TSTP Solution File: SWV885-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV885-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.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 : Wed Jul 20 16:29:02 EDT 2022
% Result : Timeout 300.02s 300.49s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV885-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Tue Jun 14 18:54:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.33/1.68 *** allocated 10000 integers for termspace/termends
% 1.33/1.68 *** allocated 10000 integers for clauses
% 1.33/1.68 *** allocated 10000 integers for justifications
% 1.33/1.68 *** allocated 15000 integers for termspace/termends
% 1.33/1.68 *** allocated 22500 integers for termspace/termends
% 1.33/1.68 *** allocated 33750 integers for termspace/termends
% 1.33/1.68 Bliksem 1.12
% 1.33/1.68
% 1.33/1.68
% 1.33/1.68 Automatic Strategy Selection
% 1.33/1.68
% 1.33/1.68 Clauses:
% 1.33/1.68 [
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ), X, 'tc_nat' ) ],
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 X, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.33/1.68 'tc_nat' ), X, 'tc_nat' ) ],
% 1.33/1.68 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.33/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.33/1.68 'tc_nat' ) ],
% 1.33/1.68 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ) ],
% 1.33/1.68 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z
% 1.33/1.68 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.33/1.68 ) ) ), =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) )
% 1.33/1.68 , X ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.33/1.68 , Y, X ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.33/1.68 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.33/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.33/1.68 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.33/1.68 , Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.33/1.68 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.33/1.68 , T, X ), X ), T, X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ 'c_Finite__Set_Ofinite'( 'c_Set_Ovimage'( X, Y, Z, T ), Z ), ~(
% 1.33/1.68 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), Z, T ) ), ~( 'c_Finite__Set_Ofinite'( Y, T ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.33/1.68 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.33/1.68 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.33/1.68 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.33/1.68 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.33/1.68 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.33/1.68 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.33/1.68 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.33/1.68 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.33/1.68 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.33/1.68 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.33/1.68 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.33/1.68 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.33/1.68 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 1.33/1.68 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.33/1.68 ), 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.33/1.68 ), 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.33/1.68 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 1.33/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.68 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.33/1.68 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 Y, Z, X ), T, X ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.33/1.68 X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 Y, Z, X ), T, X ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.33/1.68 X ), X ) ) ],
% 1.33/1.68 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.33/1.68 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.33/1.68 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.33/1.68 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.33/1.68 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.33/1.68 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ) ), =( Y, Z ) ],
% 1.33/1.68 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.33/1.68 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.33/1.68 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.33/1.68 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.33/1.68 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.33/1.68 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.33/1.68 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.33/1.68 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 1.33/1.68 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.33/1.68 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.33/1.68 , Y, X ), X ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.33/1.68 , Z, X ), X ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.33/1.68 , Z, X ), X ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.33/1.68 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.33/1.68 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.33/1.68 , X, 'tc_nat' ), X ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.33/1.68 ), 'tc_nat' ), X ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.68 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool'
% 1.33/1.68 ) ), ~( 'c_in'( Y, X, Z ) ), 'c_in'( Y, T, Z ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, T, Z ), 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.33/1.68 , 'tc_bool' ) ), ~( 'c_in'( Y, X, T ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.33/1.68 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ), 'c_in'( Y, Z, T ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.33/1.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 1.33/1.68 [ 'c_Fun_Oinj__on'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T,
% 1.33/1.68 'tc_bool' ) ), T, U ), ~( 'c_Fun_Oinj__on'( X, Y, T, U ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.33/1.68 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.33/1.68 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.33/1.68 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.33/1.68 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.33/1.68 [ =( 'c_Set_Ovimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T
% 1.33/1.68 , 'tc_bool' ) ), U, T ), 'c_HOL_Ominus__class_Ominus'( 'c_Set_Ovimage'( X
% 1.33/1.68 , Y, U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) )
% 1.33/1.68 ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.33/1.68 , 'tc_bool' ) ), ~( 'c_in'( Y, X, T ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.33/1.68 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.68 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 1.33/1.68 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.33/1.68 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.33/1.68 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.33/1.68 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 1.33/1.68 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.33/1.68 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.33/1.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.33/1.68 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.33/1.68 , X ), W, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.33/1.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.33/1.68 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.33/1.68 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.33/1.68 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.33/1.68 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.33/1.68 [ =( 'c_Set_Ovimage'( X, 'c_Set_Oimage'( X, Y, Z, T ), Z, T ), Y ), ~(
% 1.33/1.68 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), Z, T ) ) ],
% 1.33/1.68 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.33/1.68 'tc_bool' ) ), Z, Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 1.33/1.68 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ),
% 1.33/1.68 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.33/1.68 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 1.33/1.68 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.33/1.68 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.33/1.68 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.33/1.68 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.33/1.68 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 1.33/1.68 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.33/1.68 ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.33/1.68 ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 1.33/1.68 Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.33/1.68 ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.33/1.68 , T, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.33/1.68 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.33/1.68 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.33/1.68 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.33/1.68 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 X, Y, 'tc_nat' ) ), X, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 1.33/1.68 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.33/1.68 ), 'tc_nat' ) ) ],
% 1.33/1.68 [ =( hAPP( 'c_Hilbert__Choice_Oinv__into'( X, Y, Z, T ), hAPP( Y, U ) )
% 1.33/1.68 , U ), ~( 'c_in'( U, X, Z ) ), ~( 'c_Fun_Oinj__on'( Y, X, Z, T ) ) ],
% 1.33/1.68 [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_Fun_Oinj__on'( T, Y, Z, U ) ), =( hAPP(
% 1.33/1.68 'c_Hilbert__Choice_Oinv__into'( Y, T, Z, U ), hAPP( T, X ) ), X ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.33/1.68 ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 1.33/1.68 X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.33/1.68 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.33/1.68 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.33/1.68 ) ) ) ],
% 1.33/1.68 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.33/1.68 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.33/1.68 ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.33/1.68 X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.33/1.68 X ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 X, T, 'tc_nat' ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.33/1.68 X ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.33/1.68 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 1.33/1.68 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( =( 'c_Finite__Set_Ocard'( X, Y ), 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =(
% 1.33/1.68 'c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2'( X,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y ),
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.33/1.68 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_Set_Oimage'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y
% 1.33/1.68 , Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oimage'( X, Y, T, U
% 1.33/1.68 ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ), ~(
% 1.33/1.68 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T,
% 1.33/1.68 'tc_bool' ) ), T, U ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.33/1.68 , T, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.68 , Z, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.33/1.68 , T, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.68 , Z, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.33/1.68 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.33/1.68 , T, X ), X ), T, X ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.33/1.68 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.68 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ), X ) ],
% 1.33/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_fun'( Y, 'tc_bool' ) ),
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.33/1.68 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.33/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.33/1.68 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.33/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.33/1.68 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.33/1.68 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.33/1.68 , X ), W, X ), X ) ) ],
