TSTP Solution File: LCL760-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL760-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.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 07:57:38 EDT 2022
% Result : Unsatisfiable 0.91s 1.32s
% Output : Refutation 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL760-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Sat Jul 2 16:00:53 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.91/1.31 *** allocated 10000 integers for termspace/termends
% 0.91/1.31 *** allocated 10000 integers for clauses
% 0.91/1.31 *** allocated 10000 integers for justifications
% 0.91/1.31 *** allocated 15000 integers for termspace/termends
% 0.91/1.31 Bliksem 1.12
% 0.91/1.31
% 0.91/1.31
% 0.91/1.31 Automatic Strategy Selection
% 0.91/1.31
% 0.91/1.31 Clauses:
% 0.91/1.31 [
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 0.91/1.31 ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.91/1.31 ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.31 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.31 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), T
% 0.91/1.31 , X ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.91/1.31 X ), Z, X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 0.91/1.31 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 0.91/1.31 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.91/1.31 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.91/1.31 X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.91/1.31 'c_Lambda_Olift', X ), T ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), T ) ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.91/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.91/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.31 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ), U ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ), U ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.31 Y, 'tc_nat' ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.91/1.31 ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), T ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.31 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.91/1.31 , Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.91/1.31 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.31 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ) ), =( Y, Z ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.91/1.31 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 0.91/1.31 , X ) ), T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 0.91/1.31 ), Z ), T, X ) ) ],
% 0.91/1.31 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.91/1.31 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.91/1.31 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X ) ), Y ),
% 0.91/1.31 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Z ), T ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.31 Y, T, X ), X ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), T ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), T ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.91/1.31 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 0.91/1.31 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 0.91/1.31 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.31 , Y, X ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.31 , Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.31 ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.31 ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.31 'c_Suc'( Z ), X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.31 Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 0.91/1.31 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Z, T, 'tc_nat' ), X ) ) ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.91/1.31 'tc_nat' ), X, 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ), X, 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.31 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Y, T, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Y, Z, X ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.31 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Y, T, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Y, Z, X ) ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OAbs'( T ), U ),
% 0.91/1.31 hAPP( Z, T ) ) ],
% 0.91/1.31 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.91/1.31 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 0.91/1.31 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.91/1.31 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.31 Z, 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.91/1.31 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.31 , Y, X ), X ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.31 , Z, X ), X ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.31 , Z, X ), X ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.91/1.31 ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.91/1.31 ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.91/1.31 ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.91/1.31 ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.91/1.31 ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 0.91/1.31 , X, 'tc_nat' ), X ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.91/1.31 ), 'tc_nat' ), X ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.91/1.31 ],
% 0.91/1.31 [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.31 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.31 'tc_nat' ), X, 'tc_nat' ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.31 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.31 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 0.91/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 0.91/1.31 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.91/1.31 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 0.91/1.31 , X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), 'c_Divides_Odiv__class_Odiv'(
% 0.91/1.31 Z, T, X ) ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y
% 0.91/1.31 , X ), X ) ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ), T ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X
% 0.91/1.31 ), Z, X ) ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.91/1.31 , T, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.91/1.31 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.91/1.31 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.91/1.31 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 X, Y, 'tc_nat' ) ), X, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 0.91/1.31 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.91/1.31 ), 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 0.91/1.31 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubstn'( X, Y, hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.91/1.31 'tc_nat' ) ) ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 X, T, 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.91/1.31 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.31 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.91/1.31 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OAbs'( X ) ), Y
% 0.91/1.31 ), Z ), 'c_Lambda_OdB_OAbs'( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ),
% 0.91/1.31 hAPP( hAPP( 'c_Lambda_Olift', Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.91/1.31 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.91/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 0.91/1.31 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP(
% 0.91/1.31 'c_Lambda_Osubst', X ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ), 'c_Suc'(
% 0.91/1.31 T ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', U ), Y ), T ) ), Z ), hAPP(
% 0.91/1.31 hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ),
% 0.91/1.31 U ), Z ) ), Y ), T ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 0.91/1.31 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.31 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.31 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 0.91/1.31 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 0.91/1.31 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.91/1.31 , Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.91/1.31 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.91/1.31 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Z,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.91/1.31 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.91/1.31 [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OAbs'( X ),
% 0.91/1.31 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ), 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.91/1.31 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.91/1.31 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.91/1.31 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.91/1.31 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 0.91/1.31 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 0.91/1.31 , X ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 0.91/1.31 , X ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X ) ), Y ),
% 0.91/1.31 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_Olift', X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_Lambda_Olift', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.91/1.31 X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.91/1.31 'c_Lambda_Olift', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , T ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( hAPP(
% 0.91/1.31 'c_Lambda_Olift', Y ), T ) ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ),
% 0.91/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 0.91/1.31 ) ), 'c_Suc'( Z ) ), hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP(
% 0.91/1.31 'c_Lambda_Olift', X ), Z ) ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.91/1.31 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 0.91/1.31 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.91/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.31 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.91/1.31 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.31 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.31 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 X ), T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 0.91/1.31 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, X, 'tc_nat'
% 0.91/1.31 ), 'c_Power_Opower__class_Opower'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 0.91/1.31 X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'( X, hAPP( hAPP(
% 0.91/1.31 hAPP( 'c_Lambda_Osubst', U ), Y ), T ), W ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.91/1.31 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 Y, 'tc_nat' ) ), Z ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), T, X ),
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), Z, X ),
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.31 ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), T ), Z, X ) ) ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( 'c_Divides_Odiv__class_Odiv'( Y
% 0.91/1.31 , X, 'tc_nat' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 0.91/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 0.91/1.31 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.91/1.31 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.91/1.31 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 0.91/1.31 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 0.91/1.31 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), X ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.91/1.31 , 'tc_nat' ), 'tc_nat' ) ],
% 0.91/1.31 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.91/1.31 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.91/1.31 ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ) ), X ), Y,
% 0.91/1.31 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.91/1.31 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 0.91/1.31 , 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.91/1.31 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.91/1.31 , 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.91/1.31 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.91/1.31 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.91/1.31 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 0.91/1.31 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.31 , X ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.91/1.31 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.31 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.31 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.31 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.91/1.31 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.31 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.91/1.31 , T, X ), X ), T, X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.31 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 0.91/1.31 Y, Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Z ), T ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), Z, X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), T ), 'c_Divides_Odiv__class_Odiv'( Y, Z
% 0.91/1.31 , X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), T, X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), 'c_Divides_Odiv__class_Odiv'( Y, T
% 0.91/1.31 , X ) ) ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X
% 0.91/1.31 ) ), 'c_HOL_Oone__class_Oone'( X ) ), Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.91/1.31 X ), Y ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.91/1.31 X ), Y ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.91/1.31 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.31 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ) ), X ), Y,
% 0.91/1.31 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.91/1.31 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.31 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.91/1.31 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ],
% 0.91/1.31 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.91/1.31 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.91/1.31 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.31 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 Y, 'tc_nat' ) ), Z ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.91/1.31 'c_Suc'( Z ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.31 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 T, U, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, U, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.31 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 T, U, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, U, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 0.91/1.31 =( Y, T ), =( X, Z ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 0.91/1.31 =( Y, T ), =( X, Z ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.91/1.31 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.91/1.31 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.91/1.31 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 0.91/1.31 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 0.91/1.31 X ), Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.31 ), Z ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), Z
% 0.91/1.31 , X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Otimes__class_Otimes'( Z, Y
% 0.91/1.31 , X ) ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 0.91/1.31 , X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.91/1.31 , X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.31 , Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.31 , Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.31 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.91/1.31 , Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.91/1.31 ), =( Z, Y ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.91/1.31 ) ],
% 0.91/1.31 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.91/1.31 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.91/1.31 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 0.91/1.31 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.91/1.31 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.91/1.31 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 0.91/1.31 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 0.91/1.31 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.91/1.31 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 0.91/1.31 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 T, X ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 0.91/1.31 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 0.91/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 0.91/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 0.91/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.31 'tc_nat' ), 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.31 'tc_nat' ), Z, 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Odiv'(
% 0.91/1.31 Y, Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 0.91/1.31 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' ) ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.91/1.31 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.91/1.31 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 0.91/1.31 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.91/1.31 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 0.91/1.31 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.91/1.31 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.91/1.31 , Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.31 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 0.91/1.31 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.31 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( T, U, X ), X ),
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Y, U, 'tc_nat' ) ) ) ), =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' )
% 0.91/1.31 , 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.31 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 0.91/1.31 X ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.31 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.91/1.31 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.91/1.31 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.91/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.91/1.31 , X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.91/1.31 Y ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.91/1.31 Y ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.31 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.91/1.31 Y ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.91/1.31 Y ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.91/1.31 Y ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.91/1.31 Y ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.91/1.31 Y ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.91/1.31 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 'tc_nat' ) ) ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 0.91/1.31 , Y ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.31 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.91/1.31 'v_sko__List__Xlexn__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 0.91/1.31 hAPP( X, 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1'( X ) ) ) ), ~(
% 0.91/1.31 hBOOL( hAPP( X, Y ) ) ) ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 0.91/1.31 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 0.91/1.31 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ), 'tc_nat' ) ) ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 0.91/1.31 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.91/1.31 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1'( X ) ) ), ~( hBOOL( hAPP( X
% 0.91/1.31 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.31 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.91/1.31 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 0.91/1.31 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.91/1.31 'v_sko__List__Xreplicate__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__Nat__Xnat__Xinducts__1'(
% 0.91/1.31 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 0.91/1.31 ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__Nat__Xnat__Xinduct__1'(
% 0.91/1.31 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 0.91/1.31 ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.31 ), 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.31 ), 'tc_nat' ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__List__Xupt__Xinduct__1'(
% 0.91/1.31 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 0.91/1.31 ],
% 0.91/1.31 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.31 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.31 ) ), X, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.91/1.31 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.31 ) ), X, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.91/1.31 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 0.91/1.31 ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 0.91/1.31 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.31 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.91/1.31 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.91/1.31 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.91/1.31 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.91/1.31 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.91/1.31 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.31 Y ) ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 0.91/1.31 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 0.91/1.31 ) ) ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.91/1.31 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 0.91/1.31 Y ) ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.91/1.31 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 0.91/1.31 Z ) ) ) ],
% 0.91/1.31 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.91/1.31 Z ) ) ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP( hAPP(
% 0.91/1.31 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.91/1.31 Z, U ), W ) ) ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP( hAPP(
% 0.91/1.31 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.91/1.31 Z, U ), W ) ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.91/1.31 , Y ) ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.91/1.31 'c_Lambda_Olift', X ), Z ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ) )
% 0.91/1.31 ],
% 0.91/1.31 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, hAPP( hAPP( 'c_Lambda_OdB_OApp'
% 0.91/1.31 , T ), U ), W ), hAPP( hAPP( Y, T ), U ) ) ],
