TSTP Solution File: LCL748-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL748-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:57:28 EDT 2022
% Result : Unsatisfiable 17.82s 18.20s
% Output : Refutation 17.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL748-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n006.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 : Mon Jul 4 07:11:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.77/1.17 *** allocated 10000 integers for termspace/termends
% 0.77/1.17 *** allocated 10000 integers for clauses
% 0.77/1.17 *** allocated 10000 integers for justifications
% 0.77/1.17 Bliksem 1.12
% 0.77/1.17
% 0.77/1.17
% 0.77/1.17 Automatic Strategy Selection
% 0.77/1.17
% 0.77/1.17 Clauses:
% 0.77/1.17 [
% 0.77/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.77/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.77/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.77/1.17 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.77/1.17 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.77/1.17 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.77/1.17 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.77/1.17 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.77/1.17 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.77/1.17 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.77/1.17 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.77/1.17 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.77/1.17 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.77/1.17 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.77/1.17 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.77/1.17 ,
% 0.77/1.17 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.77/1.17 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.77/1.17 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.77/1.17 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.77/1.17 ,
% 0.77/1.17 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.77/1.17 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.17 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.77/1.17 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.17 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.77/1.17 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.77/1.17 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.77/1.17 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.77/1.17 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.17 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.77/1.17 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.77/1.18 'tc_nat' ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.77/1.18 ,
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.77/1.18 ,
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.77/1.18 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.77/1.18 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.77/1.18 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.77/1.18 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.77/1.18 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.77/1.18 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.77/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.77/1.18 W, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.77/1.18 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.77/1.18 , X ), T, X ), W, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.77/1.18 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.77/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.77/1.18 W, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.77/1.18 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.77/1.18 , X ), W, X ), X ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.77/1.18 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.77/1.18 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.77/1.18 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ), 'c_Lambda_Olift'(
% 0.77/1.18 'c_Lambda_Oliftn'( X, Y, Z ), Z ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.77/1.18 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.77/1.18 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.77/1.18 ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.77/1.18 ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.77/1.18 ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.77/1.18 ) ],
% 0.77/1.18 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.77/1.18 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.77/1.18 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.77/1.18 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 X, T, 'tc_nat' ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.77/1.18 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.77/1.18 ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.77/1.18 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.77/1.18 ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.77/1.18 Y, 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.77/1.18 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.77/1.18 ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.77/1.18 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.77/1.18 ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.77/1.18 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.77/1.18 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.77/1.18 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.77/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.77/1.18 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.77/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.77/1.18 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.77/1.18 , X ), W, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.77/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ), =( X
% 0.77/1.18 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.77/1.18 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.77/1.18 ) ],
% 0.77/1.18 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.77/1.18 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.77/1.18 , X ) ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.77/1.18 , Y, X ) ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.77/1.18 , Y, X ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.77/1.18 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.77/1.18 ), =( Z, Y ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.77/1.18 ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.77/1.18 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.77/1.18 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.77/1.18 ) ],
% 0.77/1.18 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 0.77/1.18 'tc_nat' ), 'tc_nat' ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.77/1.18 [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.77/1.18 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.77/1.18 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.77/1.18 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.77/1.18 , X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.77/1.18 , X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.77/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.77/1.18 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.77/1.18 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.77/1.18 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.77/1.18 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 0.77/1.18 X ) ],
% 0.77/1.18 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.77/1.18 , 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.77/1.18 ,
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.77/1.18 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.77/1.18 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.77/1.18 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.77/1.18 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.77/1.18 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.77/1.18 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.77/1.18 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.77/1.18 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.77/1.18 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.77/1.18 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.77/1.18 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 Y, T, X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.77/1.18 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 Y, T, X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.77/1.18 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.77/1.18 X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 Z, T, X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.77/1.18 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 Z, T, X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.77/1.18 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.77/1.18 X ), X ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.77/1.18 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.77/1.18 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.77/1.18 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.77/1.18 , Y, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.77/1.18 , T, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.77/1.18 , T, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.77/1.18 , Y, X ), X ) ) ],