% 1.33/1.68 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.33/1.68 'c_Finite__Set_Olinorder__class_OMax'( 'c_Set_Oinsert'( Y,
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.33/1.68 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 1.33/1.68 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.33/1.68 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.68 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.68 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.33/1.68 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.68 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 X ), T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.33/1.68 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.68 , Z, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.33/1.68 , T, X ), X ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.33/1.68 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_Fun_Oinj__on'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.33/1.68 'tc_bool' ) ), Y, Z ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 'c_Suc'( X ), 'tc_nat' ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 'c_Suc'( X ), 'tc_nat' ) ],
% 1.33/1.68 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 1.33/1.68 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 1.33/1.68 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.33/1.68 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.33/1.68 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.33/1.68 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'c_Set_Oinsert'( X,
% 1.33/1.68 Y, Z ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 1.33/1.68 ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ =( 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T
% 1.33/1.68 , 'tc_bool' ) ), T, U ), 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oimage'( X
% 1.33/1.68 , Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ),
% 1.33/1.68 ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T,
% 1.33/1.68 'tc_bool' ) ), T, U ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 1.33/1.68 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 1.33/1.68 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 1.33/1.68 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.33/1.68 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.33/1.68 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.33/1.68 X ) ) ), =( Z, T ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.33/1.68 X ) ) ), =( Z, T ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.33/1.68 X ) ) ), =( Y, T ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~( 'c_lessequals'( Z,
% 1.33/1.68 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.33/1.68 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.33/1.68 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.33/1.68 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.33/1.68 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.33/1.68 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.33/1.68 X ), X ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.33/1.68 , 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.33/1.68 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.68 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.33/1.68 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool'
% 1.33/1.68 ) ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.33/1.68 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.33/1.68 [ =( 'c_Set_Oimage'( 'c_Hilbert__Choice_Oinv__into'(
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, X, Z ),
% 1.33/1.68 'c_Set_Oimage'( Y, T, X, Z ), Z, X ), T ), ~( 'c_Fun_Oinj__on'( Y,
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X, Z ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ =( 'c_Set_Oimage'( 'c_Hilbert__Choice_Oinv__into'(
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, X, Z ),
% 1.33/1.68 'c_Set_Oimage'( Y, T, X, Z ), Z, X ), T ), ~( 'c_Fun_Oinj__on'( Y,
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X, Z ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 1.33/1.68 Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 1.33/1.68 ) ) ) ],
% 1.33/1.68 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.33/1.68 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 1.33/1.68 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.33/1.68 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.33/1.68 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.33/1.68 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 'c_Finite__Set_Ocard'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.33/1.68 'tc_bool' ) ), X ), 'tc_nat' ) ) ],
% 1.33/1.68 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.33/1.68 'c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1'( X ) ) ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 1.33/1.68 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.33/1.68 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.33/1.68 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.33/1.68 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.68 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.68 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 X ), T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.33/1.68 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 1.33/1.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 1.33/1.68 W, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.33/1.68 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.33/1.68 , X ), T, X ), W, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.33/1.68 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 1.33/1.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 1.33/1.68 W, X ), X ) ) ],
% 1.33/1.68 [ ~( =( 'c_Finite__Set_Ocard'( X, Y ), 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =(
% 1.33/1.68 'c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2'( X,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y ),
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_Fun_Ofun__upd'( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), W, V0, T, U
% 1.33/1.68 ), 'c_Fun_Ofun__upd'( 'c_Fun_Ofun__upd'( X, W, V0, T, U ), Y, Z, T, U )
% 1.33/1.68 ), =( Y, W ) ],
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.68 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.33/1.68 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 1.33/1.68 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 1.33/1.68 Z, X ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.33/1.68 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.33/1.68 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_Fun_Oinj__on'( X,
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T, 'tc_bool' ) ), T, U ) ), =(
% 1.33/1.68 Y, Z ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.33/1.68 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.33/1.68 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.33/1.68 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.33/1.68 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 'c_Finite__Set_Ocard'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.33/1.68 'tc_bool' ) ), X ), 'tc_nat' ), ~( 'c_Finite__Set_Ofinite'(
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.33/1.68 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.33/1.68 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.33/1.68 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), Y,
% 1.33/1.68 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.33/1.68 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.33/1.68 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.33/1.68 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.33/1.68 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.33/1.68 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.33/1.68 , T ), =( X, Z ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.33/1.68 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.33/1.68 , T ), =( X, Z ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.33/1.68 'c_Finite__Set_Olinorder__class_OMin'( 'c_Set_Oinsert'( Y,
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Obot__class_Obot'(
% 1.33/1.68 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'( X, 'tc_bool' ) ),
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z, T ) ) ),
% 1.33/1.68 ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), Z, T ) ), =( Y, U ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.33/1.68 ), X ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Z,
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Y,
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.33/1.68 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 1.33/1.68 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 1.33/1.68 X ), Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 , X ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 1.33/1.68 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.33/1.68 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 1.33/1.68 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.33/1.68 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 1.33/1.68 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.33/1.68 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.33/1.68 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.33/1.68 ) ), Y ) ) ) ],
% 1.33/1.68 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 1.33/1.68 T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 1.33/1.68 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 1.33/1.68 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T,
% 1.33/1.68 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.33/1.68 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( =( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.68 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ), =( X
% 1.33/1.68 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ hBOOL( hAPP( X, Y ) ), 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1'( X, Z ), Z, 'tc_nat' ), ~(
% 1.33/1.68 hBOOL( hAPP( X, Z ) ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_Fun_Ofun__upd'( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), Y, W, T, U )
% 1.33/1.68 , 'c_Fun_Ofun__upd'( X, Y, W, T, U ) ) ],
% 1.33/1.68 [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_in'( X, T, Z ) ), ~( =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( X ), X ), Y ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( X ), Y, X ), Y ) ],
% 1.33/1.68 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.33/1.68 X, 'tc_bool' ) ), Y ) ],
% 1.33/1.68 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.33/1.68 'tc_bool' ) ), X ) ],
% 1.33/1.68 [ =( 'c_Set_Oimage'( X, 'c_Set_Ovimage'( X, Y, Z, T ), Z, T ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, 'c_Set_Oimage'( X,
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ),
% 1.33/1.68 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.33/1.68 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.33/1.68 , Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y,
% 1.33/1.68 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.33/1.68 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.33/1.68 , Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.33/1.68 , Y, X ) ) ],
% 1.33/1.68 [ hBOOL( hAPP( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' )
% 1.33/1.68 ), Y ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.33/1.68 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.33/1.68 ), =( Z, Y ) ],
% 1.33/1.68 [ =( 'c_Finite__Set_Ocard'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X
% 1.33/1.68 , 'tc_bool' ) ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 'c_Finite__Set_Ocard'( X, Y ), 'tc_nat' ), ~( 'c_Finite__Set_Ofinite'( X
% 1.33/1.68 , Y ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.33/1.68 ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.68 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.33/1.68 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.33/1.68 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.68 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.33/1.68 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.33/1.68 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.33/1.68 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.33/1.68 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 1.33/1.68 'tc_bool' ) ), Y ) ) ) ],