% 0.91/1.31 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.91/1.31 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.91/1.31 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 0.91/1.31 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X, Z, T ) ),
% 0.91/1.31 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ],
% 0.91/1.31 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) ) ), =( Y
% 0.91/1.31 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.91/1.31 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X ) ) ), =( Z
% 0.91/1.31 , 'c_List_Olist_ONil'( T ) ) ],
% 0.91/1.31 [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 0.91/1.31 'c_List_Olist_ONil'( Z ) ) ],
% 0.91/1.31 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, 'c_List_Olist_ONil'( Z
% 0.91/1.31 ), Z, X ) ) ],
% 0.91/1.31 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.31 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.91/1.31 'tc_Lambda_OdB' ) ) ],
% 0.91/1.31 [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.31 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.91/1.31 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.91/1.31 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.91/1.31 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.91/1.31 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.91/1.31 [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.91/1.31 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.91/1.31 ), 'c_Lambda_OdB_OAbs'( X ) ) ],
% 0.91/1.31 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), Y ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_Lambda_Obeta'( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ), Z ),
% 0.91/1.31 hAPP( hAPP( hAPP( 'c_Lambda_Osubst', T ), Y ), Z ) ), ~( 'c_Lambda_Obeta'(
% 0.91/1.31 X, T ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( 'c_Lambda_Olift',
% 0.91/1.31 X ), Y ) ), Z ), Y ), X ) ],
% 0.91/1.31 [ 'c_Type_Otypings'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ),
% 0.91/1.31 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Y, 'tc_Lambda_OdB', 'tc_nat'
% 0.91/1.31 , 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 0.91/1.31 'c_Type_Otypings'( X, T, U ) ) ],
% 0.91/1.31 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.91/1.31 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.91/1.31 ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.91/1.31 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.91/1.31 ],
% 0.91/1.31 [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ],
% 0.91/1.31 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.91/1.31 [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y )
% 0.91/1.31 , Z ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.31 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 0.91/1.31 ), Y, X ) ), =( Z, T ) ],
% 0.91/1.31 [ =( 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.91/1.31 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 X ) ) ],
% 0.91/1.31 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.31 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.31 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.31 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.31 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.91/1.32 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.91/1.32 , X ), Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.91/1.32 , X ), Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.32 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.32 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.91/1.32 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.91/1.32 Z, 'c_Suc'( T ), 'tc_nat' ), 'tc_nat', X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.32 ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.32 , 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'(
% 0.91/1.32 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' )
% 0.91/1.32 ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ) ],
% 0.91/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 0.91/1.32 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 0.91/1.32 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.91/1.32 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.91/1.32 ],
% 0.91/1.32 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.91/1.32 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.91/1.32 ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.32 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.32 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.91/1.32 X ), T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.32 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.32 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.91/1.32 X ), T, X ) ) ],
% 0.91/1.32 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.32 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.91/1.32 , Y, X ) ) ],
% 0.91/1.32 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.32 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 0.91/1.32 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'(
% 0.91/1.32 Y, Z, 'tc_nat' ), 'tc_nat' ) ), T ), 'c_HOL_Otimes__class_Otimes'( X, Z,
% 0.91/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) )
% 0.91/1.32 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z
% 0.91/1.32 , 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.32 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Otimes__class_Otimes'( Z, U
% 0.91/1.32 , X ) ) ) ), =( T, U ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 Y, T, 'tc_nat' ) ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 0.91/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.91/1.32 , X ) ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 0.91/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.91/1.32 , X ) ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 0.91/1.32 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.32 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 0.91/1.32 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.32 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 0.91/1.32 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.32 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.91/1.32 ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.32 , Z ), Y ), 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.32 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 0.91/1.32 ],
% 0.91/1.32 [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Lambda_Obeta'( T, Y ) ), ~(
% 0.91/1.32 'c_Type_Otyping'( X, T, Z ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.91/1.32 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.91/1.32 Z, 'c_Suc'( T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 0.91/1.32 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 0.91/1.32 , X ) ), hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, X
% 0.91/1.32 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 0.91/1.32 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.91/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.91/1.32 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.91/1.32 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.32 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 0.91/1.32 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 0.91/1.32 ), 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X )
% 0.91/1.32 , Z, X ) ), Y ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 0.91/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.91/1.32 ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.32 , Y, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.32 , T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.32 , T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.32 , Y, X ), X ) ) ],
% 0.91/1.32 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.32 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), 'c_Power_Opower__class_Opower'( Y, X, 'tc_nat' ), 'tc_nat' )
% 0.91/1.32 ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.32 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.91/1.32 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.91/1.32 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.32 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.32 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), T ), Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), Z ), T, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.91/1.32 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.91/1.32 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 0.91/1.32 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_Suc'( Z ), T, 'tc_nat' )
% 0.91/1.32 , 'tc_nat', X ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.32 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.91/1.32 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.32 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.32 'c_Divides_Odiv__class_Odiv'( Z, Y, X ), X ) ),
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 0.91/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ) ),
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 0.91/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ) ),
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 0.91/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OAbs'( X ) ), Y ),
% 0.91/1.32 'c_Lambda_OdB_OAbs'( hAPP( hAPP( 'c_Lambda_Olift', X ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.91/1.32 'tc_nat' ) ) ) ) ) ],
% 0.91/1.32 [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OAbs'( X ) ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Lambda_OdB_OdB__size'( X ) ),
% 0.91/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.91/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.91/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.32 T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.91/1.32 X ), Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.32 T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.91/1.32 X ), T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.32 T, X ), X ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.32 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.91/1.32 X ), T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 Z, T, X ) ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 Z, T, X ) ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.91/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( X, hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.32 Y, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 X ), Z ), T ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 Y, T, X ) ) ) ],
% 0.91/1.32 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ), hAPP(
% 0.91/1.32 hAPP( 'c_Lambda_Olift', T ), Y ), U ), ~( 'c_Type_Otyping'( X, T, U ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.32 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.32 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.32 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.32 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.32 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.32 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OVar'( T ), U ),
% 0.91/1.32 hAPP( X, T ) ) ],
% 0.91/1.32 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 0.91/1.32 ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X ) ) ), ~(
% 0.91/1.32 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ) ), =( 'c_Finite__Set_Osetsum'( Y,
% 0.91/1.32 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 0.91/1.32 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ =( 'c_Lambda_OdB_OdB__size'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y )
% 0.91/1.32 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Lambda_OdB_OdB__size'( X ) ),
% 0.91/1.32 'c_Lambda_OdB_OdB__size'( Y ) ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ =( 'c_Nat_Osize__class_Osize'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y
% 0.91/1.32 ), 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.32 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.32 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ),
% 0.91/1.32 'c_Nat_Osize__class_Osize'( Y, 'tc_Lambda_OdB' ) ) ), 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.91/1.32 X ) ), Y ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ),
% 0.91/1.32 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( 'c_Lambda_Obeta'(
% 0.91/1.32 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), Z,
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.91/1.32 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.91/1.32 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.91/1.32 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.91/1.32 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.91/1.32 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.91/1.32 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.91/1.32 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.91/1.32 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.32 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.91/1.32 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1'( X ) )
% 0.91/1.32 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL(
% 0.91/1.32 hAPP( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1'( X ) ) )
% 0.91/1.32 ), ~( hBOOL( hAPP( X, Y ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.32 'v_sko__List__Xlexn__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 0.91/1.32 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.91/1.32 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.91/1.32 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 0.91/1.32 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 0.91/1.32 'c_Suc'( Y ), Z, T ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.32 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1'( X ) ) ) ) ), ~( hBOOL(
% 0.91/1.32 hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.32 'v_sko__List__Xreplicate__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.32 'v_sko__List__Xupt__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1'( X ) )
% 0.91/1.32 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.91/1.32 ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.32 'v_sko__Nat__Xnat__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.32 'v_sko__Nat__Xnat__Xinducts__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1'( X
% 0.91/1.32 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 0.91/1.32 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.32 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.32 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.32 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 0.91/1.32 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ) ) ],
% 0.91/1.32 [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ) ) ],
% 0.91/1.32 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.91/1.32 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.91/1.32 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OVar'( X ),
% 0.91/1.32 'tc_Lambda_OdB' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OVar'( X ) ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.91/1.32 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_Lambda_OdB_OApp', X ), Y ), Z ) ],
% 0.91/1.32 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.91/1.32 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 0.91/1.32 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.91/1.32 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.91/1.32 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.91/1.32 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.91/1.32 [ 'c_Lambda_Obeta'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.91/1.32 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( 'c_Lambda_Obeta'( X, Z )
% 0.91/1.32 ) ],
% 0.91/1.32 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.32 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 0.91/1.32 , Y ) ],
% 0.91/1.32 [ 'c_Type_Otypings'( X, 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.91/1.32 'c_Lambda_Osubst', Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.91/1.32 'tc_nat', 'tc_Lambda_OdB' ) ), Z, 'tc_Lambda_OdB', 'tc_nat',
% 0.91/1.32 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 0.91/1.32 'c_Type_Otypings'( 'c_Type_Oshift'( X, Z, W, 'tc_Type_Otype' ), T, U ) )
% 0.91/1.32 , ~( 'c_Type_Otyping'( X, Y, W ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.91/1.32 ), Z ), 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.91/1.32 ), Z ), 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 Z, X, 'tc_nat' ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( hAPP( hAPP( hAPP(
% 0.91/1.32 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y ) ],
% 0.91/1.32 [ 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'( 'c_COMBC'(
% 0.91/1.32 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_Lambda_OdB'
% 0.91/1.32 , 'tc_nat', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.91/1.32 'tc_Lambda_OdB' ), ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', X,
% 0.91/1.32 'tc_Lambda_OdB' ) ) ],
% 0.91/1.32 [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ), X ) ) ],
% 0.91/1.32 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.91/1.32 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ) ) ) ],
% 0.91/1.32 [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.32 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.91/1.32 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.32 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.91/1.32 'tc_Lambda_OdB' ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y )
% 0.91/1.32 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.91/1.32 , 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ),
% 0.91/1.32 ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y, 'tc_Lambda_OdB' ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.91/1.32 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.91/1.32 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.91/1.32 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.91/1.32 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB'
% 0.91/1.32 , 'tc_Lambda_OdB' ) ) ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.91/1.32 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_Olift', X ), Z ),
% 0.91/1.32 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Z, 'tc_Lambda_OdB', 'tc_nat'
% 0.91/1.32 , 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.91/1.32 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), T ), hAPP( hAPP(
% 0.91/1.32 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Z ), T ) )
% 0.91/1.32 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', Y ), Z ), T ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.91/1.32 ) ],
% 0.91/1.32 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.91/1.32 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.91/1.32 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.91/1.32 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.91/1.32 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.91/1.32 ), X ), Y ) ],
% 0.91/1.32 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.91/1.32 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.91/1.32 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.91/1.32 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 0.91/1.32 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.32 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OVar'( X )
% 0.91/1.32 , Y ) ],
% 0.91/1.32 [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.91/1.32 Z ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.91/1.32 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.91/1.32 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), T )
% 0.91/1.32 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP(
% 0.91/1.32 'c_Lambda_Osubst', X ), Z ), T ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.91/1.32 'c_Lambda_Osubst', Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.91/1.32 'tc_nat', 'tc_Lambda_OdB' ) ), T, 'tc_Lambda_OdB', 'tc_nat',
% 0.91/1.32 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB'
% 0.91/1.32 , 'tc_Lambda_OdB' ) ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.91/1.32 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OVar'(
% 0.91/1.32 Z ) ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.91/1.32 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_ra' ), 'v_s' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_ss', 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ) ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.91/1.32 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP(
% 0.91/1.32 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( X ) ) ),
% 0.91/1.32 'c_Suc'( Y ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' ),
% 0.91/1.32 'c_Lambda_OdB_OVar'( X ) ), Y ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.91/1.32 ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.91/1.32 'c_Lambda_OdB_OVar'( X ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.91/1.32 'tc_nat', 'tc_Lambda_OdB' ) ), Y, 'tc_Lambda_OdB', 'tc_nat',
% 0.91/1.32 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_s' ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.91/1.32 , 'v_s' ), 'c_Lambda_OdB_OVar'( X ) ), Y ) ) ) ],
% 0.91/1.32 [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.91/1.32 hAPP( 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' )
% 0.91/1.32 ) ), 'c_Suc'( 'v_ja' ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' )
% 0.91/1.32 , 'c_Lambda_OdB_OVar'( 'v_ia' ) ), 'v_ja' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.91/1.32 'c_Lambda_OdB_OVar'( 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.91/1.32 'tc_nat', 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat',
% 0.91/1.32 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ],
% 0.91/1.32 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.91/1.32 'class_Orderings_Opreorder'( Y ) ) ],
% 0.91/1.32 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.91/1.32 'class_Orderings_Oorder'( Y ) ) ],
% 0.91/1.32 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.91/1.32 ],
% 0.91/1.32 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.91/1.32 ) ],
% 0.91/1.32 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.91/1.32 ],
% 0.91/1.32 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.91/1.32 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 0.91/1.32 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ =( 'c_COMBB'( X, Y, Z, T, U, W ), hAPP( X, hAPP( Y, Z ) ) ) ],
% 0.91/1.32 [ 'c_fequal'( X, X, Y ) ],
% 0.91/1.32 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 0.91/1.32 ] .