% 0.77/1.18 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.77/1.18 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.77/1.18 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.77/1.18 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.77/1.18 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.77/1.18 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.77/1.18 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 0.77/1.18 ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.77/1.18 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.77/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.77/1.18 T, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.77/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.77/1.18 X ), Z, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.77/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.77/1.18 T, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.77/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.77/1.18 X ), T, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.77/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.77/1.18 T, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.77/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.77/1.18 X ), T, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.77/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.77/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.77/1.18 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.77/1.18 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.77/1.18 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.77/1.18 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.77/1.18 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.77/1.18 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.77/1.18 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.77/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.77/1.18 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.77/1.18 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.77/1.18 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.77/1.18 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.77/1.18 ), Y ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 0.77/1.18 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 0.77/1.18 ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.77/1.18 , Y, X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.77/1.18 ,
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.77/1.18 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.77/1.18 , Y, X ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.77/1.18 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.77/1.18 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.77/1.18 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.77/1.18 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.77/1.18 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.77/1.18 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 0.77/1.18 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.77/1.18 ), 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.77/1.18 ), 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.77/1.18 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.77/1.18 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.77/1.18 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.77/1.18 , T, X ) ) ), =( Y, Z ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.77/1.18 , T, X ) ) ), =( Z, T ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.77/1.18 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.77/1.18 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.77/1.18 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.77/1.18 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.77/1.18 'c_Suc'( X ), 'tc_nat' ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.77/1.18 'c_Suc'( X ), 'tc_nat' ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.77/1.18 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.77/1.18 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.77/1.18 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.77/1.18 ) ), =( Y, Z ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.77/1.18 ) ), =( Y, Z ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.77/1.18 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.77/1.18 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.77/1.18 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.77/1.18 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.77/1.18 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.77/1.18 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OApp'( Y, Z ), T ),
% 0.77/1.18 'c_Lambda_OdB_OApp'( 'c_Lambda_Oliftn'( X, Y, T ), 'c_Lambda_Oliftn'( X,
% 0.77/1.18 Z, T ) ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.77/1.18 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.77/1.18 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.77/1.18 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.77/1.18 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubstn'(
% 0.77/1.18 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'( X, Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.77/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.77/1.18 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.77/1.18 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.77/1.18 X ), T, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.77/1.18 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.77/1.18 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.77/1.18 , X, 'tc_nat' ), X ) ],
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.77/1.18 ), 'tc_nat' ), X ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.77/1.18 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.77/1.18 ), X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.77/1.18 ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T ),
% 0.77/1.18 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ), 'c_Lambda_Osubstn'( Y
% 0.77/1.18 , Z, T ) ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.77/1.18 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 0.77/1.18 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.77/1.18 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.77/1.18 ), Y ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.77/1.18 ,
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.77/1.18 'tc_nat' ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.77/1.18 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.77/1.18 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OVar'( Z ) ) ) ],
% 0.77/1.18 [ =( X, 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'(
% 0.77/1.18 Y, X ) ) ), ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( Y ), X ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Y ), 'c_Suc'( Z ) ),
% 0.77/1.18 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Z ), Y ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 0.77/1.18 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( T,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), 'c_Lambda_Olift'( Y,
% 0.77/1.18 T ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.18 T, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.77/1.18 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z
% 0.77/1.18 , Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.77/1.18 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( X
% 0.77/1.18 , Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.77/1.18 X ), X ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y, Z ),
% 0.77/1.18 'c_Suc'( T ) ), 'c_Lambda_Osubst'( U, Y, T ), Z ), 'c_Lambda_Osubst'(
% 0.77/1.18 'c_Lambda_Osubst'( X, U, Z ), Y, T ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( T, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.77/1.18 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 0.77/1.18 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y,
% 0.77/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oplus__class_Oplus'( Z,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.77/1.18 X ) ) ), =( Y, T ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.77/1.18 X ) ) ), =( Z, T ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.77/1.18 X ) ) ), =( Z, T ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.77/1.18 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 0.77/1.18 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.77/1.18 [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 0.77/1.18 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, T ), 'c_Lambda_Olift'( Y, T ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.77/1.18 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.77/1.18 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.77/1.18 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.77/1.18 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubst'(
% 0.77/1.18 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.77/1.18 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.77/1.18 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.77/1.18 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.77/1.18 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.77/1.18 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.77/1.18 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.77/1.18 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.77/1.18 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.77/1.18 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.77/1.18 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.77/1.18 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.77/1.18 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.77/1.18 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.77/1.18 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.77/1.18 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.77/1.18 'tc_nat' ) ],
% 0.77/1.18 [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ), 'c_Lambda_Osubst'( T,
% 0.77/1.18 Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ],
% 0.77/1.18 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 0.77/1.18 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 0.77/1.18 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.18 Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.77/1.18 X ) ) ],
% 0.77/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.77/1.18 X ) ) ],
% 0.77/1.18 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.77/1.18 X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.77/1.18 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.77/1.18 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OApp'( Y, Z ) ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 0.77/1.18 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.77/1.18 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 0.77/1.18 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.77/1.18 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 0.77/1.18 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.77/1.18 ,
% 0.77/1.18 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ),