% 1.33/1.68 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.33/1.68 'tc_bool' ) ), Y ) ) ) ],
% 1.33/1.68 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 1.33/1.68 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( =( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), X ) ), =( hAPP( X, Y ), Z )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.33/1.68 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.33/1.68 ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.33/1.68 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.33/1.68 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.33/1.68 , X ), X ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.33/1.68 , X ), X ) ],
% 1.33/1.68 [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ), U, 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), ~( 'c_lessequals'( Y, 'c_Set_Oimage'( X, U, Z, T ),
% 1.33/1.68 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X,
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.33/1.68 , X, 'tc_nat' ), X ) ],
% 1.33/1.68 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.33/1.68 ), 'tc_nat' ), X ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.33/1.68 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.33/1.68 ), X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.33/1.68 ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), X, 'tc_nat' ), Y,
% 1.33/1.68 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.33/1.68 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.33/1.68 [ =( 'c_Set_Ovimage'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y
% 1.33/1.68 , Z, 'tc_fun'( T, 'tc_bool' ) ), U, T ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Ovimage'( X, Y, U, T
% 1.33/1.68 ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_in'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z,
% 1.33/1.68 'tc_fun'( T, 'tc_bool' ) ), T ), ~( 'c_in'( X, Z, T ) ), ~( 'c_in'( X, Y
% 1.33/1.68 , T ) ) ],
% 1.33/1.68 [ 'c_in'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z,
% 1.33/1.68 'tc_fun'( T, 'tc_bool' ) ), T ), ~( 'c_in'( X, Z, T ) ), ~( 'c_in'( X, Y
% 1.33/1.68 , T ) ) ],
% 1.33/1.68 [ ~( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' )
% 1.33/1.68 ), Y ) ) ],
% 1.33/1.68 [ hBOOL( hAPP( X, Y ) ), ~( 'c_in'( Y, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.68 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 1.33/1.68 [ ~( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' )
% 1.33/1.68 ), Y ) ) ],
% 1.33/1.68 [ ~( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' )
% 1.33/1.68 ), Y ) ) ],
% 1.33/1.68 [ 'c_in'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.33/1.68 , Y ) ],
% 1.33/1.68 [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_in'( X, 'c_HOL_Ominus__class_Ominus'( T
% 1.33/1.68 , Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 1.33/1.68 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X, 'c_HOL_Ominus__class_Ominus'( Y, T,
% 1.33/1.68 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 1.33/1.68 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X, T, Z ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), Z ) ) ],
% 1.33/1.68 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), Z ) ) ],
% 1.33/1.68 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_in'( Z, T, U ) ), ~(
% 1.33/1.68 'c_in'( Y, T, U ) ), =( Y, Z ), ~( 'c_Fun_Oinj__on'( X, T, U, W ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_in'( Z, T, U ) ), ~(
% 1.33/1.68 'c_in'( Y, T, U ) ), ~( 'c_Fun_Oinj__on'( X, T, U, W ) ), =( Y, Z ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_in'( Z, T, U ) ), ~(
% 1.33/1.68 'c_in'( Y, T, U ) ), ~( 'c_Fun_Oinj__on'( X, T, U, W ) ), =( Y, Z ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_Fun_Oinj__on'( X, T, U, W
% 1.33/1.68 ) ), =( Y, Z ), ~( 'c_in'( Z, T, U ) ), ~( 'c_in'( Y, T, U ) ) ],
% 1.33/1.68 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( 'c_in'( Y,
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 1.33/1.68 [ 'c_in'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T, 'tc_bool'
% 1.33/1.68 ) ), T ), 'c_in'( X, Z, T ), ~( 'c_in'( X, Y, T ) ) ],
% 1.33/1.68 [ 'c_in'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T, 'tc_bool'
% 1.33/1.68 ) ), T ), 'c_in'( X, Z, T ), ~( 'c_in'( X, Y, T ) ) ],
% 1.33/1.68 [ 'c_in'( X, 'c_Set_Ovimage'( Y, Z, T, U ), T ), ~( 'c_in'( hAPP( Y, X )
% 1.33/1.68 , Z, U ) ) ],
% 1.33/1.68 [ 'c_in'( X, 'c_Set_Ovimage'( Y, Z, T, U ), T ), ~( 'c_in'( hAPP( Y, X )
% 1.33/1.68 , Z, U ) ) ],
% 1.33/1.68 [ 'c_in'( X, 'c_Set_Ovimage'( Y, Z, T, U ), T ), ~( 'c_in'( hAPP( Y, X )
% 1.33/1.68 , Z, U ) ) ],
% 1.33/1.68 [ 'c_in'( hAPP( X, Y ), Z, T ), ~( 'c_in'( Y, 'c_Set_Ovimage'( X, Z, U,
% 1.33/1.68 T ), U ) ) ],
% 1.33/1.68 [ 'c_in'( hAPP( X, Y ), Z, T ), ~( 'c_in'( Y, 'c_Set_Ovimage'( X, Z, U,
% 1.33/1.68 T ), U ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.33/1.68 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.33/1.68 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.33/1.68 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.33/1.68 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.33/1.68 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.33/1.68 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.33/1.68 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.33/1.68 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.33/1.68 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.33/1.68 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.33/1.68 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.33/1.68 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.33/1.68 ) ) ],
% 1.33/1.68 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), 'c_lessequals'(
% 1.33/1.68 Y, 'c_Inductive_Ocomplete__lattice__class_Ogfp'( Z, X ), X ), ~(
% 1.33/1.68 'c_lessequals'( Y, hAPP( Z, Y ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Otop'( X ) ), 'c_lessequals'( Y,
% 1.33/1.68 'c_Orderings_Otop__class_Otop'( X ), X ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.33/1.68 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.33/1.68 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.33/1.68 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.33/1.68 ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.33/1.68 ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.33/1.68 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.33/1.68 X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.33/1.68 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.33/1.68 ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.33/1.68 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.33/1.68 X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.33/1.68 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.33/1.68 ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.33/1.68 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.33/1.68 ) ],
% 1.33/1.68 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.33/1.68 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.33/1.68 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.33/1.68 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.68 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.33/1.68 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.33/1.68 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.33/1.68 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.33/1.68 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 1.33/1.68 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.33/1.68 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.33/1.68 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.33/1.68 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.33/1.68 ) ],
% 1.33/1.68 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 1.33/1.68 'tc_nat' ), 'tc_nat' ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.33/1.68 [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.68 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.33/1.68 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.68 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.33/1.68 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.33/1.68 'c_SetInterval_Oord__class_OatLeast'( Y, X ),
% 1.33/1.68 'c_SetInterval_Oord__class_OatLeast'( Z, X ) ) ), =( Y, Z ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.33/1.68 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 1.33/1.68 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_Fun_Ofun__upd'( X, Y, hAPP( X, Y ), Z, T ), X ) ],
% 1.33/1.68 [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), Y ), Z ) ],
% 1.33/1.68 [ =( 'c_Fun_Ofun__upd'( X, Y, hAPP( X, Y ), Z, T ), X ) ],
% 1.33/1.68 [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), Y ), Z ) ],
% 1.33/1.68 [ =( 'c_Fun_Ofun__upd'( X, Y, hAPP( X, Y ), Z, T ), X ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.33/1.68 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.33/1.68 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.33/1.68 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.33/1.68 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.33/1.68 , Z, 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.33/1.68 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.33/1.68 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.33/1.68 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.33/1.68 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.68 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.33/1.68 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.33/1.68 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.33/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.33/1.68 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.33/1.68 X ) ],
% 1.33/1.68 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Orderings_Otop__class_Otop'(
% 1.33/1.68 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ),
% 1.33/1.68 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.68 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.33/1.68 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.33/1.68 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.33/1.68 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.33/1.68 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.68 , X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.33/1.68 ) ), X, 'tc_nat' ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.33/1.68 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.33/1.68 ) ), X, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.33/1.68 , X ), Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.33/1.68 , X ), Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.33/1.68 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.33/1.68 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.33/1.68 ,
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.33/1.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.33/1.68 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.33/1.68 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.33/1.68 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.33/1.68 'tc_bool' ) ) ) ],