% 0.91/1.32
% 0.91/1.32
% 0.91/1.32 percentage equality = 0.351938, percentage horn = 0.871972
% 0.91/1.32 This is a problem with some equality
% 0.91/1.32
% 0.91/1.32
% 0.91/1.32
% 0.91/1.32 Options Used:
% 0.91/1.32
% 0.91/1.32 useres = 1
% 0.91/1.32 useparamod = 1
% 0.91/1.32 useeqrefl = 1
% 0.91/1.32 useeqfact = 1
% 0.91/1.32 usefactor = 1
% 0.91/1.32 usesimpsplitting = 0
% 0.91/1.32 usesimpdemod = 5
% 0.91/1.32 usesimpres = 3
% 0.91/1.32
% 0.91/1.32 resimpinuse = 1000
% 0.91/1.32 resimpclauses = 20000
% 0.91/1.32 substype = eqrewr
% 0.91/1.32 backwardsubs = 1
% 0.91/1.32 selectoldest = 5
% 0.91/1.32
% 0.91/1.32 litorderings [0] = split
% 0.91/1.32 litorderings [1] = extend the termordering, first sorting on arguments
% 0.91/1.32
% 0.91/1.32 termordering = kbo
% 0.91/1.32
% 0.91/1.32 litapriori = 0
% 0.91/1.32 termapriori = 1
% 0.91/1.32 litaposteriori = 0
% 0.91/1.32 termaposteriori = 0
% 0.91/1.32 demodaposteriori = 0
% 0.91/1.32 ordereqreflfact = 0
% 0.91/1.32
% 0.91/1.32 litselect = negord
% 0.91/1.32
% 0.91/1.32 maxweight = 15
% 0.91/1.32 maxdepth = 30000
% 0.91/1.32 maxlength = 115
% 0.91/1.32 maxnrvars = 195
% 0.91/1.32 excuselevel = 1
% 0.91/1.32 increasemaxweight = 1
% 0.91/1.32
% 0.91/1.32 maxselected = 10000000
% 0.91/1.32 maxnrclauses = 10000000
% 0.91/1.32
% 0.91/1.32 showgenerated = 0
% 0.91/1.32 showkept = 0
% 0.91/1.32 showselected = 0
% 0.91/1.32 showdeleted = 0
% 0.91/1.32 showresimp = 1
% 0.91/1.32 showstatus = 2000
% 0.91/1.32
% 0.91/1.32 prologoutput = 1
% 0.91/1.32 nrgoals = 5000000
% 0.91/1.32 totalproof = 1
% 0.91/1.32
% 0.91/1.32 Symbols occurring in the translation:
% 0.91/1.32
% 0.91/1.32 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.91/1.32 . [1, 2] (w:1, o:152, a:1, s:1, b:0),
% 0.91/1.32 ! [4, 1] (w:0, o:89, a:1, s:1, b:0),
% 0.91/1.32 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.91/1.32 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.91/1.32 'tc_nat' [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero' [40, 1] (w:1, o:94, a:1, s:1, b:0),
% 0.91/1.32 'c_HOL_Oord__class_Oless' [42, 3] (w:1, o:182, a:1, s:1, b:0),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes' [44, 3] (w:1, o:183, a:1, s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Opordered__comm__monoid__add' [46, 1] (w:1, o:96
% 0.91/1.32 , a:1, s:1, b:0),
% 0.91/1.32 'c_HOL_Oplus__class_Oplus' [47, 1] (w:1, o:98, a:1, s:1, b:0),
% 0.91/1.32 hAPP [49, 2] (w:1, o:177, a:1, s:1, b:0),
% 0.91/1.32 'class_Divides_Osemiring__div' [51, 1] (w:1, o:99, a:1, s:1, b:0),
% 0.91/1.32 'c_Divides_Odiv__class_Omod' [52, 3] (w:1, o:184, a:1, s:1, b:0),
% 0.91/1.32 'c_Ring__and__Field_Odvd__class_Odvd' [53, 3] (w:1, o:185, a:1, s:1
% 0.91/1.32 , b:0),
% 0.91/1.32 'c_Divides_Odiv__class_Odiv' [54, 3] (w:1, o:186, a:1, s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Oordered__ring__strict' [56, 1] (w:1, o:102
% 0.91/1.32 , a:1, s:1, b:0),
% 0.91/1.32 'c_Suc' [58, 1] (w:1, o:103, a:1, s:1, b:0),
% 0.91/1.32 'c_HOL_Oone__class_Oone' [59, 1] (w:1, o:97, a:1, s:1, b:0),
% 0.91/1.32 'c_Lambda_Olift' [60, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.91/1.32 'c_Lambda_Osubst' [61, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Osemiring' [66, 1] (w:1, o:106, a:1, s:1, b:0
% 0.91/1.32 ),
% 0.91/1.32 'class_Ring__and__Field_Oordered__semidom' [69, 1] (w:1, o:107, a:1
% 0.91/1.32 , s:1, b:0),
% 0.91/1.32 'c_Power_Opower__class_Opower' [70, 3] (w:1, o:187, a:1, s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Osemiring__1' [71, 1] (w:1, o:109, a:1, s:1
% 0.91/1.32 , b:0),
% 0.91/1.32 'c_Nat_Osemiring__1__class_Oof__nat' [72, 2] (w:1, o:178, a:1, s:1
% 0.91/1.32 , b:0),
% 0.91/1.32 'class_OrderedGroup_Omonoid__mult' [76, 1] (w:1, o:111, a:1, s:1, b:0
% 0.91/1.32 ),
% 0.91/1.32 'c_Lambda_OdB_OVar' [77, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Oab__group__add' [78, 1] (w:1, o:113, a:1, s:1
% 0.91/1.32 , b:0),
% 0.91/1.32 'class_Ring__and__Field_Ocomm__semiring__1' [79, 1] (w:1, o:114, a:1
% 0.91/1.32 , s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Oab__semigroup__add' [81, 1] (w:1, o:115, a:1, s:
% 0.91/1.32 1, b:0),
% 0.91/1.32 'class_OrderedGroup_Ocomm__monoid__add' [82, 1] (w:1, o:116, a:1, s:1
% 0.91/1.32 , b:0),
% 0.91/1.32 'class_Orderings_Oorder' [83, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.91/1.32 'class_Orderings_Opreorder' [84, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.91/1.32 'class_Power_Opower' [86, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Oidom' [88, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.91/1.32 'class_Int_Onumber__ring' [89, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.91/1.32 'c_Lambda_OdB_OAbs' [94, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.91/1.32 'c_Lambda_OdB_OdB__case' [95, 5] (w:1, o:198, a:1, s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Odvd' [96, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Ocomm__monoid__mult' [97, 1] (w:1, o:119, a:1, s:
% 0.91/1.32 1, b:0),
% 0.91/1.32 'c_List_Olist_ONil' [99, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.91/1.32 'c_List_Olistsp' [100, 3] (w:1, o:188, a:1, s:1, b:0),
% 0.91/1.32 'c_Lambda_Osubstn' [102, 3] (w:1, o:189, a:1, s:1, b:0),
% 0.91/1.32 'class_Nat_Osemiring__char__0' [104, 1] (w:1, o:95, a:1, s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Ocancel__ab__semigroup__add' [105, 1] (w:1, o:120
% 0.91/1.32 , a:1, s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Ocancel__semigroup__add' [106, 1] (w:1, o:121, a:
% 0.91/1.32 1, s:1, b:0),
% 0.91/1.32 'tc_Lambda_OdB' [108, 0] (w:1, o:63, a:1, s:1, b:0),
% 0.91/1.32 'c_Nat_Osize__class_Osize' [109, 2] (w:1, o:179, a:1, s:1, b:0),
% 0.91/1.32 'c_Lambda_Obeta' [111, 2] (w:1, o:180, a:1, s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Oordered__semiring__strict' [112, 1] (w:1, o:
% 0.91/1.32 136, a:1, s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Oordered__comm__semiring__strict' [113, 1]
% 0.91/1.32 (w:1, o:137, a:1, s:1, b:0),
% 0.91/1.32 'c_Type_Otyping' [116, 3] (w:1, o:191, a:1, s:1, b:0),
% 0.91/1.32 'tc_Type_Otype' [117, 0] (w:1, o:67, a:1, s:1, b:0),
% 0.91/1.32 'c_Type_Oshift' [118, 4] (w:1, o:195, a:1, s:1, b:0),
% 0.91/1.32 hBOOL [121, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Olordered__ab__group__add' [122, 1] (w:1, o:110
% 0.91/1.32 , a:1, s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Ozero__neq__one' [123, 1] (w:1, o:139, a:1
% 0.91/1.32 , s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Ono__zero__divisors' [124, 1] (w:1, o:101, a:
% 0.91/1.32 1, s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Omult__zero' [125, 1] (w:1, o:100, a:1, s:1
% 0.91/1.32 , b:0),
% 0.91/1.32 'class_Ring__and__Field_Oring__1__no__zero__divisors' [126, 1] (w:1
% 0.91/1.32 , o:104, a:1, s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Oring__no__zero__divisors' [127, 1] (w:1, o:
% 0.91/1.32 105, a:1, s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Oordered__idom' [130, 1] (w:1, o:140, a:1, s:
% 0.91/1.32 1, b:0),
% 0.91/1.32 'class_Orderings_Olinorder' [137, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [138, 1]
% 0.91/1.32 (w:1, o:123, a:1, s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Oab__semigroup__idem__mult' [139, 1] (w:1, o:124
% 0.91/1.32 , a:1, s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Omonoid__add' [142, 1] (w:1, o:125, a:1, s:1, b:0
% 0.91/1.32 ),
% 0.91/1.32 'class_Ring__and__Field_Osemiring__0' [143, 1] (w:1, o:108, a:1, s:1
% 0.91/1.32 , b:0),
% 0.91/1.32 'v_sko__List__Xlexn__Xinduct__1' [145, 1] (w:1, o:141, a:1, s:1, b:0)
% 0.91/1.32 ,
% 0.91/1.32 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1' [146, 1] (w:1, o:142
% 0.91/1.32 , a:1, s:1, b:0),
% 0.91/1.32 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1' [147, 1] (w:1, o:143
% 0.91/1.32 , a:1, s:1, b:0),
% 0.91/1.32 'v_sko__List__Xreplicate__Xinduct__1' [148, 1] (w:1, o:144, a:1, s:1
% 0.91/1.32 , b:0),
% 0.91/1.32 'v_sko__Nat__Xnat__Xinducts__1' [149, 1] (w:1, o:145, a:1, s:1, b:0)
% 0.91/1.32 ,
% 0.91/1.32 'v_sko__Nat__Xnat__Xinduct__1' [150, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.91/1.32
% 0.91/1.32 'v_sko__List__Xupt__Xinduct__1' [151, 1] (w:1, o:147, a:1, s:1, b:0)
% 0.91/1.32 ,
% 0.91/1.32 'c_Lambda_OdB_OApp' [152, 0] (w:1, o:70, a:1, s:1, b:0),
% 0.91/1.32 't_a' [156, 0] (w:1, o:71, a:1, s:1, b:0),
% 0.91/1.32 'c_List_Omap' [160, 4] (w:1, o:196, a:1, s:1, b:0),
% 0.91/1.32 'c_List_Ofoldl' [162, 5] (w:1, o:199, a:1, s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Osemigroup__add' [163, 1] (w:1, o:126, a:1, s:1
% 0.91/1.32 , b:0),
% 0.91/1.32 'c_COMBC' [165, 5] (w:1, o:200, a:1, s:1, b:0),
% 0.91/1.32 'c_Type_Otypings' [168, 3] (w:1, o:192, a:1, s:1, b:0),
% 0.91/1.32 'c_SetInterval_Oord__class_OatLeastLessThan' [170, 3] (w:1, o:190, a:
% 0.91/1.32 1, s:1, b:0),
% 0.91/1.32 'c_Finite__Set_Osetsum' [171, 4] (w:1, o:197, a:1, s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [172, 1]
% 0.91/1.32 (w:1, o:127, a:1, s:1, b:0),
% 0.91/1.32 'c_Lambda_OdB_OdB__size' [174, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.91/1.32 'class_OrderedGroup_Oab__semigroup__mult' [175, 1] (w:1, o:128, a:1
% 0.91/1.32 , s:1, b:0),
% 0.91/1.32 'class_Ring__and__Field_Ocomm__semiring' [176, 1] (w:1, o:133, a:1
% 0.91/1.32 , s:1, b:0),
% 0.91/1.32 'c_InductTermi_OIT' [178, 0] (w:1, o:75, a:1, s:1, b:0),
% 0.91/1.32 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1' [180, 3] (w:
% 0.91/1.32 1, o:193, a:1, s:1, b:0),
% 0.91/1.32 'c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1' [181, 1] (w:1, o:149
% 0.91/1.32 , a:1, s:1, b:0),
% 0.91/1.32 'c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1' [182, 1] (w:1, o:150
% 0.91/1.32 , a:1, s:1, b:0),
% 0.91/1.32 'c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1' [183, 1] (w:1
% 0.91/1.32 , o:151, a:1, s:1, b:0),
% 0.91/1.32 'tc_fun' [184, 2] (w:1, o:181, a:1, s:1, b:0),
% 0.91/1.32 'v_ra' [191, 0] (w:1, o:80, a:1, s:1, b:0),
% 0.91/1.32 'v_s' [192, 0] (w:1, o:81, a:1, s:1, b:0),
% 0.91/1.32 'v_ss' [193, 0] (w:1, o:82, a:1, s:1, b:0),
% 0.91/1.32 'v_ia' [194, 0] (w:1, o:83, a:1, s:1, b:0),
% 0.91/1.32 'v_ja' [195, 0] (w:1, o:84, a:1, s:1, b:0),
% 0.91/1.32 'c_COMBB' [198, 6] (w:1, o:201, a:1, s:1, b:0),
% 0.91/1.32 'c_fequal' [199, 3] (w:1, o:194, a:1, s:1, b:0).