% 0.77/1.18 'c_Lambda_OdB_OAbs'( 'c_Lambda_Oliftn'( X, Y, 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.18 Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 0.77/1.18 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z, T ) ) ),
% 0.77/1.18 =( Y, T ) ],
% 0.77/1.18 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z, T ) ) ),
% 0.77/1.18 =( X, Z ) ],
% 0.77/1.18 [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.77/1.18 [ 'c_Lambda_Obeta'( X, 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'( X, Y
% 0.77/1.18 ) ), ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), Y ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.77/1.18 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.77/1.18 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.77/1.18 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.77/1.18 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.77/1.18 ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.77/1.18 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.77/1.18 ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T ),
% 0.77/1.18 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubst'( X, Z, T ), 'c_Lambda_Osubst'( Y,
% 0.77/1.18 Z, T ) ) ) ],
% 0.77/1.18 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.77/1.18 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.77/1.18 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 0.77/1.18 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.77/1.18 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 0.77/1.18 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.77/1.18 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OAbs'( Z ) ) ) ],
% 0.77/1.18 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OApp'( Y, Z ) ) ) ],
% 0.77/1.18 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.77/1.18 ) ],
% 0.77/1.18 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OApp'( X, Y ), Z ),
% 0.77/1.18 'c_Lambda_OdB_OApp'( 'c_Lambda_Olift'( X, Z ), 'c_Lambda_Olift'( Y, Z ) )
% 0.77/1.18 ) ],
% 0.77/1.18 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 0.77/1.18 'c_InductTermi_OIT'( X ) ) ],
% 0.77/1.18 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X ) ],
% 0.77/1.18 [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ), 'c_Lambda_Olift'( Z, Y ) )
% 0.77/1.18 , ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.77/1.18 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.77/1.18 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 0.77/1.18 [ 'c_InductTermi_OIT'( 'v_r' ) ],
% 0.77/1.18 [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'v_r', X ) ) ],
% 0.77/1.18 [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( 'v_r' )
% 0.77/1.18 , 'v_ia' ) ) ) ],
% 0.77/1.18 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.77/1.18 ],
% 0.77/1.18 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.77/1.18 ) ],
% 0.77/1.18 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.77/1.18 ],
% 0.77/1.18 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.77/1.18 [ 'class_Orderings_Oorder'( 'tc_nat' ) ]
% 0.77/1.18 ] .
% 0.77/1.18
% 0.77/1.18
% 0.77/1.18 percentage equality = 0.351955, percentage horn = 0.882175
% 0.77/1.18 This is a problem with some equality
% 0.77/1.18
% 0.77/1.18
% 0.77/1.18
% 0.77/1.18 Options Used:
% 0.77/1.18
% 0.77/1.18 useres = 1
% 0.77/1.18 useparamod = 1
% 0.77/1.18 useeqrefl = 1
% 0.77/1.18 useeqfact = 1
% 0.77/1.18 usefactor = 1
% 0.77/1.18 usesimpsplitting = 0
% 0.77/1.18 usesimpdemod = 5
% 0.77/1.18 usesimpres = 3
% 0.77/1.18
% 0.77/1.18 resimpinuse = 1000
% 0.77/1.18 resimpclauses = 20000
% 0.77/1.18 substype = eqrewr
% 0.77/1.18 backwardsubs = 1
% 0.77/1.18 selectoldest = 5
% 0.77/1.18
% 0.77/1.18 litorderings [0] = split
% 0.77/1.18 litorderings [1] = extend the termordering, first sorting on arguments
% 0.77/1.18
% 0.77/1.18 termordering = kbo
% 0.77/1.18
% 0.77/1.18 litapriori = 0
% 0.77/1.18 termapriori = 1
% 0.77/1.18 litaposteriori = 0
% 0.77/1.18 termaposteriori = 0
% 0.77/1.18 demodaposteriori = 0
% 0.77/1.18 ordereqreflfact = 0
% 0.77/1.18
% 0.77/1.18 litselect = negord
% 0.77/1.18
% 0.77/1.18 maxweight = 15
% 0.77/1.18 maxdepth = 30000
% 0.77/1.18 maxlength = 115
% 0.77/1.18 maxnrvars = 195
% 0.77/1.18 excuselevel = 1
% 0.77/1.18 increasemaxweight = 1
% 0.77/1.18
% 0.77/1.18 maxselected = 10000000
% 0.77/1.18 maxnrclauses = 10000000
% 0.77/1.18
% 0.77/1.18 showgenerated = 0
% 0.77/1.18 showkept = 0
% 0.77/1.18 showselected = 0
% 0.77/1.18 showdeleted = 0
% 0.77/1.18 showresimp = 1
% 0.77/1.18 showstatus = 2000
% 0.77/1.18
% 0.77/1.18 prologoutput = 1
% 0.77/1.18 nrgoals = 5000000
% 0.77/1.18 totalproof = 1
% 0.77/1.18
% 0.77/1.18 Symbols occurring in the translation:
% 0.77/1.18
% 0.77/1.18 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.77/1.18 . [1, 2] (w:1, o:96, a:1, s:1, b:0),
% 0.77/1.18 ! [4, 1] (w:0, o:48, a:1, s:1, b:0),
% 0.77/1.18 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.77/1.18 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.77/1.18 'class_Ring__and__Field_Ocomm__semiring__1' [40, 1] (w:1, o:53, a:1
% 0.77/1.18 , s:1, b:0),
% 0.77/1.18 'c_HOL_Otimes__class_Otimes' [43, 3] (w:1, o:126, a:1, s:1, b:0),
% 10.30/10.68 'c_Suc' [48, 1] (w:1, o:54, a:1, s:1, b:0),
% 10.30/10.68 'tc_nat' [49, 0] (w:1, o:19, a:1, s:1, b:0),
% 10.30/10.68 'c_HOL_Oord__class_Oless' [50, 3] (w:1, o:127, a:1, s:1, b:0),
% 10.30/10.68 'c_HOL_Ominus__class_Ominus' [51, 3] (w:1, o:128, a:1, s:1, b:0),
% 10.30/10.68 'class_Ring__and__Field_Oidom' [52, 1] (w:1, o:55, a:1, s:1, b:0),
% 10.30/10.68 'class_Int_Onumber__ring' [53, 1] (w:1, o:56, a:1, s:1, b:0),
% 10.30/10.68 'c_HOL_Oplus__class_Oplus' [58, 3] (w:1, o:129, a:1, s:1, b:0),
% 10.30/10.68 'class_Ring__and__Field_Oordered__ring__strict' [63, 1] (w:1, o:59
% 10.30/10.68 , a:1, s:1, b:0),
% 10.30/10.68 'c_HOL_Ozero__class_Ozero' [64, 1] (w:1, o:60, a:1, s:1, b:0),
% 10.30/10.68 'class_Ring__and__Field_Ozero__neq__one' [65, 1] (w:1, o:61, a:1, s:1
% 10.30/10.68 , b:0),
% 10.30/10.68 'c_HOL_Oone__class_Oone' [66, 1] (w:1, o:62, a:1, s:1, b:0),
% 10.30/10.68 'class_Ring__and__Field_Oordered__semidom' [67, 1] (w:1, o:63, a:1
% 10.30/10.68 , s:1, b:0),
% 10.30/10.68 'c_Lambda_OdB_OVar' [69, 1] (w:1, o:64, a:1, s:1, b:0),
% 10.30/10.68 'c_Lambda_Osubstn' [72, 3] (w:1, o:130, a:1, s:1, b:0),
% 10.30/10.68 'class_Ring__and__Field_Oordered__semiring__strict' [73, 1] (w:1, o:
% 10.30/10.68 65, a:1, s:1, b:0),
% 10.30/10.68 'class_Ring__and__Field_Oordered__idom' [74, 1] (w:1, o:66, a:1, s:1
% 10.30/10.68 , b:0),
% 10.30/10.68 'class_OrderedGroup_Olordered__ab__group__add' [75, 1] (w:1, o:68, a:
% 10.30/10.68 1, s:1, b:0),
% 10.30/10.68 'class_Ring__and__Field_Ono__zero__divisors' [76, 1] (w:1, o:58, a:1
% 10.30/10.68 , s:1, b:0),
% 10.30/10.68 'class_Ring__and__Field_Oring__no__zero__divisors' [77, 1] (w:1, o:69
% 10.30/10.68 , a:1, s:1, b:0),
% 10.30/10.68 'class_Ring__and__Field_Opordered__ring' [78, 1] (w:1, o:71, a:1, s:1
% 10.30/10.68 , b:0),
% 10.30/10.68 'c_Lambda_Oliftn' [83, 3] (w:1, o:131, a:1, s:1, b:0),
% 10.30/10.68 'c_Lambda_Olift' [84, 2] (w:1, o:121, a:1, s:1, b:0),
% 10.30/10.68 'class_OrderedGroup_Ogroup__add' [85, 1] (w:1, o:72, a:1, s:1, b:0),
% 10.30/10.68
% 10.30/10.68 'class_OrderedGroup_Oab__group__add' [86, 1] (w:1, o:73, a:1, s:1, b:
% 10.30/10.68 0),
% 10.30/10.68 'class_Nat_Osemiring__char__0' [87, 1] (w:1, o:67, a:1, s:1, b:0),
% 10.30/10.68 'c_Nat_Osemiring__1__class_Oof__nat' [88, 2] (w:1, o:122, a:1, s:1
% 10.30/10.68 , b:0),
% 10.30/10.68 'class_Ring__and__Field_Oring' [91, 1] (w:1, o:74, a:1, s:1, b:0),
% 10.30/10.68 'class_OrderedGroup_Ocomm__monoid__mult' [92, 1] (w:1, o:75, a:1, s:1
% 10.30/10.68 , b:0),
% 10.30/10.68 'class_OrderedGroup_Omonoid__mult' [93, 1] (w:1, o:76, a:1, s:1, b:0)
% 10.30/10.68 ,
% 10.30/10.68 'class_Ring__and__Field_Omult__zero' [94, 1] (w:1, o:57, a:1, s:1, b:
% 10.30/10.68 0),
% 10.30/10.68 'class_Orderings_Oorder' [95, 1] (w:1, o:77, a:1, s:1, b:0),
% 10.30/10.68 'class_Orderings_Olinorder' [96, 1] (w:1, o:78, a:1, s:1, b:0),
% 10.30/10.68 'class_Orderings_Opreorder' [97, 1] (w:1, o:79, a:1, s:1, b:0),
% 10.30/10.68 'class_OrderedGroup_Opordered__comm__monoid__add' [98, 1] (w:1, o:80
% 10.30/10.68 , a:1, s:1, b:0),
% 10.30/10.68 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [99, 1]
% 10.30/10.68 (w:1, o:81, a:1, s:1, b:0),
% 10.30/10.68 'class_OrderedGroup_Opordered__ab__group__add' [100, 1] (w:1, o:82
% 10.30/10.68 , a:1, s:1, b:0),
% 10.30/10.68 'class_OrderedGroup_Oab__semigroup__idem__mult' [101, 1] (w:1, o:83
% 10.30/10.68 , a:1, s:1, b:0),
% 10.30/10.68 'c_Lambda_Osubst' [102, 3] (w:1, o:132, a:1, s:1, b:0),
% 10.30/10.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [104, 1]
% 10.30/10.68 (w:1, o:84, a:1, s:1, b:0),
% 10.30/10.68 'class_OrderedGroup_Oab__semigroup__mult' [107, 1] (w:1, o:85, a:1
% 10.30/10.68 , s:1, b:0),
% 10.30/10.68 'class_Ring__and__Field_Ocomm__semiring' [108, 1] (w:1, o:86, a:1, s:
% 10.30/10.68 1, b:0),
% 10.30/10.68 'class_Ring__and__Field_Osemiring__1' [110, 1] (w:1, o:87, a:1, s:1
% 10.30/10.68 , b:0),
% 10.30/10.68 'class_Ring__and__Field_Osemiring' [111, 1] (w:1, o:88, a:1, s:1, b:0
% 10.30/10.68 ),
% 10.30/10.68 'c_Lambda_OdB_OApp' [112, 2] (w:1, o:123, a:1, s:1, b:0),
% 10.30/10.68 'class_Ring__and__Field_Oordered__comm__semiring__strict' [113, 1]
% 10.30/10.68 (w:1, o:70, a:1, s:1, b:0),
% 10.30/10.68 'class_OrderedGroup_Ocomm__monoid__add' [114, 1] (w:1, o:89, a:1, s:1
% 10.30/10.68 , b:0),
% 10.30/10.68 'class_OrderedGroup_Omonoid__add' [115, 1] (w:1, o:90, a:1, s:1, b:0)
% 10.30/10.68 ,
% 10.30/10.68 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1' [119, 2] (w:1, o:124, a:1
% 10.30/10.68 , s:1, b:0),
% 10.30/10.68 'c_Lambda_OdB_OAbs' [120, 1] (w:1, o:91, a:1, s:1, b:0),
% 10.30/10.68 'c_Lambda_Obeta' [121, 2] (w:1, o:125, a:1, s:1, b:0),
% 10.30/10.68 'class_OrderedGroup_Ocancel__semigroup__add' [123, 1] (w:1, o:92, a:1
% 17.82/18.20 , s:1, b:0),
% 17.82/18.20 'class_OrderedGroup_Ocancel__ab__semigroup__add' [124, 1] (w:1, o:93
% 17.82/18.20 , a:1, s:1, b:0),
% 17.82/18.20 'class_OrderedGroup_Oab__semigroup__add' [125, 1] (w:1, o:94, a:1, s:
% 17.82/18.20 1, b:0),
% 17.82/18.20 'c_InductTermi_OIT' [130, 1] (w:1, o:95, a:1, s:1, b:0),
% 17.82/18.20 'v_r' [131, 0] (w:1, o:46, a:1, s:1, b:0),
% 17.82/18.20 'v_ia' [132, 0] (w:1, o:47, a:1, s:1, b:0).