% 1.33/1.68 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.68 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.33/1.68 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.33/1.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.33/1.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.33/1.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.33/1.68 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.68 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.33/1.68 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.33/1.68 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.33/1.68 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.33/1.68 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.33/1.68 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.33/1.68 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.33/1.68 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.68 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 1.33/1.68 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 1.33/1.68 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 1.33/1.69 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.33/1.69 , Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.69 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.33/1.69 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.33/1.69 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.33/1.69 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.69 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.33/1.69 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.33/1.69 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.33/1.69 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.33/1.69 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.33/1.69 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.33/1.69 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.33/1.69 ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.33/1.69 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.33/1.69 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 1.33/1.69 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.69 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.69 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.33/1.69 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.33/1.69 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 1.33/1.69 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 1.33/1.69 'tc_bool' ) ), X ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.33/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 Y, T, X ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.33/1.69 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 Y, T, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.33/1.69 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.33/1.69 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.33/1.69 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.33/1.69 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.33/1.69 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.33/1.69 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.33/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.33/1.69 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.33/1.69 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 1.33/1.69 'c_lessequals'( Y, Z, X ) ) ],
% 1.33/1.69 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 1.33/1.69 'c_lessequals'( Y, Z, X ) ],
% 1.33/1.69 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 1.33/1.69 'c_lessequals'( Z, Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.33/1.69 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.69 Z, T, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.33/1.69 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.69 T, Z, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 1.33/1.69 'c_lessequals'( Y, T, X ) ) ],
% 1.33/1.69 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 1.33/1.69 'c_lessequals'( Z, T, X ) ) ],
% 1.33/1.69 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.33/1.69 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.69 Z, T, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.33/1.69 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.69 T, Z, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 1.33/1.69 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.33/1.69 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.33/1.69 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.33/1.69 , X ), T, X ), W, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.33/1.69 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 1.33/1.69 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.33/1.69 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.33/1.69 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.33/1.69 , X ), W, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_in'(
% 1.33/1.69 'c_Finite__Set_Olinorder__class_OMin'( Y, X ), Y, X ), =( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_in'(
% 1.33/1.69 'c_Finite__Set_Olinorder__class_OMax'( Y, X ), Y, X ), =( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.33/1.69 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.33/1.69 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.33/1.69 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.33/1.69 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.33/1.69 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.33/1.69 X ), Z, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.33/1.69 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.33/1.69 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.69 ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.33/1.69 ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.69 ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.69 ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 1.33/1.69 ), Y ) ],
% 1.33/1.69 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.33/1.69 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.33/1.69 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.69 ) ), =( Y, Z ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.69 ) ), =( Y, Z ) ],
% 1.33/1.69 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.33/1.69 , T, X ), X ), T, X ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.33/1.69 ), Y ) ],
% 1.33/1.69 [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.33/1.69 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y ), ~( 'c_in'( X, Y
% 1.33/1.69 , Z ) ) ],
% 1.33/1.69 [ =( hAPP( X, Y ), Z ), ~( 'c_in'( Y, 'c_Set_Ovimage'( X,
% 1.33/1.69 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ), T ), U, T ), U ) ) ],
% 1.33/1.69 [ 'c_in'( X, 'c_Set_Ovimage'( Y, 'c_Set_Oinsert'( hAPP( Y, X ),
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), T, Z ),
% 1.33/1.69 T ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ),
% 1.33/1.69 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Y ), 'c_in'( X, Y, Z ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.33/1.69 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.33/1.69 'tc_bool' ) ), X ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.33/1.69 Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ), Y ) ),
% 1.33/1.69 ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.33/1.69 Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.69 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z )
% 1.33/1.69 ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.69 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z )
% 1.33/1.69 ) ],
% 1.33/1.69 [ 'c_Fun_Oinj__on'( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), W, T, U ),
% 1.33/1.69 'c_in'( Z, 'c_Set_Oimage'( X, W, T, U ), U ), ~( 'c_Fun_Oinj__on'( X, W,
% 1.33/1.69 T, U ) ) ],
% 1.33/1.69 [ 'c_in'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ), ~( 'c_in'( Y
% 1.33/1.69 , Z, T ) ), ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'(
% 1.33/1.69 'tc_fun'( T, 'tc_bool' ) ), T, U ) ) ],
% 1.33/1.69 [ 'c_in'( X, Y, Z ), ~( 'c_in'( hAPP( T, X ), 'c_Set_Oimage'( T, Y, Z, U
% 1.33/1.69 ), U ) ), ~( 'c_Fun_Oinj__on'( T, 'c_Orderings_Otop__class_Otop'(
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), Z, U ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.33/1.69 , 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.33/1.69 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.69 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool'
% 1.33/1.69 ) ) ), 'c_in'( Y, Z, T ) ],
% 1.33/1.69 [ =( 'c_Set_Oimage'( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), W, T, U ),
% 1.33/1.69 'c_Set_Oinsert'( Z, 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( W,
% 1.33/1.69 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ), T, U ), U ) ), ~( 'c_in'(
% 1.33/1.69 Y, W, T ) ) ],
% 1.33/1.69 [ 'c_Fun_Oinj__on'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ), 'c_in'( hAPP(
% 1.33/1.69 X, Y ), 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Z,
% 1.33/1.69 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ), T, U ), U ), ~(
% 1.33/1.69 'c_Fun_Oinj__on'( X, Z, T, U ) ) ],
% 1.33/1.69 [ ~( 'c_in'( hAPP( X, Y ), 'c_Set_Oimage'( X,
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Z, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.33/1.69 T, 'tc_bool' ) ), T, U ), U ) ), ~( 'c_Fun_Oinj__on'( X, 'c_Set_Oinsert'(
% 1.33/1.69 Y, Z, T ), T, U ) ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 1.33/1.69 ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.33/1.69 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.33/1.69 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.33/1.69 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.33/1.69 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.33/1.69 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.33/1.69 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.33/1.69 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.33/1.69 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.33/1.69 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.33/1.69 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.33/1.69 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.33/1.69 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.33/1.69 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 1.33/1.69 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.33/1.69 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 1.33/1.69 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.33/1.69 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 1.33/1.69 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.33/1.69 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 1.33/1.69 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.33/1.69 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 1.33/1.69 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.33/1.69 , Z ), 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.33/1.69 'c_Set_Oinsert'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 1.33/1.69 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 1.33/1.69 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 1.33/1.69 'c_Set_Oinsert'( U, Y, Z ), Z, T ) ) ],
% 1.33/1.69 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.33/1.69 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 1.33/1.69 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.33/1.69 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.33/1.69 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 1.33/1.69 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.33/1.69 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( Y, Z, 'tc_fun'( T, X ) ),
% 1.33/1.69 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_fun'( T, X ) ) ) ],
% 1.33/1.69 [ ~( 'class_HOL_Oord'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_fun'(
% 1.33/1.69 T, X ) ), 'c_lessequals'( Z, Y, 'tc_fun'( T, X ) ), ~( 'c_lessequals'( Y
% 1.33/1.69 , Z, 'tc_fun'( T, X ) ) ) ],
% 1.33/1.69 [ ~( 'class_HOL_Oord'( X ) ), ~( 'c_lessequals'( Y, Z, 'tc_fun'( T, X )
% 1.33/1.69 ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_fun'( T, X ) ) ) ],
% 1.33/1.69 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) )
% 1.33/1.69 , ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.33/1.69 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.33/1.69 X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.33/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 Z, T, X ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.33/1.69 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 Z, T, X ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.33/1.69 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.33/1.69 X ), X ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.33/1.69 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.33/1.69 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.33/1.69 , Y ) ) ],
% 1.33/1.69 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.69 'tc_nat' ) ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.33/1.69 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.69 [ =( hAPP( 'c_Hilbert__Choice_Oinv__into'(
% 1.33/1.69 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, X, Z ),
% 1.33/1.69 hAPP( Y, T ) ), T ), ~( 'c_Fun_Oinj__on'( Y,