% 0.91/1.32
% 0.91/1.32
% 0.91/1.32 Starting Search:
% 0.91/1.32
% 0.91/1.32
% 0.91/1.32 Bliksems!, er is een bewijs:
% 0.91/1.32 % SZS status Unsatisfiable
% 0.91/1.32 % SZS output start Refutation
% 0.91/1.32
% 0.91/1.32 clause( 462, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.32 .
% 0.91/1.32 clause( 496, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( hAPP( hAPP( hAPP(
% 0.91/1.32 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( X ) ) ),
% 0.91/1.32 'c_Suc'( Y ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' ),
% 0.91/1.32 'c_Lambda_OdB_OVar'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.91/1.32 , 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.91/1.32 'c_Lambda_OdB_OVar'( X ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.91/1.32 'tc_nat', 'tc_Lambda_OdB' ) ), Y, 'tc_Lambda_OdB', 'tc_nat',
% 0.91/1.32 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.91/1.32 .
% 0.91/1.32 clause( 499, [] )
% 0.91/1.32 .
% 0.91/1.32
% 0.91/1.32
% 0.91/1.32 % SZS output end Refutation
% 0.91/1.32 found a proof!
% 0.91/1.32
% 0.91/1.32 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.91/1.32
% 0.91/1.32 initialclauses(
% 0.91/1.32 [ clause( 501, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.32 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.32 , clause( 502, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.32 Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.32 , clause( 503, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.91/1.32 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.91/1.32 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.32 , clause( 504, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 0.91/1.32 , clause( 505, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.91/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ] )
% 0.91/1.32 , clause( 506, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), T
% 0.91/1.32 , X ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.91/1.32 X ), Z, X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 0.91/1.32 , clause( 507, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.32 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.32 , clause( 508, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 'c_Suc'( X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 0.91/1.32 Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 0.91/1.32 ) ] )
% 0.91/1.32 , clause( 509, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.91/1.32 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.91/1.32 'tc_nat' ) ) ] )
% 0.91/1.32 , clause( 510, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.91/1.32 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.91/1.32 ), 'tc_nat' ) ] )
% 0.91/1.32 , clause( 511, [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP(
% 0.91/1.32 'c_Lambda_Osubst', X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP(
% 0.91/1.32 'c_Lambda_Osubst', hAPP( hAPP( 'c_Lambda_Olift', X ), T ) ), hAPP( hAPP(
% 0.91/1.32 'c_Lambda_Olift', Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 0.91/1.32 )
% 0.91/1.32 , clause( 512, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP(
% 0.91/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.33 , X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ), U ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ), U ) ) ] )
% 0.91/1.33 , clause( 513, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.33 Y, 'tc_nat' ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), T ) ) ] )
% 0.91/1.33 , clause( 514, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.33 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.91/1.33 , Y, X ) ) ] )
% 0.91/1.33 , clause( 515, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ] )
% 0.91/1.33 , clause( 516, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 517, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 518, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.33 'tc_nat' ) ), =( Y, Z ) ] )
% 0.91/1.33 , clause( 519, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.91/1.33 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.91/1.33 , clause( 520, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 521, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 522, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 0.91/1.33 , X ) ), T, X ) ) ] )
% 0.91/1.33 , clause( 523, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 0.91/1.33 ), Z ), T, X ) ) ] )
% 0.91/1.33 , clause( 524, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.91/1.33 ), 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 525, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X
% 0.91/1.33 , Y, 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 526, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.91/1.33 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.91/1.33 , clause( 527, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X )
% 0.91/1.33 ), Y ), 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 0.91/1.33 , clause( 528, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ] )
% 0.91/1.33 , clause( 529, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), Z ), T ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.33 Y, T, X ), X ) ) ] )
% 0.91/1.33 , clause( 530, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 531, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.91/1.33 , clause( 532, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.91/1.33 , clause( 533, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 X ), Y ), T ) ), Z ) ) ] )
% 0.91/1.33 , clause( 534, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 X ), Y ), Z ) ), T ) ) ] )
% 0.91/1.33 , clause( 535, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.91/1.33 , clause( 536, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.91/1.33 , clause( 537, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.91/1.33 , clause( 538, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ] )
% 0.91/1.33 , clause( 539, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.91/1.33 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ] )
% 0.91/1.33 , clause( 540, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.91/1.33 , clause( 541, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 X ), Y ), Z ) ), T ) ) ] )
% 0.91/1.33 , clause( 542, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.91/1.33 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.91/1.33 , clause( 543, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 0.91/1.33 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.91/1.33 , clause( 544, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 0.91/1.33 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.91/1.33 , clause( 545, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 0.91/1.33 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ] )
% 0.91/1.33 , clause( 546, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.33 , Y, X ) ) ] )
% 0.91/1.33 , clause( 547, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 548, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.33 , Y, X ) ) ] )
% 0.91/1.33 , clause( 549, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.33 ), X ) ) ] )
% 0.91/1.33 , clause( 550, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.33 ), X ) ) ] )
% 0.91/1.33 , clause( 551, [ ~( 'class_Power_Opower'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.33 ), X ) ) ] )
% 0.91/1.33 , clause( 552, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.33 Y, X ) ) ] )
% 0.91/1.33 , clause( 553, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 0.91/1.33 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 Z, T, 'tc_nat' ), X ) ) ] )
% 0.91/1.33 , clause( 554, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.91/1.33 'tc_nat' ), X, 'tc_nat' ) ] )
% 0.91/1.33 , clause( 555, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 0.91/1.33 'tc_nat' ), X, 'tc_nat' ) ] )
% 0.91/1.33 , clause( 556, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.91/1.33 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ) ] )
% 0.91/1.33 , clause( 557, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.91/1.33 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ) ] )
% 0.91/1.33 , clause( 558, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 559, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 560, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OAbs'(
% 0.91/1.33 T ), U ), hAPP( Z, T ) ) ] )
% 0.91/1.33 , clause( 561, [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 562, [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ] )
% 0.91/1.33 , clause( 563, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.91/1.33 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 0.91/1.33 , clause( 564, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.33 Z, 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), Z, X ) ) ] )
% 0.91/1.33 , clause( 565, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.91/1.33 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 566, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.33 , Y, X ), X ) ] )
% 0.91/1.33 , clause( 567, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.33 , Z, X ), X ) ] )
% 0.91/1.33 , clause( 568, [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.33 , Z, X ), X ) ] )
% 0.91/1.33 , clause( 569, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 570, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 571, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 572, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 573, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 574, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'(
% 0.91/1.33 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 0.91/1.33 , clause( 575, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 0.91/1.33 , clause( 576, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 577, [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ] )
% 0.91/1.33 , clause( 578, [ =( 'c_Divides_Odiv__class_Odiv'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 579, [ =( 'c_Divides_Odiv__class_Odiv'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 580, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 0.91/1.33 , clause( 581, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ] )
% 0.91/1.33 , clause( 582, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 583, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 0.91/1.33 , X ) ) ] )
% 0.91/1.33 , clause( 584, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), 'c_Divides_Odiv__class_Odiv'(
% 0.91/1.33 Z, T, X ) ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ] )
% 0.91/1.33 , clause( 585, [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y
% 0.91/1.33 , X ), X ) ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ), T ), hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ] )
% 0.91/1.33 , clause( 586, [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 X ), 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X
% 0.91/1.33 ), Z, X ) ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ] )
% 0.91/1.33 , clause( 587, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ] )
% 0.91/1.33 , clause( 588, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ] )
% 0.91/1.33 , clause( 589, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ] )
% 0.91/1.33 , clause( 590, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 591, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 592, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 593, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 594, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 595, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 596, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.91/1.33 , T, X ), X ) ) ] )
% 0.91/1.33 , clause( 597, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.91/1.33 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 0.91/1.33 , clause( 598, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.91/1.33 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 599, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.91/1.33 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 0.91/1.33 , clause( 600, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), X, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 601, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 602, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 0.91/1.33 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubstn'( X, Y, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.91/1.33 'tc_nat' ) ) ) ) ) ] )
% 0.91/1.33 , clause( 603, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.91/1.33 , clause( 604, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.91/1.33 , clause( 605, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.91/1.33 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 606, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) )
% 0.91/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( X, T, 'tc_nat' ) ] )
% 0.91/1.33 , clause( 607, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.91/1.33 , clause( 608, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.33 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 609, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 0.91/1.33 , clause( 610, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.91/1.33 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 611, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) )
% 0.91/1.33 ), =( Y, Z ) ] )
% 0.91/1.33 , clause( 612, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) )
% 0.91/1.33 ), =( X, Z ) ] )
% 0.91/1.33 , clause( 613, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) )
% 0.91/1.33 ), =( Y, Z ) ] )
% 0.91/1.33 , clause( 614, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.91/1.33 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.91/1.33 , clause( 615, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) )
% 0.91/1.33 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.91/1.33 , clause( 616, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.91/1.33 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.91/1.33 , clause( 617, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.91/1.33 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ] )
% 0.91/1.33 , clause( 618, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.91/1.33 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z ), 'c_Lambda_OdB_OAbs'( hAPP( hAPP(
% 0.91/1.33 hAPP( 'c_Lambda_Osubst', X ), hAPP( hAPP( 'c_Lambda_Olift', Y ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.91/1.33 'tc_nat' ) ) ) ) ) ] )
% 0.91/1.33 , clause( 619, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 0.91/1.33 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 0.91/1.33 , clause( 620, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP(
% 0.91/1.33 'c_Lambda_Osubst', X ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ), 'c_Suc'(
% 0.91/1.33 T ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', U ), Y ), T ) ), Z ), hAPP(
% 0.91/1.33 hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ),
% 0.91/1.33 U ), Z ) ), Y ), T ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 0.91/1.33 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 621, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 0.91/1.33 , clause( 622, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 0.91/1.33 , clause( 623, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 0.91/1.33 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ] )
% 0.91/1.33 , clause( 624, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 0.91/1.33 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 0.91/1.33 , clause( 625, [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.91/1.33 , Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 626, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 627, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Z,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 628, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) )
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 629, [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OAbs'( X ),
% 0.91/1.33 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 630, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.33 , clause( 631, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 0.91/1.33 , clause( 632, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 0.91/1.33 , clause( 633, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y,
% 0.91/1.33 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 0.91/1.33 , clause( 634, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 0.91/1.33 , clause( 635, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y,
% 0.91/1.33 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 0.91/1.33 , clause( 636, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'(
% 0.91/1.33 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 0.91/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 637, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 0.91/1.33 , X ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 0.91/1.33 , clause( 638, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 0.91/1.33 , X ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 0.91/1.33 , clause( 639, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X )
% 0.91/1.33 ), Y ), 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 640, [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_Olift', X ), Y ),
% 0.91/1.33 hAPP( hAPP( 'c_Lambda_Olift', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 641, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.91/1.33 , clause( 642, [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP(
% 0.91/1.33 'c_Lambda_Osubst', X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP(
% 0.91/1.33 'c_Lambda_Osubst', hAPP( hAPP( 'c_Lambda_Olift', X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 0.91/1.33 'tc_nat' ) ) ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), T ) ), Z ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 643, [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP(
% 0.91/1.33 'c_Lambda_Olift', X ), Y ) ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 0.91/1.33 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_Olift', X ), Z ) ), Y ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 644, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 645, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 0.91/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 646, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.91/1.33 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat'