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Starting Search:
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 8507
% 17.82/18.20 Kept: 2088
% 17.82/18.20 Inuse: 105
% 17.82/18.20 Deleted: 6
% 17.82/18.20 Deletedinuse: 0
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 15816
% 17.82/18.20 Kept: 4090
% 17.82/18.20 Inuse: 144
% 17.82/18.20 Deleted: 6
% 17.82/18.20 Deletedinuse: 0
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 23834
% 17.82/18.20 Kept: 6095
% 17.82/18.20 Inuse: 186
% 17.82/18.20 Deleted: 6
% 17.82/18.20 Deletedinuse: 0
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 33883
% 17.82/18.20 Kept: 8108
% 17.82/18.20 Inuse: 237
% 17.82/18.20 Deleted: 6
% 17.82/18.20 Deletedinuse: 0
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 46410
% 17.82/18.20 Kept: 10227
% 17.82/18.20 Inuse: 309
% 17.82/18.20 Deleted: 8
% 17.82/18.20 Deletedinuse: 1
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 65429
% 17.82/18.20 Kept: 12707
% 17.82/18.20 Inuse: 340
% 17.82/18.20 Deleted: 9
% 17.82/18.20 Deletedinuse: 2
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 77065
% 17.82/18.20 Kept: 14842
% 17.82/18.20 Inuse: 390
% 17.82/18.20 Deleted: 11
% 17.82/18.20 Deletedinuse: 3
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 91966
% 17.82/18.20 Kept: 16843
% 17.82/18.20 Inuse: 420
% 17.82/18.20 Deleted: 11
% 17.82/18.20 Deletedinuse: 3
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 106276
% 17.82/18.20 Kept: 18846
% 17.82/18.20 Inuse: 452
% 17.82/18.20 Deleted: 11
% 17.82/18.20 Deletedinuse: 3
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying clauses:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 118307
% 17.82/18.20 Kept: 20895
% 17.82/18.20 Inuse: 497
% 17.82/18.20 Deleted: 1426
% 17.82/18.20 Deletedinuse: 3
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 130216
% 17.82/18.20 Kept: 22921
% 17.82/18.20 Inuse: 533
% 17.82/18.20 Deleted: 1460
% 17.82/18.20 Deletedinuse: 37
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 152367
% 17.82/18.20 Kept: 25009
% 17.82/18.20 Inuse: 577
% 17.82/18.20 Deleted: 1462
% 17.82/18.20 Deletedinuse: 39
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 167920
% 17.82/18.20 Kept: 27206
% 17.82/18.20 Inuse: 622
% 17.82/18.20 Deleted: 1462
% 17.82/18.20 Deletedinuse: 39
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 191543
% 17.82/18.20 Kept: 29299
% 17.82/18.20 Inuse: 661
% 17.82/18.20 Deleted: 1468
% 17.82/18.20 Deletedinuse: 39
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 212713
% 17.82/18.20 Kept: 31422
% 17.82/18.20 Inuse: 695
% 17.82/18.20 Deleted: 1470
% 17.82/18.20 Deletedinuse: 40
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 230460
% 17.82/18.20 Kept: 34004
% 17.82/18.20 Inuse: 715
% 17.82/18.20 Deleted: 1471
% 17.82/18.20 Deletedinuse: 41
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 246841
% 17.82/18.20 Kept: 36021
% 17.82/18.20 Inuse: 739
% 17.82/18.20 Deleted: 1472
% 17.82/18.20 Deletedinuse: 42
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 261530
% 17.82/18.20 Kept: 38021
% 17.82/18.20 Inuse: 762
% 17.82/18.20 Deleted: 1472
% 17.82/18.20 Deletedinuse: 42
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 278444
% 17.82/18.20 Kept: 40035
% 17.82/18.20 Inuse: 792
% 17.82/18.20 Deleted: 1472
% 17.82/18.20 Deletedinuse: 42
% 17.82/18.20
% 17.82/18.20 Resimplifying clauses:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 290899
% 17.82/18.20 Kept: 42040
% 17.82/18.20 Inuse: 823
% 17.82/18.20 Deleted: 2203
% 17.82/18.20 Deletedinuse: 42
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 310960
% 17.82/18.20 Kept: 44192
% 17.82/18.20 Inuse: 890
% 17.82/18.20 Deleted: 2203
% 17.82/18.20 Deletedinuse: 42
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 330557
% 17.82/18.20 Kept: 46675
% 17.82/18.20 Inuse: 930
% 17.82/18.20 Deleted: 2203
% 17.82/18.20 Deletedinuse: 42
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 358772
% 17.82/18.20 Kept: 48844
% 17.82/18.20 Inuse: 945
% 17.82/18.20 Deleted: 2203
% 17.82/18.20 Deletedinuse: 42
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 379564
% 17.82/18.20 Kept: 51674
% 17.82/18.20 Inuse: 955
% 17.82/18.20 Deleted: 2203
% 17.82/18.20 Deletedinuse: 42
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 395773
% 17.82/18.20 Kept: 53682
% 17.82/18.20 Inuse: 986
% 17.82/18.20 Deleted: 2207
% 17.82/18.20 Deletedinuse: 46
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 414340
% 17.82/18.20 Kept: 55781
% 17.82/18.20 Inuse: 1009
% 17.82/18.20 Deleted: 2208
% 17.82/18.20 Deletedinuse: 46
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 429006
% 17.82/18.20 Kept: 57867
% 17.82/18.20 Inuse: 1039
% 17.82/18.20 Deleted: 2208
% 17.82/18.20 Deletedinuse: 46
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 448433
% 17.82/18.20 Kept: 61134
% 17.82/18.20 Inuse: 1059
% 17.82/18.20 Deleted: 2208
% 17.82/18.20 Deletedinuse: 46
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying clauses:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 461118
% 17.82/18.20 Kept: 63461
% 17.82/18.20 Inuse: 1064
% 17.82/18.20 Deleted: 3128
% 17.82/18.20 Deletedinuse: 46
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20 Done
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 Intermediate Status:
% 17.82/18.20 Generated: 472496
% 17.82/18.20 Kept: 65542
% 17.82/18.20 Inuse: 1094
% 17.82/18.20 Deleted: 3128
% 17.82/18.20 Deletedinuse: 46
% 17.82/18.20
% 17.82/18.20 Resimplifying inuse:
% 17.82/18.20
% 17.82/18.20 Bliksems!, er is een bewijs:
% 17.82/18.20 % SZS status Unsatisfiable
% 17.82/18.20 % SZS output start Refutation
% 17.82/18.20
% 17.82/18.20 clause( 249, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oone__class_Oone'(
% 17.82/18.20 'tc_nat' ), 'tc_nat' ), 'c_Suc'( X ) ) ] )
% 17.82/18.20 .
% 17.82/18.20 clause( 270, [ =( 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_Suc'( Y ) )
% 17.82/18.20 ), 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ) ) ] )
% 17.82/18.20 .
% 17.82/18.20 clause( 275, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 17.82/18.20 'c_InductTermi_OIT'( X ) ) ] )
% 17.82/18.20 .
% 17.82/18.20 clause( 280, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'v_r', X ) ) ] )
% 17.82/18.20 .
% 17.82/18.20 clause( 281, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 17.82/18.20 'c_Lambda_OdB_OAbs'( 'v_r' ), 'v_ia' ) ) ) ] )
% 17.82/18.20 .
% 17.82/18.20 clause( 647, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'(
% 17.82/18.20 'v_r', X ) ) ) ] )
% 17.82/18.20 .
% 17.82/18.20 clause( 65539, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'(
% 17.82/18.20 'v_r' ), X ) ) ] )
% 17.82/18.20 .
% 17.82/18.20 clause( 65542, [] )
% 17.82/18.20 .
% 17.82/18.20
% 17.82/18.20
% 17.82/18.20 % SZS output end Refutation
% 17.82/18.20 found a proof!