% 1.33/1.69 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X, Z ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.33/1.69 'tc_bool' ) ), Y, Z ) ), =( hAPP( 'c_Hilbert__Choice_Oinv__into'(
% 1.33/1.69 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), X, Y, Z ),
% 1.33/1.69 hAPP( X, T ) ), T ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.33/1.69 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 1.33/1.69 Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.33/1.69 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.33/1.69 , 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 1.33/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.33/1.69 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.33/1.69 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.33/1.69 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.69 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.33/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.33/1.69 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 1.33/1.69 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.33/1.69 ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.69 , Y, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.33/1.69 , T, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.33/1.69 , T, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.33/1.69 , Y, X ), X ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP( 'c_Set_Ovimage'( Y,
% 1.33/1.69 X, T, U ), Z ) ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~( hBOOL( hAPP( Y,
% 1.33/1.69 hAPP( X, U ) ) ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.33/1.69 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.33/1.69 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.33/1.69 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.33/1.69 'tc_nat' ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 1.33/1.69 hAPP( X, T ) ) ) ],
% 1.33/1.69 [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), W ), hAPP( X, W ) ), =( W
% 1.33/1.69 , Y ) ],
% 1.33/1.69 [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), W ), hAPP( X, W ) ), =( W
% 1.33/1.69 , Y ) ],
% 1.33/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.33/1.69 ) ) ],
% 1.33/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.33/1.69 ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.33/1.69 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 1.33/1.69 ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.33/1.69 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.33/1.69 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.33/1.69 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.33/1.69 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.33/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.33/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.33/1.69 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.33/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.33/1.69 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.33/1.69 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.33/1.69 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.33/1.69 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 1.33/1.69 , X ) ) ],
% 1.33/1.69 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 1.33/1.69 , X ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.33/1.69 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ) ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.33/1.69 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.33/1.69 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.33/1.69 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.33/1.69 T, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.33/1.69 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.33/1.69 X ), Z, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.33/1.69 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.33/1.69 T, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.33/1.69 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.33/1.69 X ), T, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.33/1.69 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.33/1.69 T, X ), X ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.33/1.69 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.33/1.69 X ), T, X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.33/1.69 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.33/1.69 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.33/1.69 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.33/1.69 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.33/1.69 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.33/1.69 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.33/1.69 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.33/1.69 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.33/1.69 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_Finite__Set_Olinorder__class_OMax'( Y, X ),
% 1.33/1.69 'c_Finite__Set_Olinorder__class_OMax'( Z, X ), X ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Y, Z, 'tc_fun'( X,
% 1.33/1.69 'tc_bool' ) ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_Finite__Set_Olinorder__class_OMin'( Y, X ),
% 1.33/1.69 'c_Finite__Set_Olinorder__class_OMin'( Z, X ), X ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Y, X ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Z, Y, 'tc_fun'( X,
% 1.33/1.69 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.33/1.69 Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_in'( Y, X, Z ) ),
% 1.33/1.69 ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y, T, Z ), 'tc_fun'( Z, 'tc_bool'
% 1.33/1.69 ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.33/1.69 ) ), ~( 'c_in'( Y, X, T ) ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.33/1.69 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.33/1.69 ) ), ~( 'c_in'( Y, X, T ) ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.33/1.69 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( 'c_Finite__Set_Ocard'( X, Z ),
% 1.33/1.69 'c_Finite__Set_Ocard'( Y, Z ), 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.33/1.69 Z, 'tc_bool' ) ), Z ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_Finite__Set_Ocard'( X, Z ), 'c_Finite__Set_Ocard'(
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), Z ), 'tc_nat' ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), Z ) ) ],
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.69 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( 'c_Finite__Set_Ocard'( X, Z ),
% 1.33/1.69 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), ~( 'c_in'( Y, X, Z )
% 1.33/1.69 ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.33/1.69 [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_in'( Z,
% 1.33/1.69 'c_SetInterval_Oord__class_OatLeast'( Y, X ), X ) ) ],
% 1.33/1.69 [ ~( 'class_HOL_Oord'( X ) ), 'c_in'( Y,
% 1.33/1.69 'c_SetInterval_Oord__class_OatLeast'( Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.33/1.69 Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.33/1.69 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.33/1.69 , X ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.33/1.69 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ), T,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ),
% 1.33/1.69 'c_in'( X, T, Z ) ],
% 1.33/1.69 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.33/1.69 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ) ), 'c_in'( X, T, Z ) ],
% 1.33/1.69 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 1.33/1.69 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ) ), 'c_in'( Y, X, T ) ],
% 1.33/1.69 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ) ) ), 'c_in'( X, Y, Z ) ],
% 1.33/1.69 [ =( X, Y ), ~( 'c_in'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ), T,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'(
% 1.33/1.69 Z, 'tc_bool' ) ) ), ~( 'c_in'( X, T, Z ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_in'(
% 1.33/1.69 T, Y, Z ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( T, Y, Z )
% 1.33/1.69 , 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.33/1.69 , 'tc_bool' ) ), ~( 'c_in'( Y, Z, T ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.33/1.69 , Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.33/1.69 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), Z ) ), ~( 'c_in'( X, T, Z ) ) ],
% 1.33/1.69 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 1.33/1.69 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ), T ) ), ~( 'c_in'( Y, X, T ) ) ],
% 1.33/1.69 [ 'c_in'( X, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( Y, 'tc_bool' ) ), Y ), Y ) ],
% 1.33/1.69 [ 'c_in'( X, 'c_Inductive_Ocomplete__lattice__class_Ogfp'( Y, 'tc_fun'(
% 1.33/1.69 Z, 'tc_bool' ) ), Z ), ~( 'c_lessequals'( T, hAPP( Y, T ), 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ) ), ~( 'c_in'( X, T, Z ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.33/1.69 'c_lessequals'( 'c_SetInterval_Oord__class_OatLeast'( Z, X ),
% 1.33/1.69 'c_SetInterval_Oord__class_OatLeast'( Y, X ), 'tc_fun'( X, 'tc_bool' ) )
% 1.33/1.69 ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), =( X, Y )
% 1.33/1.69 , ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.33/1.69 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), Z ), ~(
% 1.33/1.69 'c_lessequals'( X, Y, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( Z
% 1.33/1.69 , X, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.69 T, U, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.33/1.69 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.33/1.69 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.33/1.69 'c_lessequals'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.33/1.69 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_lessequals'( Y, U, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, U, Z, T ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.33/1.69 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z
% 1.33/1.69 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 1.33/1.69 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.33/1.69 , Y, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z
% 1.33/1.69 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 1.33/1.69 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.33/1.69 , Y, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.33/1.69 ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.33/1.69 'tc_fun'( X, 'tc_bool' ) ) ],
% 1.33/1.69 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.33/1.69 ~( 'c_lessequals'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.33/1.69 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( T, U, 'tc_fun'( Z, 'tc_bool'
% 1.33/1.69 ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( U, Y, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.33/1.69 ) ), Y, 'tc_fun'( X, 'tc_bool' ) ) ],
% 1.33/1.69 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), X ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) )
% 1.33/1.69 ],
% 1.33/1.69 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) )
% 1.33/1.69 ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ), 'c_Set_Ovimage'( X, U,
% 1.33/1.69 Z, T ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( T
% 1.33/1.69 , 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 1.33/1.69 , 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 1.33/1.69 , 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 1.33/1.69 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.69 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.33/1.69 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.69 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' )
% 1.33/1.69 ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.33/1.69 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.69 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.33/1.69 ) ],
% 1.33/1.69 [ =( 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T
% 1.33/1.69 , 'tc_bool' ) ), T, U ), 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oimage'( X
% 1.33/1.69 , Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ),
% 1.33/1.69 ~( 'c_lessequals'( Z, W, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'(