% 0.91/1.33 ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 647, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.91/1.33 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.91/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 648, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.91/1.33 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.91/1.33 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.91/1.33 , X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 649, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.91/1.33 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat'
% 0.91/1.33 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.91/1.33 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 650, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.91/1.33 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 651, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.91/1.33 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.91/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 652, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.33 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.33 , clause( 653, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.33 , clause( 654, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.33 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 X ), T, X ) ) ] )
% 0.91/1.33 , clause( 655, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.91/1.33 , clause( 656, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.91/1.33 , clause( 657, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.91/1.33 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.33 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.91/1.33 , clause( 658, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.91/1.33 , clause( 659, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.33 , clause( 660, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 0.91/1.33 , clause( 661, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.91/1.33 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.33 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.91/1.33 , clause( 662, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.91/1.33 , clause( 663, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.33 , clause( 664, [ ~(
% 0.91/1.33 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.91/1.33 , clause( 665, [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 0.91/1.33 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 666, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, X, 'tc_nat'
% 0.91/1.33 ), 'c_Power_Opower__class_Opower'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 667, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 668, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 669, [ =( 'c_Divides_Odiv__class_Odiv'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 670, [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'(
% 0.91/1.33 'c_Type_Oshift'( X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'(
% 0.91/1.33 X, hAPP( hAPP( hAPP( 'c_Lambda_Osubst', U ), Y ), T ), W ) ] )
% 0.91/1.33 , clause( 671, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.91/1.33 'c_HOL_Oone__class_Oone'( X ) ), X ) ] )
% 0.91/1.33 , clause( 672, [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 Y, 'tc_nat' ) ), Z ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 673, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), T, X ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ] )
% 0.91/1.33 , clause( 674, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), Z, X ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 0.91/1.33 , clause( 675, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), T ), Z, X ) ) ] )
% 0.91/1.33 , clause( 676, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( 'c_Divides_Odiv__class_Odiv'( Y
% 0.91/1.33 , X, 'tc_nat' ) ), 'tc_nat' ), 'tc_nat' ) ] )
% 0.91/1.33 , clause( 677, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.91/1.33 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 0.91/1.33 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 678, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.91/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 0.91/1.33 , clause( 679, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.91/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 0.91/1.33 , clause( 680, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 0.91/1.33 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 681, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 0.91/1.33 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 682, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), X ) ) ] )
% 0.91/1.33 , clause( 683, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ] )
% 0.91/1.33 , clause( 684, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ),
% 0.91/1.33 'c_Lambda_OdB_OAbs'( Y ) ), ~( 'c_Lambda_Obeta'( X, Y ) ) ] )
% 0.91/1.33 , clause( 685, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 0.91/1.33 , clause( 686, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 687, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ) ), X ), Y,
% 0.91/1.33 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ] )
% 0.91/1.33 , clause( 688, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.91/1.33 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 689, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.91/1.33 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 690, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 0.91/1.33 , clause( 691, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.91/1.33 , clause( 692, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.91/1.33 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 693, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.91/1.33 ), 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 694, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.91/1.33 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.91/1.33 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.91/1.33 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.33 ) ) ] )
% 0.91/1.33 , clause( 695, [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.91/1.33 X ) ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.33 ) ) ] )
% 0.91/1.33 , clause( 696, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 697, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 698, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 699, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.91/1.33 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y,
% 0.91/1.33 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 700, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.91/1.33 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.33 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 701, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 702, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 703, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.33 , X ) ] )
% 0.91/1.33 , clause( 704, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.91/1.33 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 0.91/1.33 , clause( 705, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 0.91/1.33 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 706, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 0.91/1.33 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 707, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.91/1.33 ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.33 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 708, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 709, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 710, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.33 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.33 ) ) ] )
% 0.91/1.33 , clause( 711, [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.91/1.33 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 712, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.91/1.33 , T, X ), X ), T, X ) ) ] )
% 0.91/1.33 , clause( 713, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.33 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 0.91/1.33 Y, Z, X ), X ) ) ] )
% 0.91/1.33 , clause( 714, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), Z ), T ), X ) ) ] )
% 0.91/1.33 , clause( 715, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), Z, X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), T ), 'c_Divides_Odiv__class_Odiv'( Y, Z
% 0.91/1.33 , X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 716, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), T, X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), 'c_Divides_Odiv__class_Odiv'( Y, T
% 0.91/1.33 , X ) ) ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 717, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ), Y, X
% 0.91/1.33 ) ) ] )
% 0.91/1.33 , clause( 718, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.91/1.33 X ), Y ) ] )
% 0.91/1.33 , clause( 719, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.91/1.33 X ), Y ) ] )
% 0.91/1.33 , clause( 720, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.91/1.33 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ] )
% 0.91/1.33 , clause( 721, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.33 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.33 , clause( 722, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.33 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.33 , clause( 723, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.33 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.33 , clause( 724, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.33 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.33 , clause( 725, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.91/1.33 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.91/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.91/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 0.91/1.33 , clause( 726, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.91/1.33 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.91/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.91/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 0.91/1.33 , clause( 727, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.91/1.33 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.91/1.33 , clause( 728, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.33 , clause( 729, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.33 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.33 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 730, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.91/1.33 , clause( 731, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.91/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.91/1.33 , 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 732, [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat'
% 0.91/1.33 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 733, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat'
% 0.91/1.33 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 734, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ) ), X ), Y,
% 0.91/1.33 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ] )
% 0.91/1.33 , clause( 735, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.91/1.33 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.33 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 0.91/1.33 , clause( 736, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ] )
% 0.91/1.33 , clause( 737, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.91/1.33 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.91/1.33 'tc_nat' ) ] )
% 0.91/1.33 , clause( 738, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.33 , clause( 739, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.91/1.33 ), =( X, Y ) ] )
% 0.91/1.33 , clause( 740, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.33 ), X ) ) ] )
% 0.91/1.33 , clause( 741, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.33 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 0.91/1.33 , clause( 742, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 Y, 'tc_nat' ) ), Z ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 0.91/1.33 'c_Suc'( Z ), Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 743, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.91/1.33 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( T, U, X ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, U, X )
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 744, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.91/1.33 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( T, U, X ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, U, X )
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 745, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 0.91/1.33 =( Y, T ), =( X, Z ) ] )
% 0.91/1.33 , clause( 746, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 0.91/1.33 =( Y, T ), =( X, Z ) ] )
% 0.91/1.33 , clause( 747, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.91/1.33 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 748, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.91/1.33 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 749, [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) )
% 0.91/1.33 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.91/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 750, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.91/1.33 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 0.91/1.33 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 0.91/1.33 X ), Z, X ) ) ] )
% 0.91/1.33 , clause( 751, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 0.91/1.33 , clause( 752, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 0.91/1.33 , clause( 753, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 0.91/1.33 , clause( 754, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 Y, Z, X ) ), Z ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), Z
% 0.91/1.33 , X ) ) ] )
% 0.91/1.33 , clause( 755, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 0.91/1.33 'c_HOL_Oone__class_Oone'( X ) ), Y, X ) ) ] )
% 0.91/1.33 , clause( 756, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 757, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.91/1.33 ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 758, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 759, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ),
% 0.91/1.33 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 760, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 761, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 762, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.91/1.33 , clause( 763, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.91/1.33 , clause( 764, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.91/1.33 , clause( 765, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.91/1.33 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.91/1.33 , clause( 766, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.33 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.91/1.33 , Y, X ) ) ] )
% 0.91/1.33 , clause( 767, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.91/1.33 ), =( Z, Y ) ] )
% 0.91/1.33 , clause( 768, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 769, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X
% 0.91/1.33 , 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 0.91/1.33 ) ) ] )
% 0.91/1.33 , clause( 770, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X
% 0.91/1.33 , 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 0.91/1.33 ) ) ] )
% 0.91/1.33 , clause( 771, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.91/1.33 ), =( Y, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 772, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X
% 0.91/1.33 , 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 0.91/1.33 ) ) ] )
% 0.91/1.33 , clause( 773, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 0.91/1.33 , clause( 774, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), =( Z, Y ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ] )
% 0.91/1.33 , clause( 775, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y
% 0.91/1.33 , 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 0.91/1.33 ) ) ] )
% 0.91/1.33 , clause( 776, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.91/1.33 ), =( Y, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 777, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.91/1.33 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 778, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 0.91/1.33 , clause( 779, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.91/1.33 ), =( Z, Y ) ] )
% 0.91/1.33 , clause( 780, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 0.91/1.33 , clause( 781, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 782, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.91/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 783, [ ~(
% 0.91/1.33 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.33 T, X ) ) ] )
% 0.91/1.33 , clause( 784, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 785, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 0.91/1.33 , clause( 786, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ] )
% 0.91/1.33 , clause( 787, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 788, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 789, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.91/1.33 ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 790, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 0.91/1.33 , clause( 791, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 792, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 0.91/1.33 , clause( 793, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ] )
% 0.91/1.33 , clause( 794, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ] )
% 0.91/1.33 , clause( 795, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ] )
% 0.91/1.33 , clause( 796, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.33 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 0.91/1.33 , clause( 797, [ =( 'c_Divides_Odiv__class_Odiv'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ), 'tc_nat' ) ),
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' )
% 0.91/1.33 ) ) ] )
% 0.91/1.33 , clause( 798, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.91/1.33 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 799, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.91/1.33 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 800, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 801, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.91/1.33 ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.33 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat'