% 17.82/18.20
% 17.82/18.20 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 17.82/18.20
% 17.82/18.20 initialclauses(
% 17.82/18.20 [ clause( 65544, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 17.82/18.20 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 17.82/18.20 , clause( 65545, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 17.82/18.20 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 17.82/18.20 , clause( 65546, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 17.82/18.20 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 17.82/18.20 , clause( 65547, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 17.82/18.20 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65548, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X )
% 17.82/18.20 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65549, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 17.82/18.20 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65550, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'(
% 17.82/18.20 Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65551, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 17.82/18.20 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 17.82/18.20 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 17.82/18.20 =( Y, T ) ] )
% 17.82/18.20 , clause( 65552, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 17.82/18.20 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 17.82/18.20 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 17.82/18.20 =( Y, T ) ] )
% 17.82/18.20 , clause( 65553, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 17.82/18.20 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65554, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 17.82/18.20 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 17.82/18.20 )
% 17.82/18.20 , clause( 65555, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 17.82/18.20 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65556, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z )
% 17.82/18.20 , 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X
% 17.82/18.20 , 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65557, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65558, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 17.82/18.20 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 17.82/18.20 , clause( 65559, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 17.82/18.20 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 17.82/18.20 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 17.82/18.20 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 17.82/18.20 , clause( 65560, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 17.82/18.20 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 17.82/18.20 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 17.82/18.20 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 17.82/18.20 , clause( 65561, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 17.82/18.20 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65562, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 17.82/18.20 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 17.82/18.20 , clause( 65563, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65564, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65565, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 17.82/18.20 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65566, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 17.82/18.20 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65567, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 17.82/18.20 ] )
% 17.82/18.20 , clause( 65568, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 17.82/18.20 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65569, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 17.82/18.20 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65570, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 17.82/18.20 ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 17.82/18.20 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65571, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 17.82/18.20 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 17.82/18.20 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 17.82/18.20 W, X ), X ) ) ] )
% 17.82/18.20 , clause( 65572, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 17.82/18.20 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 17.82/18.20 , X ), T, X ), W, X ) ) ] )
% 17.82/18.20 , clause( 65573, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 17.82/18.20 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 17.82/18.20 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 17.82/18.20 W, X ), X ) ) ] )
% 17.82/18.20 , clause( 65574, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 17.82/18.20 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 17.82/18.20 , X ), W, X ), X ) ) ] )
% 17.82/18.20 , clause( 65575, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 17.82/18.20 , clause( 65576, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 17.82/18.20 , clause( 65577, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 17.82/18.20 , clause( 65578, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 17.82/18.20 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65579, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65580, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65581, [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ),
% 17.82/18.20 'c_Lambda_Olift'( 'c_Lambda_Oliftn'( X, Y, Z ), Z ) ) ] )
% 17.82/18.20 , clause( 65582, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 17.82/18.20 , clause( 65583, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65584, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 17.82/18.20 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 17.82/18.20 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65585, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65586, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65587, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65588, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65589, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) )
% 17.82/18.20 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65590, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X )
% 17.82/18.20 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65591, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 17.82/18.20 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 17.82/18.20 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65592, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 17.82/18.20 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 17.82/18.20 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 17.82/18.20 , clause( 65593, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.20 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 17.82/18.20 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65594, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 X, T, 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65595, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 17.82/18.20 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 17.82/18.20 , clause( 65596, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 17.82/18.20 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65597, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 17.82/18.20 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65598, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 17.82/18.20 Y, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65599, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 17.82/18.20 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65600, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 17.82/18.20 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65601, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65602, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65603, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65604, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 17.82/18.20 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 17.82/18.20 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 17.82/18.20 , clause( 65605, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 17.82/18.20 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 17.82/18.20 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 17.82/18.20 , X ), W, X ) ) ] )
% 17.82/18.20 , clause( 65606, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 17.82/18.20 ) ) ] )
% 17.82/18.20 , clause( 65607, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 17.82/18.20 ) ) ) ] )
% 17.82/18.20 , clause( 65608, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 17.82/18.20 ) ) ) ] )
% 17.82/18.20 , clause( 65609, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 17.82/18.20 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 17.82/18.20 , clause( 65610, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat'
% 17.82/18.20 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 17.82/18.20 , clause( 65611, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 17.82/18.20 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 17.82/18.20 , clause( 65612, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65613, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 17.82/18.20 ] )
% 17.82/18.20 , clause( 65614, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 17.82/18.20 ] )
% 17.82/18.20 , clause( 65615, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 17.82/18.20 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65616, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 17.82/18.20 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65617, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 17.82/18.20 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 17.82/18.20 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65618, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 17.82/18.20 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 17.82/18.20 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65619, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65620, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65621, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 17.82/18.20 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65622, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X,
% 17.82/18.20 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ), =( X
% 17.82/18.20 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65623, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.20 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 17.82/18.20 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65624, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 17.82/18.20 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65625, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65626, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65627, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 17.82/18.20 , clause( 65628, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 17.82/18.20 , clause( 65629, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 17.82/18.20 , clause( 65630, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 17.82/18.20 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65631, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 17.82/18.20 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 17.82/18.20 , clause( 65632, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 17.82/18.20 ), =( Z, Y ) ] )
% 17.82/18.20 , clause( 65633, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65634, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 17.82/18.20 , clause( 65635, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 17.82/18.20 , clause( 65636, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 17.82/18.20 , clause( 65637, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 17.82/18.20 ), =( Z, Y ) ] )
% 17.82/18.20 , clause( 65638, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 17.82/18.20 , clause( 65639, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65640, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 17.82/18.20 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 17.82/18.20 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65641, [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 17.82/18.20 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 17.82/18.20 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65642, [ ~(
% 17.82/18.20 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 17.82/18.20 , clause( 65643, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 17.82/18.20 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' )
% 17.82/18.20 , ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65644, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 17.82/18.20 ) ) ) ] )
% 17.82/18.20 , clause( 65645, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 17.82/18.20 ) ) ) ] )
% 17.82/18.20 , clause( 65646, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 17.82/18.20 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 17.82/18.20 , X ) ) ] )
% 17.82/18.20 , clause( 65647, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 17.82/18.20 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 17.82/18.20 , X ) ) ] )
% 17.82/18.20 , clause( 65648, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 17.82/18.20 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65649, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 17.82/18.20 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 17.82/18.20 , clause( 65650, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 17.82/18.20 )
% 17.82/18.20 , clause( 65651, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 17.82/18.20 )