% 1.33/1.69 Y, W, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, W, T, U ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'c_Fun_Oinj__on'( 'c_Hilbert__Choice_Oinv__into'( X, Y, Z, T ), U, T,
% 1.33/1.69 Z ), ~( 'c_lessequals'( U, 'c_Set_Oimage'( Y, X, Z, T ), 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z
% 1.33/1.69 , T ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'(
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.33/1.69 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U ), 'tc_fun'( U,
% 1.33/1.69 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( T, 'c_Orderings_Otop__class_Otop'(
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), Z, U ) ) ],
% 1.33/1.69 [ =( 'c_Set_Oimage'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y
% 1.33/1.69 , Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ),
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oimage'( X, Y, T, U
% 1.33/1.69 ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ), ~(
% 1.33/1.69 'c_lessequals'( Z, W, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( Y
% 1.33/1.69 , W, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, W, T, U ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ =( 'c_Set_Oimage'( 'c_Hilbert__Choice_Oinv__into'( X, Y, Z, T ),
% 1.33/1.69 'c_Set_Oimage'( Y, U, Z, T ), T, Z ), U ), ~( 'c_lessequals'( U, X,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( Y, X, Z, T ) ) ],
% 1.33/1.69 [ ~( =( 'c_Finite__Set_Ocard'( X, Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.69 'tc_nat' ) ) ), ~( 'c_Finite__Set_Ofinite'( X, Y ) ), =( X,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_Finite__Set_Ocard'( X, Y ),
% 1.33/1.69 'c_Finite__Set_Ocard'( Z, Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) )
% 1.33/1.69 ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Finite__Set_Ocard'( X, Y ),
% 1.33/1.69 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.33/1.69 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.33/1.69 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.33/1.69 'c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1'( X, Z ) ) ) ), ~( hBOOL(
% 1.33/1.69 hAPP( X, Z ) ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.33/1.69 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.33/1.69 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.33/1.69 'tc_nat' ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 1.33/1.69 'tc_nat' ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.33/1.69 'tc_nat' ) ],
% 1.33/1.69 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 1.33/1.69 ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.33/1.69 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.33/1.69 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.33/1.69 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.33/1.69 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.33/1.69 ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 1.33/1.69 'tc_nat' ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 1.33/1.69 'tc_nat' ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 1.33/1.69 ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 1.33/1.69 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.33/1.69 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( =( hAPP( X, 'c_ATP__Linkup_Osko__Set__Ximage__cong__1__1'( Y, X, Z
% 1.33/1.69 , T, U ) ), hAPP( Z, 'c_ATP__Linkup_Osko__Set__Ximage__cong__1__1'( Y, X
% 1.33/1.69 , Z, T, U ) ) ) ), =( 'c_Set_Oimage'( X, Y, T, U ), 'c_Set_Oimage'( Z, Y
% 1.33/1.69 , T, U ) ) ],
% 1.33/1.69 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.33/1.69 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.33/1.69 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.33/1.69 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ) ) ],
% 1.33/1.69 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.33/1.69 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 1.33/1.69 ) ), Z, X ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.33/1.69 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.33/1.69 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.33/1.69 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 1.33/1.69 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.33/1.69 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.33/1.69 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.33/1.69 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.33/1.69 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 1.33/1.69 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 1.33/1.69 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 1.33/1.69 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 1.33/1.69 'c_lessequals'( T, X, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 1.33/1.69 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U ) ],
% 1.33/1.69 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.33/1.69 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 1.33/1.69 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.33/1.69 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.33/1.69 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.33/1.69 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.33/1.69 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.33/1.69 ) ],
% 1.33/1.69 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.33/1.69 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.33/1.69 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.33/1.69 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.69 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ) ), hBOOL(
% 1.33/1.69 hAPP( X, Z ) ) ],
% 1.33/1.69 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ) ), hBOOL(
% 1.33/1.69 hAPP( X, Z ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ),
% 1.33/1.69 ~( hBOOL( hAPP( X, 'c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1'(
% 1.33/1.69 X ) ) ) ), ~( hBOOL( hAPP( X, Y ) ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.33/1.69 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.33/1.69 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.33/1.69 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.33/1.69 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.33/1.69 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.33/1.69 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_Finite__Set_Ocard'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.33/1.69 Z, 'tc_bool' ) ), Z ), 'c_Finite__Set_Ocard'( X, Z ), 'tc_nat' ), ~(
% 1.33/1.69 'c_in'( Y, X, Z ) ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_Finite__Set_Ocard'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.69 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( T,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.33/1.69 Z, 'tc_bool' ) ), Z ), 'c_Finite__Set_Ocard'( X, Z ), 'tc_nat' ), ~(
% 1.33/1.69 'c_in'( T, X, Z ) ), ~( 'c_in'( Y, X, Z ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.33/1.69 X, Z ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_SetInterval_Oord__class_OatLeast'( Y, X ),
% 1.33/1.69 'c_SetInterval_Oord__class_OatLeast'( Z, X ), 'tc_fun'( X, 'tc_bool' ) )
% 1.33/1.69 , ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.33/1.69 [ 'c_in'( hAPP( X, Y ), 'c_Set_Oimage'( X,
% 1.33/1.69 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), T ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'c_in'( hAPP( 'c_Hilbert__Choice_Oinv__into'( X, Y, Z, T ), U ), X, Z
% 1.33/1.69 ), ~( 'c_in'( U, 'c_Set_Oimage'( Y, X, Z, T ), T ) ) ],
% 1.33/1.69 [ ~( =( hAPP( 'c_Hilbert__Choice_Oinv__into'( X, Y, Z, T ), U ), hAPP(
% 1.33/1.69 'c_Hilbert__Choice_Oinv__into'( X, Y, Z, T ), W ) ) ), =( U, W ), ~(
% 1.33/1.69 'c_in'( W, 'c_Set_Oimage'( Y, X, Z, T ), T ) ), ~( 'c_in'( U,
% 1.33/1.69 'c_Set_Oimage'( Y, X, Z, T ), T ) ) ],
% 1.33/1.69 [ 'c_in'( 'c_ATP__Linkup_Osko__Set__XimageE__1__1'( X, Y, Z, T, U ), X,
% 1.33/1.69 T ), ~( 'c_in'( Y, 'c_Set_Oimage'( Z, X, T, U ), U ) ) ],
% 1.33/1.69 [ =( X, hAPP( Y, 'c_ATP__Linkup_Osko__Set__Ximage__iff__1__1'( Z, Y, X,
% 1.33/1.69 T, U ) ) ), ~( 'c_in'( X, 'c_Set_Oimage'( Y, Z, T, U ), U ) ) ],
% 1.33/1.69 [ =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( U, Y, Z, T ) ),
% 1.33/1.69 'c_in'( 'c_ATP__Linkup_Osko__Set__Ximage__cong__1__1'( Y, X, U, Z, T ), Y
% 1.33/1.69 , Z ) ],
% 1.33/1.69 [ =( hAPP( X, hAPP( 'c_Hilbert__Choice_Oinv__into'( Y, X, Z, T ), U ) )
% 1.33/1.69 , U ), ~( 'c_in'( U, 'c_Set_Oimage'( X, Y, Z, T ), T ) ) ],
% 1.33/1.69 [ 'c_in'( 'c_ATP__Linkup_Osko__Set__Ximage__iff__1__1'( X, Y, Z, T, U )
% 1.33/1.69 , X, T ), ~( 'c_in'( Z, 'c_Set_Oimage'( Y, X, T, U ), U ) ) ],
% 1.33/1.69 [ =( 'c_Set_Oimage'( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), W, T, U ),
% 1.33/1.69 'c_Set_Oimage'( X, W, T, U ) ), 'c_in'( Y, W, T ) ],
% 1.33/1.69 [ =( X, hAPP( Y, 'c_ATP__Linkup_Osko__Set__XimageE__1__1'( Z, X, Y, T, U
% 1.33/1.69 ) ) ), ~( 'c_in'( X, 'c_Set_Oimage'( Y, Z, T, U ), U ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.33/1.69 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 1.33/1.69 Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.33/1.69 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.33/1.69 Y, X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.33/1.69 Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z
% 1.33/1.69 , 'tc_bool' ) ), Z ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.69 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), T ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T
% 1.33/1.69 , 'tc_bool' ) ), T ) ) ],
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.69 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ),
% 1.33/1.69 'c_Finite__Set_Ocard'( X, Z ) ), 'c_in'( Y, X, Z ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Fun_Oinj__on'( Z, X, Y, T ) ),
% 1.33/1.69 ~( 'c_Finite__Set_Ofinite'( 'c_Set_Oimage'( Z, X, Y, T ), T ) ) ],
% 1.33/1.69 [ =( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.33/1.69 , 'tc_bool' ) ), Z ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.33/1.69 , 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.33/1.69 Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_lessequals'(
% 1.33/1.69 'c_Suc'( Z ), 'c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1'( X ),
% 1.33/1.69 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 1.33/1.69 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 1.33/1.69 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.33/1.69 'c_Suc'( X ), 'tc_nat' ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.33/1.69 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.33/1.69 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.33/1.69 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'c_Suc'(
% 1.33/1.69 'c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1'( X, Z ) ) ) ), ~( hBOOL(
% 1.33/1.69 hAPP( X, Z ) ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1'( X ) ) ),
% 1.33/1.69 ~( 'c_lessequals'( 'c_Suc'( Y ), X, 'tc_nat' ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, Y ) ), 'c_lessequals'( Z,
% 1.33/1.69 'c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1'( X, Z ), 'tc_nat' ),
% 1.33/1.69 ~( 'c_lessequals'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.33/1.69 'c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1'( X, Z ) ) ) ) ), ~(
% 1.33/1.69 'c_lessequals'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.33/1.69 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( 'c_Set_Oinsert'( X, Y, Z ), Z ), 'c_Suc'(
% 1.33/1.69 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( Y, 'c_Set_Oinsert'(
% 1.33/1.69 X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ),
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) )
% 1.33/1.69 ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( X
% 1.33/1.69 , 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ),
% 1.33/1.69 'c_Finite__Set_Ocard'( X, Z ), 'tc_nat' ), ~( 'c_Finite__Set_Ofinite'( X
% 1.33/1.69 , Z ) ) ],
% 1.33/1.69 [ =( X, 'c_Set_Oimage'( Y,
% 1.33/1.69 'c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1'( Z, X, Y, T, U ), T
% 1.33/1.69 , U ) ), ~( 'c_lessequals'( X, 'c_Set_Oimage'( Y, Z, T, U ), 'tc_fun'( U
% 1.33/1.69 , 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oimage'( X, Y, Z
% 1.33/1.69 , T ), 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.33/1.69 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, U, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1'(