% 0.91/1.33 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.33 ), Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 802, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.91/1.33 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.33 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 803, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ] )
% 0.91/1.33 , clause( 804, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X
% 0.91/1.33 , Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 805, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 0.91/1.33 , =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.33 , X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 0.91/1.33 , clause( 806, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( T, U, X ), X ),
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 0.91/1.33 , clause( 807, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 Y, U, 'tc_nat' ) ) ) ), =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' )
% 0.91/1.33 , 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 808, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 809, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.33 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 0.91/1.33 , clause( 810, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 0.91/1.33 X ) ] )
% 0.91/1.33 , clause( 811, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.91/1.33 'class_Int_Onumber__ring'( X ) ), ~( =( Y, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), =( Z,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 812, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 813, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 814, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 815, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.33 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 816, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ] )
% 0.91/1.33 , clause( 817, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.91/1.33 , X ) ) ] )
% 0.91/1.33 , clause( 818, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 X ) ), Y ), Y ) ] )
% 0.91/1.33 , clause( 819, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.91/1.33 , Y ), Y ) ] )
% 0.91/1.33 , clause( 820, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.91/1.33 'class_Int_Onumber__ring'( X ) ), =( Y, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 821, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.33 ) ), Y ) ] )
% 0.91/1.33 , clause( 822, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.91/1.33 Y ) ] )
% 0.91/1.33 , clause( 823, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.91/1.33 Y ) ] )
% 0.91/1.33 , clause( 824, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 0.91/1.33 , clause( 825, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 X ) ), Y ), Y ) ] )
% 0.91/1.33 , clause( 826, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.91/1.33 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.33 X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.91/1.33 , clause( 827, [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.33 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 828, [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 0.91/1.33 , Y ) ) ] )
% 0.91/1.33 , clause( 829, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 830, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 831, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.91/1.33 'v_sko__List__Xlexn__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 832, [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )
% 0.91/1.33 , ~( hBOOL( hAPP( X, 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1'( X )
% 0.91/1.33 ) ) ), ~( hBOOL( hAPP( X, Y ) ) ) ] )
% 0.91/1.33 , clause( 833, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 834, [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 0.91/1.33 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 835, [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.91/1.33 ) ) ), hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 836, [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 0.91/1.33 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 837, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 838, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.91/1.33 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1'( X ) ) ), ~( hBOOL( hAPP( X
% 0.91/1.33 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 839, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 840, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 841, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 842, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 843, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 844, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 0.91/1.33 , clause( 845, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 0.91/1.33 , clause( 846, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 847, [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.91/1.33 ), X ), Y ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 848, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 X ), Y ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 849, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.91/1.33 'v_sko__List__Xreplicate__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 850, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.91/1.33 'v_sko__Nat__Xnat__Xinducts__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 851, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 852, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.91/1.33 'v_sko__Nat__Xnat__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 853, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 854, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 855, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.91/1.33 'v_sko__List__Xupt__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 856, [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 857, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ] )
% 0.91/1.33 , clause( 858, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.91/1.33 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ] )
% 0.91/1.33 , clause( 859, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 X, Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.33 ) ), X, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 860, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.33 ) ), X, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 861, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 0.91/1.33 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.33 ) ), Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 862, [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 0.91/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) )
% 0.91/1.33 , =( Y, Z ) ] )
% 0.91/1.33 , clause( 863, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.91/1.33 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 864, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 865, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat'
% 0.91/1.33 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'(
% 0.91/1.33 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 866, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.91/1.33 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 867, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 868, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 869, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ),
% 0.91/1.33 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 0.91/1.33 , clause( 870, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ),
% 0.91/1.33 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 0.91/1.33 , clause( 871, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.91/1.33 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 872, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_Suc'( X ) ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), X ), Y ) ) ) ] )
% 0.91/1.33 , clause( 873, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.91/1.33 , 'c_Suc'( Y ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), X ), Y ) ) ) ] )
% 0.91/1.33 , clause( 874, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat'
% 0.91/1.33 ), 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 0.91/1.33 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ] )
% 0.91/1.33 , clause( 875, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 X ), 'c_Suc'( Y ) ) ) ] )
% 0.91/1.33 , clause( 876, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.91/1.33 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 877, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.91/1.33 , clause( 878, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 879, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 0.91/1.33 , clause( 880, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.91/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 881, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 882, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.91/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 883, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.91/1.33 'c_Lambda_OdB_OAbs'( Z ) ) ) ] )
% 0.91/1.33 , clause( 884, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP(
% 0.91/1.33 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 0.91/1.33 , clause( 885, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP(
% 0.91/1.33 hAPP( 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP(
% 0.91/1.33 hAPP( Z, U ), W ) ) ) ] )
% 0.91/1.33 , clause( 886, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP(
% 0.91/1.33 hAPP( 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP(
% 0.91/1.33 hAPP( Z, U ), W ) ) ) ] )
% 0.91/1.33 , clause( 887, [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP(
% 0.91/1.33 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.91/1.33 hAPP( hAPP( 'c_Lambda_Olift', X ), Z ) ), hAPP( hAPP( 'c_Lambda_Olift', Y
% 0.91/1.33 ), Z ) ) ) ] )
% 0.91/1.33 , clause( 888, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, hAPP( hAPP(
% 0.91/1.33 'c_Lambda_OdB_OApp', T ), U ), W ), hAPP( hAPP( Y, T ), U ) ) ] )
% 0.91/1.33 , clause( 889, [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y
% 0.91/1.33 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ), ~( 'c_Lambda_Obeta'( Y,
% 0.91/1.33 Z ) ) ] )
% 0.91/1.33 , clause( 890, [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y
% 0.91/1.33 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X,
% 0.91/1.33 Z ) ) ] )
% 0.91/1.33 , clause( 891, [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 0.91/1.33 ), Y ), Z, T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X,
% 0.91/1.33 Z, T ) ), 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ] )
% 0.91/1.33 , clause( 892, [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T
% 0.91/1.33 ) ) ), =( Y, 'c_List_Olist_ONil'( Z ) ) ] )
% 0.91/1.33 , clause( 893, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X
% 0.91/1.33 ) ) ), =( Z, 'c_List_Olist_ONil'( T ) ) ] )
% 0.91/1.33 , clause( 894, [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 0.91/1.33 'c_List_Olist_ONil'( Z ) ) ] )
% 0.91/1.33 , clause( 895, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y,
% 0.91/1.33 'c_List_Olist_ONil'( Z ), Z, X ) ) ] )
% 0.91/1.33 , clause( 896, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 0.91/1.33 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.91/1.33 , clause( 897, [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'(
% 0.91/1.33 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.91/1.33 , clause( 898, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.91/1.33 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.91/1.33 , clause( 899, [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.33 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ) ] )
% 0.91/1.33 , clause( 900, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z )
% 0.91/1.33 , Y ) ] )
% 0.91/1.33 , clause( 901, [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =(
% 0.91/1.33 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), T, X, X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ] )
% 0.91/1.33 , clause( 902, [ 'c_Lambda_Obeta'( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X )
% 0.91/1.33 , Y ), Z ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', T ), Y ), Z ) ), ~(
% 0.91/1.33 'c_Lambda_Obeta'( X, T ) ) ] )
% 0.91/1.33 , clause( 903, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.91/1.33 'c_Lambda_Olift', X ), Y ) ), Z ), Y ), X ) ] )
% 0.91/1.33 , clause( 904, [ 'c_Type_Otypings'( 'c_Type_Oshift'( X, Y, Z,
% 0.91/1.33 'tc_Type_Otype' ), 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Y,
% 0.91/1.33 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB',
% 0.91/1.33 'tc_Lambda_OdB' ), U ), ~( 'c_Type_Otypings'( X, T, U ) ) ] )
% 0.91/1.33 , clause( 905, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) )
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 906, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.91/1.33 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 907, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.91/1.33 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 908, [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 0.91/1.33 , clause( 909, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 910, [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X,
% 0.91/1.33 'c_Lambda_OdB_OVar'( Y ), Z ) ) ] )
% 0.91/1.33 , clause( 911, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.91/1.33 =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 0.91/1.33 , T ) ] )
% 0.91/1.33 , clause( 912, [ =( 'c_Power_Opower__class_Opower'( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.91/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 913, [ ~( 'class_Power_Opower'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.91/1.33 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.91/1.33 , clause( 914, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.91/1.33 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.91/1.33 , clause( 915, [ =( 'c_Divides_Odiv__class_Odiv'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 916, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 X ) ) ] )
% 0.91/1.33 , clause( 917, [ =( 'c_Divides_Odiv__class_Odiv'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.33 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 918, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.33 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ] )
% 0.91/1.33 , clause( 919, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.33 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ] )
% 0.91/1.33 , clause( 920, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 0.91/1.33 , clause( 921, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 0.91/1.33 , clause( 922, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U )
% 0.91/1.33 ), ~( 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 923, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.91/1.33 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.33 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.91/1.33 , clause( 924, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.91/1.33 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.33 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.91/1.33 , clause( 925, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.91/1.33 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.33 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.91/1.33 , clause( 926, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.91/1.33 , X ), Z, X ) ) ] )
% 0.91/1.33 , clause( 927, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.91/1.33 , X ), Z, X ) ) ] )
% 0.91/1.33 , clause( 928, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.33 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 0.91/1.33 , clause( 929, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.33 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 0.91/1.33 , clause( 930, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.91/1.33 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.91/1.33 Z, 'c_Suc'( T ), 'tc_nat' ), 'tc_nat', X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.33 ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 931, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.91/1.33 , clause( 932, [ =( 'c_Divides_Odiv__class_Omod'( X,
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 0.91/1.33 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Divides_Odiv__class_Omod'( X
% 0.91/1.33 , Y, 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 933, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 0.91/1.33 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ] )
% 0.91/1.33 , clause( 934, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.91/1.33 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 935, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.91/1.33 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 936, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 0.91/1.33 , clause( 937, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.33 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.91/1.33 X ), T, X ) ) ] )
% 0.91/1.33 , clause( 938, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 939, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.33 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.91/1.33 X ), T, X ) ) ] )
% 0.91/1.33 , clause( 940, [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 941, [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 942, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.33 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.91/1.33 , Y, X ) ) ] )
% 0.91/1.33 , clause( 943, [ =( 'c_Divides_Odiv__class_Odiv'( X,
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 0.91/1.33 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 944, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 0.91/1.33 , clause( 945, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), T ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 946, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.91/1.33 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Otimes__class_Otimes'( Z, T
% 0.91/1.33 , X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, U, X ) ) ) ), =( T, U ), =( Z,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 947, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 Y, T, 'tc_nat' ) ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 948, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 949, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 950, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 0.91/1.33 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 951, [ ~(
% 0.91/1.33 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.91/1.33 , clause( 952, [ ~(
% 0.91/1.33 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.91/1.33 , clause( 953, [ ~(