% 17.82/18.20 , clause( 65652, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 17.82/18.20 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65653, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 17.82/18.20 , clause( 65654, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 17.82/18.20 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 17.82/18.20 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 17.82/18.20 , clause( 65655, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 17.82/18.20 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65656, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 17.82/18.20 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 17.82/18.20 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 17.82/18.20 , clause( 65657, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 17.82/18.20 ] )
% 17.82/18.20 , clause( 65658, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ), X, Y ), X ) ] )
% 17.82/18.20 , clause( 65659, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65660, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 17.82/18.20 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 17.82/18.20 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 17.82/18.20 , clause( 65661, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 17.82/18.20 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 17.82/18.20 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 17.82/18.20 , clause( 65662, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 17.82/18.20 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 17.82/18.20 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65663, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ) ), 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ) ) ) ] )
% 17.82/18.20 , clause( 65664, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 17.82/18.20 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 17.82/18.20 , clause( 65665, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65666, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65667, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 17.82/18.20 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65668, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 17.82/18.20 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 17.82/18.20 ) ) ] )
% 17.82/18.20 , clause( 65669, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 17.82/18.20 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 17.82/18.20 ) ) ] )
% 17.82/18.20 , clause( 65670, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 17.82/18.20 , Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65671, [ 'c_HOL_Oord__class_Oless'( X,
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 17.82/18.20 Y, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65672, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65673, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 17.82/18.20 , clause( 65674, [ ~(
% 17.82/18.20 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 Y, T, X ) ) ] )
% 17.82/18.20 , clause( 65675, [ ~(
% 17.82/18.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 Y, T, X ) ) ] )
% 17.82/18.20 , clause( 65676, [ ~(
% 17.82/18.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 17.82/18.20 X ), X ) ) ] )
% 17.82/18.20 , clause( 65677, [ ~(
% 17.82/18.20 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 Z, T, X ) ) ] )
% 17.82/18.20 , clause( 65678, [ ~(
% 17.82/18.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 Z, T, X ) ) ] )
% 17.82/18.20 , clause( 65679, [ ~(
% 17.82/18.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 17.82/18.20 X ), X ) ) ] )
% 17.82/18.20 , clause( 65680, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 17.82/18.20 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 17.82/18.20 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65681, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65682, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 17.82/18.20 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 17.82/18.20 , ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65683, [ =( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 17.82/18.20 , clause( 65684, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 17.82/18.20 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 17.82/18.20 , clause( 65685, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65686, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 17.82/18.20 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65687, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65688, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 17.82/18.20 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65689, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 17.82/18.20 ) ) ] )
% 17.82/18.20 , clause( 65690, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 17.82/18.20 , Y, X ), X ) ) ] )
% 17.82/18.20 , clause( 65691, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 17.82/18.20 , T, X ), X ) ) ] )
% 17.82/18.20 , clause( 65692, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 17.82/18.20 , T, X ), X ) ) ] )
% 17.82/18.20 , clause( 65693, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 17.82/18.20 , Y, X ), X ) ) ] )
% 17.82/18.20 , clause( 65694, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 17.82/18.20 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65695, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.20 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 17.82/18.20 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65696, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 17.82/18.20 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 17.82/18.20 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 17.82/18.20 , clause( 65697, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 17.82/18.20 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 17.82/18.20 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 17.82/18.20 , clause( 65698, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65699, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.20 X, 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65700, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 17.82/18.20 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 17.82/18.20 , clause( 65701, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 17.82/18.20 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65702, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 17.82/18.20 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 17.82/18.20 T, X ), X ) ) ] )
% 17.82/18.20 , clause( 65703, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 17.82/18.20 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 17.82/18.20 T, X ), Z, X ) ) ] )
% 17.82/18.20 , clause( 65704, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 17.82/18.20 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 Z, T, X ), X ) ) ] )
% 17.82/18.20 , clause( 65705, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 17.82/18.20 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 17.82/18.20 , X ), T, X ) ) ] )
% 17.82/18.20 , clause( 65706, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 17.82/18.20 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 17.82/18.20 , T, X ), X ) ) ] )
% 17.82/18.20 , clause( 65707, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 17.82/18.20 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 17.82/18.20 , X ), T, X ) ) ] )
% 17.82/18.20 , clause( 65708, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 17.82/18.20 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 17.82/18.20 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 17.82/18.20 , clause( 65709, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 17.82/18.20 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 17.82/18.20 , clause( 65710, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 17.82/18.20 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 17.82/18.20 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 17.82/18.20 , clause( 65711, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 17.82/18.20 Y, X ) ) ] )
% 17.82/18.20 , clause( 65712, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 17.82/18.20 Y, X ) ) ] )
% 17.82/18.20 , clause( 65713, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 17.82/18.20 Y, X ) ) ] )
% 17.82/18.20 , clause( 65714, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 17.82/18.20 Y, X ) ) ] )
% 17.82/18.20 , clause( 65715, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 17.82/18.20 ] )
% 17.82/18.20 , clause( 65716, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65717, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65718, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65719, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 17.82/18.20 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 17.82/18.20 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 17.82/18.20 , clause( 65720, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 17.82/18.20 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 17.82/18.20 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 17.82/18.20 , clause( 65721, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65722, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 17.82/18.20 ), Y ) ] )
% 17.82/18.20 , clause( 65723, [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 17.82/18.20 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 17.82/18.20 ] )
% 17.82/18.20 , clause( 65724, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 Z, Y, X ) ) ] )
% 17.82/18.20 , clause( 65725, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 17.82/18.20 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 17.82/18.20 )
% 17.82/18.20 , clause( 65726, [ =( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65727, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 Z, Y, X ) ) ] )
% 17.82/18.20 , clause( 65728, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.20 X, Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65729, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 17.82/18.20 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 17.82/18.20 , clause( 65730, [ ~( 'class_Orderings_Oorder'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 17.82/18.20 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 17.82/18.20 , clause( 65731, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65732, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65733, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65734, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 17.82/18.20 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65735, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65736, [ =( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 17.82/18.20 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65737, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 17.82/18.20 , T, X ) ) ), =( Y, Z ) ] )
% 17.82/18.20 , clause( 65738, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 17.82/18.20 , T, X ) ) ), =( Z, T ) ] )
% 17.82/18.20 , clause( 65739, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 17.82/18.20 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 17.82/18.20 )
% 17.82/18.20 , clause( 65740, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 17.82/18.20 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65741, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 17.82/18.20 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 17.82/18.20 , clause( 65742, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 17.82/18.20 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 17.82/18.20 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 17.82/18.20 , clause( 65743, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 17.82/18.20 ), 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65744, [ =( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65745, [ =( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 Z, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 17.82/18.20 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65746, [ =( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 X, Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 17.82/18.20 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65747, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65748, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65749, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 17.82/18.20 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 17.82/18.20 , clause( 65750, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 17.82/18.20 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65751, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 17.82/18.20 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65752, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 17.82/18.20 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 17.82/18.20 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 17.82/18.20 , clause( 65753, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 17.82/18.20 ) ), =( Y, Z ) ] )
% 17.82/18.20 , clause( 65754, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 17.82/18.20 ) ), =( Y, Z ) ] )
% 17.82/18.20 , clause( 65755, [ =( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 17.82/18.20 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65756, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 17.82/18.20 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65757, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 17.82/18.20 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 17.82/18.20 )
% 17.82/18.20 , clause( 65758, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 17.82/18.20 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65759, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 17.82/18.20 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 17.82/18.20 , clause( 65760, [ =( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.20 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 17.82/18.20 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 17.82/18.20 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65761, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ),
% 17.82/18.20 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 17.82/18.20 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65762, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65763, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 17.82/18.20 , clause( 65764, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 17.82/18.20 ~( 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X