% 1.33/1.69 X, Y, Z, T, U ), X, 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y,
% 1.33/1.69 'c_Set_Oimage'( Z, X, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Set_Oimage'( X, 'c_Set_Ovimage'( X, Y, Z, T ), Z, T
% 1.33/1.69 ), Y, 'tc_fun'( T, 'tc_bool' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Set_Oimage'( X,
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.33/1.69 'c_Set_Oimage'( X, Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U,
% 1.33/1.69 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ],
% 1.33/1.69 [ ~( =( 'c_Finite__Set_Ocard'( X, Y ), 'c_Finite__Set_Ocard'(
% 1.33/1.69 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.33/1.69 'tc_bool' ) ), Y ) ), =( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.33/1.69 'tc_bool' ) ) ) ],
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.33/1.69 ) ), 'c_Finite__Set_Ofinite'( X, Y ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.69 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ),
% 1.33/1.69 hBOOL( hAPP( X, 'c_Suc'(
% 1.33/1.69 'c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1'( X ) ) ) ), ~(
% 1.33/1.69 hBOOL( hAPP( X, Y ) ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 1.33/1.69 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.33/1.69 [ ~( =( 'c_Finite__Set_Ocard'( X, Y ), 'c_Suc'( Z ) ) ), =(
% 1.33/1.69 'c_Finite__Set_Ocard'(
% 1.33/1.69 'c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2'( X, Z, Y ), Y )
% 1.33/1.69 , Z ) ],
% 1.33/1.69 [ ~( =( 'c_Finite__Set_Ocard'( X, Y ), 'c_Suc'( Z ) ) ), =(
% 1.33/1.69 'c_Finite__Set_Ocard'(
% 1.33/1.69 'c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2'( X, Z, Y ), Y ),
% 1.33/1.69 Z ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.69 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.69 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 1.33/1.69 , 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.33/1.69 'tc_nat' ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.33/1.69 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 1.33/1.69 , Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Z
% 1.33/1.69 , Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z,
% 1.33/1.69 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 1.33/1.69 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 1.33/1.69 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.33/1.69 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.33/1.69 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 1.33/1.69 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 1.33/1.69 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.33/1.69 'tc_nat' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.33/1.69 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.33/1.69 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 1.33/1.69 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.33/1.69 Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 1.33/1.69 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 1.33/1.69 ), X, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.33/1.69 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.33/1.69 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.33/1.69 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.33/1.69 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.33/1.69 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.33/1.69 ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.69 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.33/1.69 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( 'c_Set_Oimage'( X, Y, Z, T ), T ),
% 1.33/1.69 'c_Finite__Set_Ocard'( Y, Z ) ), ~( 'c_Fun_Oinj__on'( X, Y, Z, T ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ =( 'c_Suc'( 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.69 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ) ),
% 1.33/1.69 'c_Finite__Set_Ocard'( X, Z ) ), ~( 'c_in'( Y, X, Z ) ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.33/1.69 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), T ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( 'c_Finite__Set_Ocard'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ), T ),
% 1.33/1.69 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), 'c_in'( Y, Z, T ),
% 1.33/1.69 ~( 'c_in'( Y, X, T ) ), ~( 'c_Finite__Set_Ofinite'( X, T ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.33/1.69 'c_Finite__Set_Olinorder__class_OMin'( Y, X ), Z, X ), ~( 'c_in'( Z, Y, X
% 1.33/1.69 ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.33/1.69 'c_Finite__Set_Olinorder__class_OMax'( Z, X ), X ), ~( 'c_in'( Y, Z, X )
% 1.33/1.69 ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), 'c_in'( T, X, Z ),
% 1.33/1.69 'c_in'( T, Y, Z ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( T, Y
% 1.33/1.69 , Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.33/1.69 , 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.33/1.69 'c_in'( Y, X, T ), 'c_in'( Y, Z, T ) ],
% 1.33/1.69 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.33/1.69 , 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.33/1.69 'c_in'( Y, X, T ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( hAPP( Y, Z ), hAPP(
% 1.33/1.69 Y, T ), X ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.33/1.69 hAPP( Y,
% 1.33/1.69 'c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1'( Y,
% 1.33/1.69 X ) ), hAPP( Y, 'c_Suc'(
% 1.33/1.69 'c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1'( Y,
% 1.33/1.69 X ) ) ), X ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), U, 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ), 'c_in'( 'c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1'(
% 1.33/1.69 Y, U, X, Z, T ), Y, Z ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), U, 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ), ~( 'c_in'( hAPP( X,
% 1.33/1.69 'c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1'( Y, U, X, Z, T ) ),
% 1.33/1.69 U, T ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), U, 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ), 'c_in'(
% 1.33/1.69 'c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1'( Y, U, X, Z, T ), Y
% 1.33/1.69 , Z ) ],
% 1.33/1.69 [ 'c_in'( hAPP( X, Y ), 'c_Inductive_Ocomplete__lattice__class_Ogfp'( Z
% 1.33/1.69 , 'tc_fun'( T, 'tc_bool' ) ), T ), ~( 'c_lessequals'( 'c_Set_Oimage'( X,
% 1.33/1.69 U, W, T ), hAPP( Z, 'c_Set_Oimage'( X, U, W, T ) ), 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ) ), ~( 'c_in'( Y, U, W ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), U, 'tc_fun'( T,
% 1.33/1.69 'tc_bool' ) ), ~( 'c_in'( hAPP( X,
% 1.33/1.69 'c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1'( Y, U, X, Z, T ) ), U, T
% 1.33/1.69 ) ) ],
% 1.33/1.69 [ 'c_Fun_Oinj__on'( X, Y, Z, Z ), ~( 'c_lessequals'( Y, 'c_Set_Oimage'(
% 1.33/1.69 X, Y, Z, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y
% 1.33/1.69 , Z ) ) ],
% 1.33/1.69 [ =( X, 'c_Set_Oimage'( Y,
% 1.33/1.69 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1'( Z, X, Y
% 1.33/1.69 , T, U ), T, U ) ), ~( 'c_lessequals'( X, 'c_Set_Oimage'( Y, Z, T, U ),
% 1.33/1.69 'tc_fun'( U, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( X, U ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'(
% 1.33/1.69 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1'( X, Y, Z
% 1.33/1.69 , T, U ), T ), ~( 'c_lessequals'( Y, 'c_Set_Oimage'( Z, X, T, U ),
% 1.33/1.69 'tc_fun'( U, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, U ) ) ],
% 1.33/1.69 [ =( 'c_Set_Oimage'( X, Y, Z, Z ), Y ), ~( 'c_Fun_Oinj__on'( X, Y, Z, Z
% 1.33/1.69 ) ), ~( 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, Z ), Y, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.33/1.69 [ 'c_lessequals'(
% 1.33/1.69 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1'( X, Y, Z
% 1.33/1.69 , T, U ), X, 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y,
% 1.33/1.69 'c_Set_Oimage'( Z, X, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Y, U ) ) ],
% 1.33/1.69 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.33/1.69 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.33/1.69 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.33/1.69 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 1.33/1.69 , Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( =( 'c_Finite__Set_Ocard'( 'c_Set_Oimage'( X, Y, Z, T ), T ),
% 1.33/1.69 'c_Finite__Set_Ocard'( Y, Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ),
% 1.33/1.69 'c_Fun_Oinj__on'( X, Y, Z, T ) ],
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( 'c_Set_Oimage'( X, Y, Z, T ), T ),
% 1.33/1.69 'c_Finite__Set_Ocard'( Y, Z ) ), ~( 'c_Fun_Oinj__on'( X, Y, Z, T ) ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.33/1.69 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.33/1.69 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.33/1.69 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.33/1.69 , Y ), =( 'c_Finite__Set_Ocard'( 'c_Set_Oinsert'( X,
% 1.33/1.69 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ), Y ),
% 1.33/1.69 'c_Suc'( 'c_Finite__Set_Ocard'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.33/1.69 Y, 'tc_bool' ) ), Y ) ) ) ],
% 1.33/1.69 [ 'c_in'( X, Y, Z ), =( 'c_Finite__Set_Ocard'( 'c_Set_Oinsert'( X, Y, Z
% 1.33/1.69 ), Z ), 'c_Suc'( 'c_Finite__Set_Ocard'( Y, Z ) ) ), =(
% 1.33/1.69 'c_Finite__Set_Ocard'( Y, Z ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( X, Y ), 'c_Finite__Set_Ocard'( Z, T ) ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Z, T ) ), ~( 'c_Finite__Set_Ofinite'( X, Y ) ),
% 1.33/1.69 ~( 'c_lessequals'( 'c_Set_Oimage'( U, Z, T, Y ), X, 'tc_fun'( Y,
% 1.33/1.69 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( U, Z, T, Y ) ), ~( 'c_lessequals'(
% 1.33/1.69 'c_Set_Oimage'( W, X, Y, T ), Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 1.33/1.69 'c_Fun_Oinj__on'( W, X, Y, T ) ) ],
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.33/1.69 Z, 'tc_bool' ) ), Z ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_Finite__Set_Ocard'( X, Z ), 'c_Finite__Set_Ocard'( Y, Z ), 'tc_nat' )
% 1.33/1.69 ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Finite__Set_Ocard'( X, Y ), 'c_Finite__Set_Ocard'(
% 1.33/1.69 Z, T ), 'tc_nat' ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), ~(
% 1.33/1.69 'c_lessequals'( 'c_Set_Oimage'( U, X, Y, T ), Z, 'tc_fun'( T, 'tc_bool' )
% 1.33/1.69 ) ), ~( 'c_Fun_Oinj__on'( U, X, Y, T ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.33/1.69 'c_lessequals'( Z, Y, X ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 1.33/1.69 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z )
% 1.33/1.69 , 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ) ) ],
% 1.33/1.69 [ ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), 'c_lessequals'(
% 1.33/1.69 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U ), 'tc_fun'( U,
% 1.33/1.69 'tc_bool' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z
% 1.33/1.69 , T ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ) ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.33/1.69 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.33/1.69 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'c_in'( X, 'c_Set_Oinsert'( Y, Z, T ), T ), ~( 'c_in'( X, Z, T ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'c_in'( X, 'c_Set_Oinsert'( Y, Z, T ), T ), ~( 'c_in'( X, Z, T ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y
% 1.33/1.69 , 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, Y ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool'
% 1.33/1.69 ) ) ), ~( hBOOL( hAPP( Z, Y ) ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) )
% 1.33/1.69 , ~( 'c_lessequals'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~( 'c_lessequals'(
% 1.33/1.69 Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( T
% 1.33/1.69 , Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 1.33/1.69 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.33/1.69 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X, T, Z ) ), ~( 'c_lessequals'( T, Y,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_in'( X, Y, Z ), ~( 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) )