% 0.91/1.33 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 0.91/1.33 , clause( 954, [ ~(
% 0.91/1.33 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.91/1.33 , clause( 955, [ ~(
% 0.91/1.33 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.91/1.33 , clause( 956, [ ~(
% 0.91/1.33 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 0.91/1.33 , clause( 957, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 958, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.33 , Z ), Y ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 959, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 960, [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Lambda_Obeta'( T, Y ) )
% 0.91/1.33 , ~( 'c_Type_Otyping'( X, T, Z ) ) ] )
% 0.91/1.33 , clause( 961, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.91/1.33 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.91/1.33 Z, 'c_Suc'( T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 0.91/1.33 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 0.91/1.33 , X ) ), hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 962, [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, X
% 0.91/1.33 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 963, [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 0.91/1.33 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 964, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 0.91/1.33 , =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 0.91/1.33 , clause( 965, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.91/1.33 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 966, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.91/1.33 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 967, [ =( 'c_Divides_Odiv__class_Omod'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), X, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 968, [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 0.91/1.33 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 969, [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X )
% 0.91/1.33 , Z, X ) ), Y ) ] )
% 0.91/1.33 , clause( 970, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 971, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.33 , Y, X ), X ) ) ] )
% 0.91/1.33 , clause( 972, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.33 , T, X ), X ) ) ] )
% 0.91/1.33 , clause( 973, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.33 , T, X ), X ) ) ] )
% 0.91/1.33 , clause( 974, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.91/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.33 , Y, X ), X ) ) ] )
% 0.91/1.33 , clause( 975, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.91/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), 'c_Power_Opower__class_Opower'( Y, X, 'tc_nat' ), 'tc_nat' )
% 0.91/1.33 ) ] )
% 0.91/1.33 , clause( 976, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.91/1.33 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ] )
% 0.91/1.33 , clause( 977, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.33 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ] )
% 0.91/1.33 , clause( 978, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.33 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ] )
% 0.91/1.33 , clause( 979, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), T ), Z, X ) ) ] )
% 0.91/1.33 , clause( 980, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), Z ), T, X ) ) ] )
% 0.91/1.33 , clause( 981, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.91/1.33 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.91/1.33 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 0.91/1.33 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_Suc'( Z ), T, 'tc_nat' )
% 0.91/1.33 , 'tc_nat', X ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 982, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.91/1.33 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.33 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ] )
% 0.91/1.33 , clause( 983, [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Z, Y, X ), X ) ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ] )
% 0.91/1.33 , clause( 984, [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ) ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ] )
% 0.91/1.33 , clause( 985, [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ) ),
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ] )
% 0.91/1.33 , clause( 986, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 0.91/1.33 , X ) ) ] )
% 0.91/1.33 , clause( 987, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 0.91/1.33 , X ) ) ] )
% 0.91/1.33 , clause( 988, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OAbs'( X )
% 0.91/1.33 ), Y ), 'c_Lambda_OdB_OAbs'( hAPP( hAPP( 'c_Lambda_Olift', X ), hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 0.91/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ) ) ] )
% 0.91/1.33 , clause( 989, [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OAbs'( X ) ),
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_Lambda_OdB_OdB__size'( X ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 990, [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.91/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 991, [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.91/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 992, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.33 T, X ), X ) ) ] )
% 0.91/1.33 , clause( 993, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.91/1.33 X ), Z, X ) ) ] )
% 0.91/1.33 , clause( 994, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.33 T, X ), X ) ) ] )
% 0.91/1.33 , clause( 995, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.91/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.91/1.33 X ), T, X ) ) ] )
% 0.91/1.33 , clause( 996, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.91/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.33 T, X ), X ) ) ] )
% 0.91/1.33 , clause( 997, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.91/1.33 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 998, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.91/1.33 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.91/1.33 X ), T, X ) ) ] )
% 0.91/1.33 , clause( 999, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 Z, T, X ) ) ) ] )
% 0.91/1.33 , clause( 1000, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.33 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.33 Z, T, X ) ) ) ] )
% 0.91/1.33 , clause( 1001, [ =( 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ),
% 0.91/1.33 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1002, [ =( 'c_HOL_Otimes__class_Otimes'( X, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.33 Y, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1003, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.91/1.33 =( 'c_HOL_Otimes__class_Otimes'( Y, hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.33 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ) ) ] )
% 0.91/1.33 , clause( 1004, [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z,
% 0.91/1.33 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_Olift', T ), Y ), U ), ~(
% 0.91/1.33 'c_Type_Otyping'( X, T, U ) ) ] )
% 0.91/1.33 , clause( 1005, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.33 Y, X ) ) ] )
% 0.91/1.33 , clause( 1006, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.33 Y, X ) ) ] )
% 0.91/1.33 , clause( 1007, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1008, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.91/1.33 ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.91/1.33 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1009, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.33 Y, X ) ) ] )
% 0.91/1.33 , clause( 1010, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.33 Y, X ) ) ] )
% 0.91/1.33 , clause( 1011, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OVar'(
% 0.91/1.33 T ), U ), hAPP( X, T ) ) ] )
% 0.91/1.33 , clause( 1012, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y
% 0.91/1.33 ) ) ] )
% 0.91/1.33 , clause( 1013, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.91/1.33 'c_Lambda_Olift', X ), Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X )
% 0.91/1.33 ) ) ] )
% 0.91/1.33 , clause( 1014, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X
% 0.91/1.33 ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.91/1.33 , clause( 1015, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =(
% 0.91/1.33 hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_Finite__Set_Osetsum'( Y,
% 0.91/1.33 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 0.91/1.33 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 1016, [ =( 'c_Lambda_OdB_OdB__size'( hAPP( hAPP(
% 0.91/1.33 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.33 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_Lambda_OdB_OdB__size'( X ) ), 'c_Lambda_OdB_OdB__size'( Y ) ) ),
% 0.91/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 1017, [ =( 'c_Nat_Osize__class_Osize'( hAPP( hAPP(
% 0.91/1.33 'c_Lambda_OdB_OApp', X ), Y ), 'tc_Lambda_OdB' ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Nat_Osize__class_Osize'( X,
% 0.91/1.33 'tc_Lambda_OdB' ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_Lambda_OdB' ) ) )
% 0.91/1.33 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 1018, [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.91/1.33 'c_Lambda_OdB_OAbs'( X ) ), Y ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X )
% 0.91/1.33 , Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1019, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.33 'c_Lambda_OdB_OVar'( Y ),
% 0.91/1.33 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( 'c_Lambda_Obeta'(
% 0.91/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), Z,
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ) ] )
% 0.91/1.33 , clause( 1020, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.91/1.33 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.91/1.33 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.91/1.33 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.91/1.33 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1021, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.91/1.33 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.33 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1022, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.91/1.33 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.91/1.33 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.91/1.33 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 0.91/1.33 , clause( 1023, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 1024, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.91/1.33 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.91/1.33 , clause( 1025, [ =( X, 'c_Suc'(
% 0.91/1.33 'c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1'( X ) ) ), =( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1026, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.33 , X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1027, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.33 , X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y,
% 0.91/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1028, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1029, [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.91/1.33 ), hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.33 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1'( X ) ) ) ), ~( hBOOL( hAPP(
% 0.91/1.33 X, Y ) ) ) ] )
% 0.91/1.33 , clause( 1030, [ ~( =( 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1031, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1032, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.33 'v_sko__List__Xlexn__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 1033, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1034, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1035, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ] )
% 0.91/1.33 , clause( 1036, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1037, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 0.91/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1038, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 1039, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1040, [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 0.91/1.33 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 0.91/1.33 'c_Suc'( Y ), Z, T ) ) ] )
% 0.91/1.33 , clause( 1041, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.33 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1'( X ) ) ) ) ), ~( hBOOL(
% 0.91/1.33 hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 1042, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1043, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1044, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.33 'v_sko__List__Xreplicate__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 1045, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.33 'v_sko__List__Xupt__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 1046, [ =( X, 'c_Suc'(
% 0.91/1.33 'c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1'( X ) ) ), =( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1047, [ =( 'c_Power_Opower__class_Opower'( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1048, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.33 'v_sko__Nat__Xnat__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 1049, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1050, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1051, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.33 'v_sko__Nat__Xnat__Xinducts__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 1052, [ =( X, 'c_Suc'(
% 0.91/1.33 'c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1'( X ) ) ), =( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1053, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ] )
% 0.91/1.33 , clause( 1054, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.91/1.33 , clause( 1055, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 0.91/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1056, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.91/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1057, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.91/1.33 , clause( 1058, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.91/1.33 , clause( 1059, [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.91/1.33 'tc_nat' ) ), Y ) ), =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 0.91/1.33 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1060, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.33 , X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y,
% 0.91/1.33 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1061, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.33 , X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1062, [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1063, [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1064, [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )
% 0.91/1.33 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1065, [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ] )
% 0.91/1.33 , clause( 1066, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 0.91/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.91/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.91/1.33 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.91/1.33 )
% 0.91/1.33 , clause( 1067, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.33 'tc_nat' ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.91/1.33 , clause( 1068, [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OVar'( X ),
% 0.91/1.33 'tc_Lambda_OdB' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1069, [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OVar'( X ) ),
% 0.91/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1070, [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.91/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 0.91/1.33 ), Y ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 0.91/1.33 'tc_Lambda_OdB' ) ) ] )
% 0.91/1.33 , clause( 1071, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.91/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'(
% 0.91/1.33 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.91/1.33 'c_Lambda_OdB_OApp', X ), Y ), Z ) ] )
% 0.91/1.33 , clause( 1072, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.91/1.33 'c_Lambda_OdB_OAbs'( Z ) ) ] )
% 0.91/1.33 , clause( 1073, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.33 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.91/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.91/1.33 , clause( 1074, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.33 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.91/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 0.91/1.33 , clause( 1075, [ 'c_Lambda_Obeta'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X
% 0.91/1.33 , Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~(
% 0.91/1.33 'c_Lambda_Obeta'( X, Z ) ) ] )
% 0.91/1.33 , clause( 1076, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 0.91/1.33 'c_Lambda_OdB_OAbs'( X ), Y ) ] )
% 0.91/1.33 , clause( 1077, [ 'c_Type_Otypings'( X, 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.91/1.33 'c_Lambda_Osubst', Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.91/1.33 'tc_nat', 'tc_Lambda_OdB' ) ), Z, 'tc_Lambda_OdB', 'tc_nat',
% 0.91/1.33 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 0.91/1.33 'c_Type_Otypings'( 'c_Type_Oshift'( X, Z, W, 'tc_Type_Otype' ), T, U ) )
% 0.91/1.33 , ~( 'c_Type_Otyping'( X, Y, W ) ) ] )
% 0.91/1.33 , clause( 1078, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.91/1.33 'c_Lambda_OdB_OVar'( X ) ), Y ), Z ), 'c_Lambda_OdB_OVar'( X ) ), ~(
% 0.91/1.33 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.91/1.33 , clause( 1079, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.91/1.33 'c_Lambda_OdB_OVar'( X ) ), Y ), Z ), 'c_Lambda_OdB_OVar'( X ) ), =( X, Z
% 0.91/1.33 ), 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ] )
% 0.91/1.33 , clause( 1080, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( hAPP(
% 0.91/1.33 hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y )
% 0.91/1.33 ] )
% 0.91/1.33 , clause( 1081, [ 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'(
% 0.91/1.33 'c_COMBC'( 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.33 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB',
% 0.91/1.33 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), ~( 'c_List_Olistsp'(
% 0.91/1.33 'c_InductTermi_OIT', X, 'tc_Lambda_OdB' ) ) ] )
% 0.91/1.33 , clause( 1082, [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.91/1.33 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.91/1.33 'tc_Lambda_OdB' ), X ) ) ] )