% 17.82/18.20 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65765, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z )
% 17.82/18.20 , 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 17.82/18.20 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65766, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 17.82/18.20 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 17.82/18.20 ) ) ] )
% 17.82/18.20 , clause( 65767, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OApp'( Y, Z ), T
% 17.82/18.20 ), 'c_Lambda_OdB_OApp'( 'c_Lambda_Oliftn'( X, Y, T ), 'c_Lambda_Oliftn'(
% 17.82/18.20 X, Z, T ) ) ) ] )
% 17.82/18.20 , clause( 65768, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 17.82/18.20 , clause( 65769, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 17.82/18.20 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 17.82/18.20 X ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 17.82/18.20 , clause( 65770, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 17.82/18.20 , clause( 65771, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 17.82/18.20 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 17.82/18.20 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 17.82/18.20 , clause( 65772, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 17.82/18.20 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'(
% 17.82/18.20 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 17.82/18.20 , clause( 65773, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65774, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65775, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 17.82/18.20 , clause( 65776, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 17.82/18.20 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65777, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65778, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 17.82/18.20 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.20 X ), T, X ) ) ] )
% 17.82/18.20 , clause( 65779, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 17.82/18.20 , clause( 65780, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 17.82/18.20 , clause( 65781, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 17.82/18.20 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 17.82/18.20 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 17.82/18.20 , clause( 65782, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 17.82/18.20 , clause( 65783, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65784, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 17.82/18.20 , clause( 65785, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 17.82/18.20 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 17.82/18.20 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 17.82/18.20 , clause( 65786, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 17.82/18.20 , clause( 65787, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65788, [ ~(
% 17.82/18.20 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 17.82/18.20 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 17.82/18.20 , clause( 65789, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 17.82/18.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 17.82/18.20 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 17.82/18.20 , clause( 65790, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 17.82/18.20 ) ) ] )
% 17.82/18.20 , clause( 65791, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65792, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 17.82/18.20 ] )
% 17.82/18.20 , clause( 65793, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.20 , clause( 65794, [ =( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 17.82/18.20 , clause( 65795, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 17.82/18.20 , clause( 65796, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 17.82/18.20 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 17.82/18.20 , clause( 65797, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 17.82/18.20 ] )
% 17.82/18.20 , clause( 65798, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 17.82/18.20 ] )
% 17.82/18.20 , clause( 65799, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 17.82/18.20 ] )
% 17.82/18.20 , clause( 65800, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65801, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.20 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 17.82/18.20 ) ] )
% 17.82/18.20 , clause( 65802, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 17.82/18.20 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 17.82/18.20 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.20 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 17.82/18.20 , clause( 65803, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T
% 17.82/18.21 ), 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ),
% 17.82/18.21 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ] )
% 17.82/18.21 , clause( 65804, [ =( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ) ] )
% 17.82/18.21 , clause( 65805, [ =( 'c_HOL_Ominus__class_Ominus'(
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 17.82/18.21 , clause( 65806, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 17.82/18.21 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 17.82/18.21 ), Y ) ] )
% 17.82/18.21 , clause( 65807, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 17.82/18.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 17.82/18.21 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 17.82/18.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 17.82/18.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 17.82/18.21 , clause( 65808, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 17.82/18.21 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65809, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 17.82/18.21 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65810, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 17.82/18.21 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65811, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.21 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 17.82/18.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 17.82/18.21 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65812, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 17.82/18.21 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 17.82/18.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 17.82/18.21 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65813, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 17.82/18.21 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 17.82/18.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 17.82/18.21 , clause( 65814, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 17.82/18.21 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 17.82/18.21 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 17.82/18.21 , clause( 65815, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OVar'(
% 17.82/18.21 Z ) ) ) ] )
% 17.82/18.21 , clause( 65816, [ =( X, 'c_Lambda_OdB_OAbs'(
% 17.82/18.21 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'( Y, X ) ) ), ~(
% 17.82/18.21 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( Y ), X ) ) ] )
% 17.82/18.21 , clause( 65817, [ =( 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Y ), 'c_Suc'(
% 17.82/18.21 Z ) ), 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Z ), Y ) ), ~(
% 17.82/18.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65818, [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 17.82/18.21 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( T,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), 'c_Lambda_Olift'( Y,
% 17.82/18.21 T ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.21 T, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65819, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 17.82/18.21 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 17.82/18.21 ) ) ] )
% 17.82/18.21 , clause( 65820, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ),
% 17.82/18.21 'c_Lambda_OdB_OApp'( Z, Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ] )
% 17.82/18.21 , clause( 65821, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ),
% 17.82/18.21 'c_Lambda_OdB_OApp'( X, Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ] )
% 17.82/18.21 , clause( 65822, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.21 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 17.82/18.21 X ), X ) ) ] )
% 17.82/18.21 , clause( 65823, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X,
% 17.82/18.21 'c_Lambda_Olift'( Y, Z ), 'c_Suc'( T ) ), 'c_Lambda_Osubst'( U, Y, T ), Z
% 17.82/18.21 ), 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X, U, Z ), Y, T ) ), ~(
% 17.82/18.21 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oplus__class_Oplus'( T,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65824, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 17.82/18.21 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y,
% 17.82/18.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oplus__class_Oplus'( Z,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ] )
% 17.82/18.21 , clause( 65825, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 17.82/18.21 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.21 T, Z, X ) ) ), =( Y, T ) ] )
% 17.82/18.21 , clause( 65826, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 17.82/18.21 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.21 Y, T, X ) ) ), =( Z, T ) ] )
% 17.82/18.21 , clause( 65827, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 17.82/18.21 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 17.82/18.21 , clause( 65828, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 17.82/18.21 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 17.82/18.21 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 17.82/18.21 , clause( 65829, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 17.82/18.21 , clause( 65830, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 17.82/18.21 , clause( 65831, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 17.82/18.21 , clause( 65832, [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 17.82/18.21 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, T ), 'c_Lambda_Olift'( Y, T ),
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 17.82/18.21 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 17.82/18.21 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65833, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 17.82/18.21 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 17.82/18.21 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 17.82/18.21 , clause( 65834, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 17.82/18.21 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ] )
% 17.82/18.21 , clause( 65835, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 17.82/18.21 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( X,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ),
% 17.82/18.21 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65836, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 17.82/18.21 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 17.82/18.21 , clause( 65837, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.21 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 17.82/18.21 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 17.82/18.21 , X ) ) ] )
% 17.82/18.21 , clause( 65838, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.21 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 17.82/18.21 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 17.82/18.21 , X ) ) ] )
% 17.82/18.21 , clause( 65839, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.21 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 17.82/18.21 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 17.82/18.21 , X ) ) ] )
% 17.82/18.21 , clause( 65840, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.21 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 17.82/18.21 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 17.82/18.21 , X ) ) ] )
% 17.82/18.21 , clause( 65841, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 17.82/18.21 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 17.82/18.21 ) ) ] )
% 17.82/18.21 , clause( 65842, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 17.82/18.21 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 17.82/18.21 ) ) ] )
% 17.82/18.21 , clause( 65843, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 17.82/18.21 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 17.82/18.21 ) ) ] )
% 17.82/18.21 , clause( 65844, [ =( 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat'
% 17.82/18.21 ), 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65845, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 17.82/18.21 ), 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65846, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 17.82/18.21 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 17.82/18.21 ) ) ] )
% 17.82/18.21 , clause( 65847, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.21 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 17.82/18.21 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 17.82/18.21 , X ) ) ] )
% 17.82/18.21 , clause( 65848, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 17.82/18.21 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 17.82/18.21 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65849, [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ),
% 17.82/18.21 'c_Lambda_Osubst'( T, Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ] )
% 17.82/18.21 , clause( 65850, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65851, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65852, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OAbs'( X ), Y, Z )
% 17.82/18.21 , 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubstn'( X, Y,
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 17.82/18.21 'tc_nat' ) ) ) ) ] )
% 17.82/18.21 , clause( 65853, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.21 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 17.82/18.21 Y, X ) ) ] )
% 17.82/18.21 , clause( 65854, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 17.82/18.21 X ) ) ] )
