitution( 1, [ :=( X, X ), :=( Y, T ), :=( Z, Z ), :=( T,
% 32.08/32.52 'c_Lambda_Olift'( Y, Z ) )] )).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 subsumption(
% 32.08/32.52 clause( 94494, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( T,
% 32.08/32.52 'c_Lambda_Olift'( X, Y ) ), Z, Y ), 'c_Lambda_OdB_OApp'(
% 32.08/32.52 'c_Lambda_Osubstn'( T, Z, Y ), X ) ) ] )
% 32.08/32.52 , clause( 99436, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X,
% 32.08/32.52 'c_Lambda_Olift'( Y, Z ) ), T, Z ), 'c_Lambda_OdB_OApp'(
% 32.08/32.52 'c_Lambda_Osubstn'( X, T, Z ), Y ) ) ] )
% 32.08/32.52 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] ),
% 32.08/32.52 permutation( 0, [ ==>( 0, 0 )] ) ).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 paramod(
% 32.08/32.52 clause( 99441, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'(
% 32.08/32.52 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'v_s____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 32.08/32.52 'v_ta____' ) ) ] )
% 32.08/32.52 , clause( 94494, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( T,
% 32.08/32.52 'c_Lambda_Olift'( X, Y ) ), Z, Y ), 'c_Lambda_OdB_OApp'(
% 32.08/32.52 'c_Lambda_Osubstn'( T, Z, Y ), X ) ) ] )
% 32.08/32.52 , 0, clause( 290, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubstn'(
% 32.08/32.52 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OVar'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'c_Lambda_Olift'( 'v_ta____', 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ) ), 'v_s____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 32.08/32.52 )
% 32.08/32.52 , 0, 1, substitution( 0, [ :=( X, 'v_ta____' ), :=( Y,
% 32.08/32.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), :=( Z, 'v_s____' ), :=( T,
% 32.08/32.52 'c_Lambda_OdB_OVar'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )] ),
% 32.08/32.52 substitution( 1, [] )).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 paramod(
% 32.08/32.52 clause( 99442, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( 'v_s____',
% 32.08/32.52 'v_ta____' ) ) ] )
% 32.08/32.52 , clause( 80558, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'(
% 32.08/32.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), X ) ] )
% 32.08/32.52 , 0, clause( 99441, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'(
% 32.08/32.52 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( 'c_HOL_Ozero__class_Ozero'(
% 32.08/32.52 'tc_nat' ) ), 'v_s____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 32.08/32.52 'v_ta____' ) ) ] )
% 32.08/32.52 , 0, 2, substitution( 0, [ :=( X, 'v_s____' )] ), substitution( 1, [] )
% 32.08/32.52 ).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 resolution(
% 32.08/32.52 clause( 99443, [] )
% 32.08/32.52 , clause( 291, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( 'v_s____',
% 32.08/32.52 'v_ta____' ) ) ) ] )
% 32.08/32.52 , 0, clause( 99442, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( 'v_s____',
% 32.08/32.52 'v_ta____' ) ) ] )
% 32.08/32.52 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 subsumption(
% 32.08/32.52 clause( 94862, [] )
% 32.08/32.52 , clause( 99443, [] )
% 32.08/32.52 , substitution( 0, [] ), permutation( 0, [] ) ).
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 end.
% 32.08/32.52
% 32.08/32.52 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 32.08/32.52
% 32.08/32.52 Memory use:
% 32.08/32.52
% 32.08/32.52 space for terms: 2237360
% 32.08/32.52 space for clauses: 4299561
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 clauses generated: 641367
% 32.08/32.52 clauses kept: 94863
% 32.08/32.52 clauses selected: 1160
% 32.08/32.52 clauses deleted: 2355
% 32.08/32.52 clauses inuse deleted: 45
% 32.08/32.52
% 32.08/32.52 subsentry: 5288225
% 32.08/32.52 literals s-matched: 2944965
% 32.08/32.52 literals matched: 2667540
% 32.08/32.52 full subsumption: 1867338
% 32.08/32.52
% 32.08/32.52 checksum: -193778696
% 32.08/32.52
% 32.08/32.52
% 32.08/32.52 Bliksem ended
%------------------------------------------------------------------------------