% 0.91/1.33 , clause( 1083, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.33 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.91/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.91/1.33 , clause( 1084, [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'(
% 0.91/1.33 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.91/1.33 , clause( 1085, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 0.91/1.33 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.91/1.33 , clause( 1086, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.91/1.33 'c_Lambda_OdB_OAbs'( X ) ), Y ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.33 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.91/1.33 , clause( 1087, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB',
% 0.91/1.33 'tc_Lambda_OdB' ) ) ), ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y,
% 0.91/1.33 'tc_Lambda_OdB' ) ) ] )
% 0.91/1.33 , clause( 1088, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.91/1.33 X ) ), Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.91/1.33 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.91/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.91/1.33 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB'
% 0.91/1.33 , 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.91/1.33 , clause( 1089, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ),
% 0.91/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_Olift', X ),
% 0.91/1.33 Z ), 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Z, 'tc_Lambda_OdB',
% 0.91/1.33 'tc_nat', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.91/1.33 , clause( 1090, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.91/1.33 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), T ), hAPP( hAPP(
% 0.91/1.33 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Z ), T ) )
% 0.91/1.33 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', Y ), Z ), T ) ) ) ] )
% 0.91/1.33 , clause( 1091, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y )
% 0.91/1.33 ) ), =( X, Y ) ] )
% 0.91/1.33 , clause( 1092, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.33 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.91/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.91/1.33 , clause( 1093, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.33 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.91/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 0.91/1.33 , clause( 1094, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.91/1.33 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y ) ] )
% 0.91/1.33 , clause( 1095, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 0.91/1.33 , clause( 1096, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 0.91/1.33 , clause( 1097, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.33 ) ) ) ] )
% 0.91/1.33 , clause( 1098, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.33 ) ) ) ] )
% 0.91/1.33 , clause( 1099, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.91/1.33 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ] )
% 0.91/1.33 , clause( 1100, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.91/1.33 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ] )
% 0.91/1.33 , clause( 1101, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 0.91/1.33 'c_Lambda_OdB_OVar'( X ), Y ) ] )
% 0.91/1.33 , clause( 1102, [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP(
% 0.91/1.33 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 0.91/1.33 , clause( 1103, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 0.91/1.33 , clause( 1104, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 0.91/1.33 , clause( 1105, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), T )
% 0.91/1.33 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP(
% 0.91/1.33 'c_Lambda_Osubst', X ), Z ), T ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.91/1.33 'c_Lambda_Osubst', Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.91/1.33 'tc_nat', 'tc_Lambda_OdB' ) ), T, 'tc_Lambda_OdB', 'tc_nat',
% 0.91/1.33 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB'
% 0.91/1.33 , 'tc_Lambda_OdB' ) ) ] )
% 0.91/1.33 , clause( 1106, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 0.91/1.33 ) ) ) ] )
% 0.91/1.33 , clause( 1107, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 0.91/1.33 ) ) ) ] )
% 0.91/1.33 , clause( 1108, [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X,
% 0.91/1.33 W ), Y ) ) ] )
% 0.91/1.33 , clause( 1109, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.91/1.33 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.91/1.33 , clause( 1110, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.91/1.33 'c_Lambda_OdB_OVar'( Z ) ) ) ] )
% 0.91/1.33 , clause( 1111, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_ra' ), 'v_s'
% 0.91/1.33 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_ss', 'tc_Lambda_OdB',
% 0.91/1.33 'tc_Lambda_OdB' ) ) ) ] )
% 0.91/1.33 , clause( 1112, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.91/1.33 hAPP( 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( X ) ) )
% 0.91/1.33 , 'c_Suc'( Y ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' ),
% 0.91/1.33 'c_Lambda_OdB_OVar'( X ) ), Y ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.91/1.33 ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.91/1.33 'c_Lambda_OdB_OVar'( X ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.91/1.33 'tc_nat', 'tc_Lambda_OdB' ) ), Y, 'tc_Lambda_OdB', 'tc_nat',
% 0.91/1.33 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.91/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.91/1.33 , clause( 1113, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_s' ) ) ] )
% 0.91/1.33 , clause( 1114, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 0.91/1.33 'c_Lambda_Osubst', 'v_s' ), 'c_Lambda_OdB_OVar'( X ) ), Y ) ) ) ] )
% 0.91/1.33 , clause( 1115, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.91/1.33 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.91/1.33 hAPP( 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' )
% 0.91/1.33 ) ), 'c_Suc'( 'v_ja' ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' )
% 0.95/1.34 , 'c_Lambda_OdB_OVar'( 'v_ia' ) ), 'v_ja' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.95/1.34 'tc_nat' ) ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.95/1.34 'c_Lambda_OdB_OVar'( 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.95/1.34 'tc_nat', 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat',
% 0.95/1.34 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.95/1.34 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.95/1.34 , clause( 1116, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.95/1.34 'class_Orderings_Opreorder'( Y ) ) ] )
% 0.95/1.34 , clause( 1117, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.95/1.34 'class_Orderings_Oorder'( Y ) ) ] )
% 0.95/1.34 , clause( 1118, [
% 0.95/1.34 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 0.95/1.34 )
% 0.95/1.34 , clause( 1119, [
% 0.95/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 0.95/1.34 )
% 0.95/1.34 , clause( 1120, [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.95/1.34 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1121, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.95/1.34 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1122, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.95/1.34 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1123, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.95/1.34 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1124, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 0.95/1.34 ] )
% 0.95/1.34 , clause( 1125, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 0.95/1.34 ] )
% 0.95/1.34 , clause( 1126, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 0.95/1.34 )
% 0.95/1.34 , clause( 1127, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ]
% 0.95/1.34 )
% 0.95/1.34 , clause( 1128, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 0.95/1.34 )
% 0.95/1.34 , clause( 1129, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1130, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1131, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1132, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1133, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ] )
% 0.95/1.34 , clause( 1134, [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1135, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1136, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1137, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1138, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1139, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1140, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1141, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1142, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1143, [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1144, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1145, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1146, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1147, [ 'class_Power_Opower'( 'tc_nat' ) ] )
% 0.95/1.35 , clause( 1148, [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X,
% 0.95/1.35 W ), Y ) ) ] )
% 0.95/1.35 , clause( 1149, [ =( 'c_COMBB'( X, Y, Z, T, U, W ), hAPP( X, hAPP( Y, Z ) )
% 0.95/1.35 ) ] )
% 0.95/1.35 , clause( 1150, [ 'c_fequal'( X, X, Y ) ] )
% 0.95/1.35 , clause( 1151, [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ] )
% 0.95/1.35 ] ).
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 eqswap(
% 0.95/1.35 clause( 1831, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.95/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y,
% 0.95/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.95/1.35 , clause( 1067, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.95/1.35 'tc_nat' ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.95/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.95/1.35 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 subsumption(
% 0.95/1.35 clause( 462, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.95/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y,
% 0.95/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.95/1.35 , clause( 1831, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.95/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y,
% 0.95/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.95/1.35 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.95/1.35 )] ) ).
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 paramod(
% 0.95/1.35 clause( 3187, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.95/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( hAPP( hAPP( hAPP(
% 0.95/1.35 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( X ) ) ),
% 0.95/1.35 'c_Suc'( Y ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' ),
% 0.95/1.35 'c_Lambda_OdB_OVar'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.95/1.35 , 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.95/1.35 'c_Lambda_OdB_OVar'( X ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.95/1.35 'tc_nat', 'tc_Lambda_OdB' ) ), Y, 'tc_Lambda_OdB', 'tc_nat',
% 0.95/1.35 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.95/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.95/1.35 , clause( 462, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.95/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y,
% 0.95/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.95/1.35 , 0, clause( 1112, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.95/1.35 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.95/1.35 hAPP( 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( X ) ) )
% 0.95/1.35 , 'c_Suc'( Y ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' ),
% 0.95/1.35 'c_Lambda_OdB_OVar'( X ) ), Y ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.95/1.35 ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.95/1.35 'c_Lambda_OdB_OVar'( X ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.95/1.35 'tc_nat', 'tc_Lambda_OdB' ) ), Y, 'tc_Lambda_OdB', 'tc_nat',
% 0.95/1.35 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.95/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.95/1.35 , 0, 5, substitution( 0, [ :=( X, hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.95/1.35 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( X ) ) ), 'c_Suc'( Y ) ) ), :=( Y
% 0.95/1.35 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' ), 'c_Lambda_OdB_OVar'( X )
% 0.95/1.35 ), Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 subsumption(
% 0.95/1.35 clause( 496, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.95/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( hAPP( hAPP( hAPP(
% 0.95/1.35 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( X ) ) ),
% 0.95/1.35 'c_Suc'( Y ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' ),
% 0.95/1.35 'c_Lambda_OdB_OVar'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.95/1.35 , 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.95/1.35 'c_Lambda_OdB_OVar'( X ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.95/1.35 'tc_nat', 'tc_Lambda_OdB' ) ), Y, 'tc_Lambda_OdB', 'tc_nat',
% 0.95/1.35 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.95/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.95/1.35 , clause( 3187, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.95/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( hAPP( hAPP( hAPP(
% 0.95/1.35 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( X ) ) ),
% 0.95/1.35 'c_Suc'( Y ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' ),
% 0.95/1.35 'c_Lambda_OdB_OVar'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.95/1.35 , 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.95/1.35 'c_Lambda_OdB_OVar'( X ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.95/1.35 'tc_nat', 'tc_Lambda_OdB' ) ), Y, 'tc_Lambda_OdB', 'tc_nat',
% 0.95/1.35 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.95/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.95/1.35 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.95/1.35 )] ) ).
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 paramod(
% 0.95/1.35 clause( 4547, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.95/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( hAPP( hAPP( hAPP(
% 0.95/1.35 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' ) ) ),
% 0.95/1.35 'c_Suc'( 'v_ja' ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' ),
% 0.95/1.35 'c_Lambda_OdB_OVar'( 'v_ia' ) ), 'v_ja' ), 'c_HOL_Ozero__class_Ozero'(
% 0.95/1.35 'tc_nat' ) ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.95/1.35 'c_Lambda_OdB_OVar'( 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.95/1.35 'tc_nat', 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat',
% 0.95/1.35 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.95/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.95/1.35 , clause( 462, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.95/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y,
% 0.95/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.95/1.35 , 0, clause( 1115, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.95/1.35 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.95/1.35 hAPP( 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' )
% 0.95/1.35 ) ), 'c_Suc'( 'v_ja' ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' )
% 0.95/1.35 , 'c_Lambda_OdB_OVar'( 'v_ia' ) ), 'v_ja' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.95/1.35 'tc_nat' ) ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.95/1.35 'c_Lambda_OdB_OVar'( 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.95/1.35 'tc_nat', 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat',
% 0.95/1.35 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.95/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.95/1.35 , 0, 6, substitution( 0, [ :=( X, hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.95/1.35 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' ) ) ), 'c_Suc'( 'v_ja' ) )
% 0.95/1.35 ), :=( Y, hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' ),
% 0.95/1.35 'c_Lambda_OdB_OVar'( 'v_ia' ) ), 'v_ja' ) )] ), substitution( 1, [] )
% 0.95/1.35 ).
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 resolution(
% 0.95/1.35 clause( 4548, [] )
% 0.95/1.35 , clause( 4547, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.95/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( hAPP( hAPP( hAPP(
% 0.95/1.35 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( 'v_ia' ) ) ),
% 0.95/1.35 'c_Suc'( 'v_ja' ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' ),
% 0.95/1.35 'c_Lambda_OdB_OVar'( 'v_ia' ) ), 'v_ja' ), 'c_HOL_Ozero__class_Ozero'(
% 0.95/1.35 'tc_nat' ) ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.95/1.35 'c_Lambda_OdB_OVar'( 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.95/1.35 'tc_nat', 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat',
% 0.95/1.35 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.95/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.95/1.35 , 0, clause( 496, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.95/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( hAPP( hAPP( hAPP(
% 0.95/1.35 'c_Lambda_Osubst', 'v_ra' ), 'c_Lambda_OdB_OVar'( 'c_Suc'( X ) ) ),
% 0.95/1.35 'c_Suc'( Y ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_s' ),
% 0.95/1.35 'c_Lambda_OdB_OVar'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.95/1.35 , 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst',
% 0.95/1.35 'c_Lambda_OdB_OVar'( X ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.95/1.35 'tc_nat', 'tc_Lambda_OdB' ) ), Y, 'tc_Lambda_OdB', 'tc_nat',
% 0.95/1.35 'tc_Lambda_OdB' ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.95/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.95/1.35 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_ia' ), :=( Y,
% 0.95/1.35 'v_ja' )] )).
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 subsumption(
% 0.95/1.35 clause( 499, [] )
% 0.95/1.35 , clause( 4548, [] )
% 0.95/1.35 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 end.
% 0.95/1.35
% 0.95/1.35 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.95/1.35
% 0.95/1.35 Memory use:
% 0.95/1.35
% 0.95/1.35 space for terms: 34557
% 0.95/1.35 space for clauses: 49598
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 clauses generated: 615
% 0.95/1.35 clauses kept: 500
% 0.95/1.35 clauses selected: 0
% 0.95/1.35 clauses deleted: 0
% 0.95/1.35 clauses inuse deleted: 0
% 0.95/1.35
% 0.95/1.35 subsentry: 18246
% 0.95/1.35 literals s-matched: 7039
% 0.95/1.35 literals matched: 6945
% 0.95/1.35 full subsumption: 1422
% 0.95/1.35
% 0.95/1.35 checksum: -1622441386
% 0.95/1.35
% 0.95/1.35
% 0.95/1.35 Bliksem ended
%------------------------------------------------------------------------------