% 17.82/18.21 , clause( 65855, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65856, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.21 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 17.82/18.21 Y, X ) ) ] )
% 17.82/18.21 , clause( 65857, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.21 =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 17.82/18.21 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 17.82/18.21 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 17.82/18.21 , clause( 65858, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OApp'( Y,
% 17.82/18.21 Z ) ) ) ] )
% 17.82/18.21 , clause( 65859, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.21 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 17.82/18.21 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ] )
% 17.82/18.21 , clause( 65860, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 17.82/18.21 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 17.82/18.21 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 17.82/18.21 , clause( 65861, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'(
% 17.82/18.21 'c_Lambda_OdB_OAbs'( X ), Y ), 'c_Lambda_Osubst'( X, Y,
% 17.82/18.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 17.82/18.21 , clause( 65862, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ),
% 17.82/18.21 'c_Lambda_OdB_OAbs'( 'c_Lambda_Oliftn'( X, Y, 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.21 Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ] )
% 17.82/18.21 , clause( 65863, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'(
% 17.82/18.21 Z, T ) ) ), =( Y, T ) ] )
% 17.82/18.21 , clause( 65864, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'(
% 17.82/18.21 Z, T ) ) ), =( X, Z ) ] )
% 17.82/18.21 , clause( 65865, [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ]
% 17.82/18.21 )
% 17.82/18.21 , clause( 65866, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 17.82/18.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 17.82/18.21 , clause( 65867, [ 'c_Lambda_Obeta'( X,
% 17.82/18.21 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'( X, Y ) ), ~(
% 17.82/18.21 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), Y ) ) ] )
% 17.82/18.21 , clause( 65868, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 17.82/18.21 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 17.82/18.21 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65869, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 17.82/18.21 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 17.82/18.21 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 17.82/18.21 , clause( 65870, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 17.82/18.21 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 17.82/18.21 ) ) ] )
% 17.82/18.21 , clause( 65871, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ),
% 17.82/18.21 Y ) ] )
% 17.82/18.21 , clause( 65872, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y )
% 17.82/18.21 ) ), =( X, Y ) ] )
% 17.82/18.21 , clause( 65873, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T
% 17.82/18.21 ), 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubst'( X, Z, T ), 'c_Lambda_Osubst'(
% 17.82/18.21 Y, Z, T ) ) ) ] )
% 17.82/18.21 , clause( 65874, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 17.82/18.21 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 17.82/18.21 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 17.82/18.21 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 17.82/18.21 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 17.82/18.21 , clause( 65875, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 17.82/18.21 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ] )
% 17.82/18.21 , clause( 65876, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y )
% 17.82/18.21 ) ) ] )
% 17.82/18.21 , clause( 65877, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OAbs'(
% 17.82/18.21 Z ) ) ) ] )
% 17.82/18.21 , clause( 65878, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OApp'( Y,
% 17.82/18.21 Z ) ) ) ] )
% 17.82/18.21 , clause( 65879, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 17.82/18.21 ) ), =( X, Y ) ] )
% 17.82/18.21 , clause( 65880, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 17.82/18.21 ) ) ] )
% 17.82/18.21 , clause( 65881, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OApp'( X, Y ), Z ),
% 17.82/18.21 'c_Lambda_OdB_OApp'( 'c_Lambda_Olift'( X, Z ), 'c_Lambda_Olift'( Y, Z ) )
% 17.82/18.21 ) ] )
% 17.82/18.21 , clause( 65882, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 17.82/18.21 'c_InductTermi_OIT'( X ) ) ] )
% 17.82/18.21 , clause( 65883, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ),
% 17.82/18.21 X ) ] )
% 17.82/18.21 , clause( 65884, [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ),
% 17.82/18.21 'c_Lambda_Olift'( Z, Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ] )
% 17.82/18.21 , clause( 65885, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ),
% 17.82/18.21 'c_Lambda_OdB_OAbs'( Y ) ), ~( 'c_Lambda_Obeta'( X, Y ) ) ] )
% 17.82/18.21 , clause( 65886, [ 'c_InductTermi_OIT'( 'v_r' ) ] )
% 17.82/18.21 , clause( 65887, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'v_r', X ) ) ] )
% 17.82/18.21 , clause( 65888, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 17.82/18.21 'c_Lambda_OdB_OAbs'( 'v_r' ), 'v_ia' ) ) ) ] )
% 17.82/18.21 , clause( 65889, [
% 17.82/18.21 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 17.82/18.21 )
% 17.82/18.21 , clause( 65890, [
% 17.82/18.21 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 17.82/18.21 )
% 17.82/18.21 , clause( 65891, [
% 17.82/18.21 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' ) ]
% 17.82/18.21 )
% 17.82/18.21 , clause( 65892, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 17.82/18.21 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65893, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 17.82/18.21 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65894, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 17.82/18.21 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65895, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 17.82/18.21 ] )
% 17.82/18.21 , clause( 65896, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 17.82/18.21 ] )
% 17.82/18.21 , clause( 65897, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 17.82/18.21 )
% 17.82/18.21 , clause( 65898, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 17.82/18.21 ] )
% 17.82/18.21 , clause( 65899, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 17.82/18.21 )
% 17.82/18.21 , clause( 65900, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ]
% 17.82/18.21 )
% 17.82/18.21 , clause( 65901, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 17.82/18.21 )
% 17.82/18.21 , clause( 65902, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ]
% 17.82/18.21 )
% 17.82/18.21 , clause( 65903, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65904, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ]
% 17.82/18.21 )
% 17.82/18.21 , clause( 65905, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65906, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65907, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65908, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65909, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65910, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65911, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65912, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 17.82/18.21 , clause( 65913, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 17.82/18.21 ] ).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 eqswap(
% 17.82/18.21 clause( 66281, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oone__class_Oone'(
% 17.82/18.21 'tc_nat' ), 'tc_nat' ), 'c_Suc'( X ) ) ] )
% 17.82/18.21 , clause( 65850, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 17.82/18.21 , 0, substitution( 0, [ :=( X, X )] )).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 subsumption(
% 17.82/18.21 clause( 249, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oone__class_Oone'(
% 17.82/18.21 'tc_nat' ), 'tc_nat' ), 'c_Suc'( X ) ) ] )
% 17.82/18.21 , clause( 66281, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'( X ) ) ] )
% 17.82/18.21 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 paramod(
% 17.82/18.21 clause( 67056, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 17.82/18.21 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_Suc'( Y ) ) ) ) ] )
% 17.82/18.21 , clause( 249, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oone__class_Oone'(
% 17.82/18.21 'tc_nat' ), 'tc_nat' ), 'c_Suc'( X ) ) ] )
% 17.82/18.21 , 0, clause( 65875, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 17.82/18.21 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 17.82/18.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ] )
% 17.82/18.21 , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 17.82/18.21 :=( Y, Y )] )).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 eqswap(
% 17.82/18.21 clause( 67057, [ =( 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_Suc'( Y )
% 17.82/18.21 ) ), 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ) ) ] )
% 17.82/18.21 , clause( 67056, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 17.82/18.21 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_Suc'( Y ) ) ) ) ] )
% 17.82/18.21 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 subsumption(
% 17.82/18.21 clause( 270, [ =( 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_Suc'( Y ) )
% 17.82/18.21 ), 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ) ) ] )
% 17.82/18.21 , clause( 67057, [ =( 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_Suc'( Y
% 17.82/18.21 ) ) ), 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ) ) ] )
% 17.82/18.21 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 17.82/18.21 )] ) ).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 subsumption(
% 17.82/18.21 clause( 275, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 17.82/18.21 'c_InductTermi_OIT'( X ) ) ] )
% 17.82/18.21 , clause( 65882, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 17.82/18.21 'c_InductTermi_OIT'( X ) ) ] )
% 17.82/18.21 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 17.82/18.21 1 )] ) ).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 subsumption(
% 17.82/18.21 clause( 280, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'v_r', X ) ) ] )
% 17.82/18.21 , clause( 65887, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'v_r', X ) ) ] )
% 17.82/18.21 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 subsumption(
% 17.82/18.21 clause( 281, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 17.82/18.21 'c_Lambda_OdB_OAbs'( 'v_r' ), 'v_ia' ) ) ) ] )
% 17.82/18.21 , clause( 65888, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 17.82/18.21 'c_Lambda_OdB_OAbs'( 'v_r' ), 'v_ia' ) ) ) ] )
% 17.82/18.21 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 resolution(
% 17.82/18.21 clause( 68233, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'(
% 17.82/18.21 'v_r', X ) ) ) ] )
% 17.82/18.21 , clause( 275, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 17.82/18.21 'c_InductTermi_OIT'( X ) ) ] )
% 17.82/18.21 , 1, clause( 280, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'v_r', X ) ) ]
% 17.82/18.21 )
% 17.82/18.21 , 0, substitution( 0, [ :=( X, 'c_Lambda_Olift'( 'v_r', X ) )] ),
% 17.82/18.21 substitution( 1, [ :=( X, X )] )).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 subsumption(
% 17.82/18.21 clause( 647, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'(
% 17.82/18.21 'v_r', X ) ) ) ] )
% 17.82/18.21 , clause( 68233, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'(
% 17.82/18.21 'c_Lambda_Olift'( 'v_r', X ) ) ) ] )
% 17.82/18.21 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 paramod(
% 17.82/18.21 clause( 68235, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'(
% 17.82/18.21 'v_r' ), X ) ) ] )
% 17.82/18.21 , clause( 270, [ =( 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_Suc'( Y )
% 17.82/18.21 ) ), 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ) ) ] )
% 17.82/18.21 , 0, clause( 647, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'(
% 17.82/18.21 'c_Lambda_Olift'( 'v_r', X ) ) ) ] )
% 17.82/18.21 , 0, 1, substitution( 0, [ :=( X, 'v_r' ), :=( Y, X )] ), substitution( 1
% 17.82/18.21 , [ :=( X, 'c_Suc'( X ) )] )).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 subsumption(
% 17.82/18.21 clause( 65539, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'(
% 17.82/18.21 'v_r' ), X ) ) ] )
% 17.82/18.21 , clause( 68235, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 17.82/18.21 'c_Lambda_OdB_OAbs'( 'v_r' ), X ) ) ] )
% 17.82/18.21 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 resolution(
% 17.82/18.21 clause( 68236, [] )
% 17.82/18.21 , clause( 281, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 17.82/18.21 'c_Lambda_OdB_OAbs'( 'v_r' ), 'v_ia' ) ) ) ] )
% 17.82/18.21 , 0, clause( 65539, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 17.82/18.21 'c_Lambda_OdB_OAbs'( 'v_r' ), X ) ) ] )
% 17.82/18.21 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_ia' )] )).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 subsumption(
% 17.82/18.21 clause( 65542, [] )
% 17.82/18.21 , clause( 68236, [] )
% 17.82/18.21 , substitution( 0, [] ), permutation( 0, [] ) ).
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 end.
% 17.82/18.21
% 17.82/18.21 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 17.82/18.21
% 17.82/18.21 Memory use:
% 17.82/18.21
% 17.82/18.21 space for terms: 1540124
% 17.82/18.21 space for clauses: 2968838
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 clauses generated: 472497
% 17.82/18.21 clauses kept: 65543
% 17.82/18.21 clauses selected: 1094
% 17.82/18.21 clauses deleted: 3129
% 17.82/18.21 clauses inuse deleted: 47
% 17.82/18.21
% 17.82/18.21 subsentry: 1939756
% 17.82/18.21 literals s-matched: 1098484
% 17.82/18.21 literals matched: 1033917
% 17.82/18.21 full subsumption: 541084
% 17.82/18.21
% 17.82/18.21 checksum: -1105681408
% 17.82/18.21
% 17.82/18.21
% 17.82/18.21 Bliksem ended
%------------------------------------------------------------------------------