% 1.33/1.69 ), ~( 'c_in'( X, T, Z ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.33/1.69 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X, T, Z ) ), ~( 'c_lessequals'( T, Y,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.33/1.69 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X, T, Z ) ), ~( 'c_lessequals'( T, Y,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.33/1.69 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.33/1.69 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.33/1.69 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.33/1.69 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool'
% 1.33/1.69 ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_in'( X
% 1.33/1.69 , T, Z ) ) ],
% 1.33/1.69 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 1.33/1.69 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 1.33/1.69 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_Set_Oimage'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ),
% 1.33/1.69 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ) ],
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.33/1.69 'c_Finite__Set_Ocard'( Y, Z ) ), ~( 'c_in'( X, Y, Z ) ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( 'c_Set_Oimage'( X, Y, Z, T ), T ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.33/1.69 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.33/1.69 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.33/1.69 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.33/1.69 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.33/1.69 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.33/1.69 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.33/1.69 , Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.33/1.69 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_in'( X, Y, Z ), =( X, T ), ~( 'c_in'( X, 'c_Set_Oinsert'( T, Y, Z )
% 1.33/1.69 , Z ) ) ],
% 1.33/1.69 [ =( X, Y ), ~( 'c_lessequals'( 'c_Finite__Set_Ocard'( Y, Z ),
% 1.33/1.69 'c_Finite__Set_Ocard'( X, Z ), 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 1.33/1.69 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.33/1.69 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Finite__Set_Ocard'( X, Y ), 'c_Finite__Set_Ocard'(
% 1.33/1.69 'c_Set_Oinsert'( Z, X, Y ), Y ), 'tc_nat' ), ~( 'c_Finite__Set_Ofinite'(
% 1.33/1.69 X, Y ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( 'c_Set_Oinsert'( X, Y, Z ), Z ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.33/1.69 'c_Set_Oinsert'( Z, X, Y ), Y ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, X, Z ), 'tc_fun'( Z, 'tc_bool'
% 1.33/1.69 ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.33/1.69 , X, 'tc_nat' ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 1.33/1.69 X, T ), Y ) ) ) ],
% 1.33/1.69 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.33/1.69 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.33/1.69 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.33/1.69 'c_Set_Oinsert'( T, X, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_lessequals'( X, 'c_Set_Oimage'(
% 1.33/1.69 Z, T, U, Y ), 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( T
% 1.33/1.69 , U ) ) ],
% 1.33/1.69 [ 'c_in'( hAPP( X, Y ), Z, T ), ~( 'c_in'( Y, U, W ) ), ~(
% 1.33/1.69 'c_lessequals'( 'c_Set_Oimage'( X, U, W, T ), Z, 'tc_fun'( T, 'tc_bool' )
% 1.33/1.69 ) ) ],
% 1.33/1.69 [ 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ],
% 1.33/1.69 [ 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ],
% 1.33/1.69 [ 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ],
% 1.33/1.69 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 1.33/1.69 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 1.33/1.69 [ 'c_in'( X, Y, Z ), ~( hBOOL( hAPP( Y, X ) ) ) ],
% 1.33/1.69 [ hBOOL( hAPP( X, Y ) ), ~( 'c_in'( Y, X, Z ) ) ],
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( 'c_Set_Oinsert'( X, Y, Z ), Z ), 'c_Suc'(
% 1.33/1.69 'c_Finite__Set_Ocard'( Y, Z ) ) ), 'c_in'( X, Y, Z ), ~(
% 1.33/1.69 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.33/1.69 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.33/1.69 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.33/1.69 ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.33/1.69 , T, X ) ) ), =( Y, Z ) ],
% 1.33/1.69 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.33/1.69 , T, X ) ) ), =( Z, T ) ],
% 1.33/1.69 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.33/1.69 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 1.33/1.69 'tc_nat' ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.33/1.69 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_in'( X, Y, Z ), ~( 'c_lessequals'( 'c_Set_Oinsert'( X, T, Z ), Y,
% 1.33/1.69 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.33/1.69 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 1.33/1.69 , X, 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.33/1.69 'tc_nat' ) ],
% 1.33/1.69 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 1.33/1.69 ) ) ],
% 1.33/1.69 [ =( 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ),
% 1.33/1.69 'c_Set_Oimage'( X, Z, T, U ) ), ~( 'c_in'( Y, Z, T ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.33/1.69 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), 'c_in'( Y, X
% 1.33/1.69 , T ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), 'c_in'( T, X, Z ),
% 1.33/1.69 ~( 'c_lessequals'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool'
% 1.33/1.69 ) ) ) ],
% 1.33/1.69 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.33/1.69 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), 'c_in'( Y, X
% 1.33/1.69 , T ) ],
% 1.33/1.69 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 1.33/1.69 , 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ), 'c_in'( T, X
% 1.33/1.69 , Z ) ],
% 1.33/1.69 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ) ) ),
% 1.33/1.69 'c_in'( X, T, Z ), 'c_in'( X, Y, Z ), =( Y, T ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.33/1.69 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.33/1.69 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.33/1.69 [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( 'c_in'( X, Y, Z ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Finite__Set_Ocard'( X, Y ), 'c_Finite__Set_Ocard'(
% 1.33/1.69 Z, Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) )
% 1.33/1.69 , ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Finite__Set_Ocard'( 'c_Set_Oimage'( X, Y, Z, T ), T
% 1.33/1.69 ), 'c_Finite__Set_Ocard'( Y, Z ), 'tc_nat' ), ~( 'c_Finite__Set_Ofinite'(
% 1.33/1.69 Y, Z ) ) ],
% 1.33/1.69 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.33/1.69 Y, X ) ],
% 1.33/1.69 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.33/1.69 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.33/1.69 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.33/1.69 [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( hAPP( T, X ), 'c_Set_Oimage'( T, Y, Z
% 1.33/1.69 , U ), U ) ],
% 1.33/1.69 [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( hAPP( T, X ), 'c_Set_Oimage'( T, Y, Z
% 1.33/1.69 , U ), U ) ],
% 1.33/1.69 [ 'c_in'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ), ~( 'c_in'( Y
% 1.33/1.69 , Z, T ) ) ],
% 1.33/1.69 [ 'c_in'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ), ~( 'c_in'( Y
% 1.33/1.69 , Z, T ) ) ],
% 1.33/1.69 [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( hAPP( Y, Z ), hAPP( T, Z )
% 1.33/1.69 , X ), ~( 'c_lessequals'( Y, T, 'tc_fun'( U, X ) ) ) ],
% 1.33/1.69 [ 'c_Finite__Set_Ofinite'( 'v_U', 'tc_Com_Opname' ) ],
% 1.33/1.69 [ 'c_lessequals'( 'v_G', 'c_Set_Oimage'( 'v_mgt__call', 'v_U',
% 1.33/1.69 'tc_Com_Opname', 't_a' ), 'tc_fun'( 't_a', 'tc_bool' ) ) ],
% 1.33/1.69 [ 'c_lessequals'( 'c_Suc'( 'v_na' ), 'c_Finite__Set_Ocard'(
% 1.33/1.69 'c_Set_Oimage'( 'v_mgt__call', 'v_U', 'tc_Com_Opname', 't_a' ), 't_a' ),
% 1.33/1.69 'tc_nat' ) ],
% 1.33/1.69 [ =( 'c_Finite__Set_Ocard'( 'v_G', 't_a' ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_Finite__Set_Ocard'( 'c_Set_Oimage'( 'v_mgt__call', 'v_U',
% 1.33/1.69 'tc_Com_Opname', 't_a' ), 't_a' ), 'c_Suc'( 'v_na' ), 'tc_nat' ) ) ],
% 1.33/1.69 [ 'c_in'( 'v_pn', 'v_U', 'tc_Com_Opname' ) ],
% 1.33/1.69 [ ~( 'c_in'( hAPP( 'v_mgt__call', 'v_pn' ), 'v_G', 't_a' ) ) ],
% 1.33/1.69 [ ~( =( 'c_Finite__Set_Ocard'( 'c_Set_Oinsert'( hAPP( 'v_mgt__call',
% 1.33/1.69 'v_pn' ), 'v_G', 't_a' ), 't_a' ), 'c_HOL_Ominus__class_Ominus'(
% 1.33/1.69 'c_Finite__Set_Ocard'( 'c_Set_Oimage'( 'v_mgt__call', 'v_U',
% 1.33/1.69 'tc_Com_Opname', 't_a' ), 't_a' ), 'v_na', 'tc_nat' ) ) ) ],
% 1.33/1.69 [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.33/1.69 'class_Complete__Lattice_Ocomplete__lattice'( Y ) ) ],
% 1.33/1.69 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.33/1.69 'class_Lattices_Olattice'( Y ) ) ],
% 1.33/1.69 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.33/1.69 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 1.33/1.69 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_fun'( X, Y ) ), ~(
% 1.33/1.69 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.33/1.69 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.33/1.69 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.33/1.69 'class_Orderings_Opreorder'( Y ) ) ],
% 1.33/1.69 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.33/1.69 'class_Lattices_Olattice'( Y ) ) ],
% 1.33/1.69 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.33/1.69 'class_Orderings_Oorder'( Y ) ) ],
% 1.33/1.69 [ 'class_Orderings_Otop'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Otop'(
% 1.33/1.69 Y ) ) ],
% 1.33/1.69 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.33/1.69 Y ) ) ],
% 1.33/1.69 [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Oord'( Y ) ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.33/1.69 ],
% 1.33/1.69 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.33/1.69 ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.33/1.69 ],
% 1.33/1.69 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.33/1.69 ,
% 1.33/1.69 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_HOL_Oord'( 'tc_nat' ) ],
% 1.33/1.69 [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_bool' ) ],
% 1.33/1.69 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.33/1.69 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.33/1.69 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_bool' ) ],
% 1.33/1.69 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.33/1.69 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.33/1.69 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.33/1.69 [ 'class_Orderings_Otop'( 'tc_bool' ) ],
% 1.33/1.69 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.33/1.69 [ 'class_HOL_Oord'( 'tc_bool' ) ],
% 1.33/1.69 [ 'c_fequal'( X, X, Y ) ],
% 1.33/1.69 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.33/1.69 ] .
% 1.33/1.69
% 1.33/1.69
% 1.33/1.69 percentage equality = 0.234646, percentage horn = 0.883436
% 1.33/1.69 This is a problem with some equality
% 1.33/1.69
% 1.33/1.69
% 1.33/1.69
% 1.33/1.69 Options Used:
% 1.33/1.69
% 1.33/1.69 useres = 1
% 1.33/1.69 useparamod = 1
% 1.33/1.69 useeqrefl = 1
% 1.33/1.69 useeqfact = 1
% 1.33/1.69 usefactor = 1
% 1.33/1.69 usesimpsplitting = 0
% 1.33/1.69 usesimpdemod = 5
% 1.33/1.69 usesimpres = 3
% 1.33/1.69
% 1.33/1.69 resimpinuse = 1000
% 1.33/1.69 resimpclauses = 20000
% 1.33/1.69 substype = eqrewr
% 1.33/1.69 backwardsubs = 1
% 1.33/1.69 selectoldest = 5
% 1.33/1.69
% 1.33/1.69 litorderings [0] = split
% 1.33/1.69 litorderings [1] = extend the termordering, first sorting on arguments
% 1.33/1.69
% 1.33/1.69 termordering = kbo
% 1.33/1.69
% 1.33/1.69 litapriori = 0
% 1.33/1.69 termapriori = 1
% 1.33/1.69 litaposteriori = 0
% 1.33/1.69 termaposteriori = 0
% 1.33/1.69 demodaposteriori = 0
% 1.33/1.69 ordereqreflfact = 0
% 1.33/1.69
% 1.33/1.69 litselect = negord
% 1.33/1.69
% 1.33/1.69 maxweight = 15
% 1.33/1.69 maxdepth = 30000
% 1.33/1.69 maxlength = 115
% 1.33/1.69 maxnrvars = 195
% 1.33/1.69 excuselevel = 1
% 1.33/1.69 increasemaxweight = 1
% 1.33/1.69
% 1.33/1.69 maxselected = 10000000
% 1.33/1.69 maxnrclauses = 10000000
% 1.33/1.69
% 1.33/1.69 showgenerated = 0
% 1.33/1.69 showkept = 0
% 1.33/1.69 showselected = 0
% 1.33/1.69 showdeleted = 0
% 1.33/1.69 showresimp = 1
% 1.33/1.69 showstatus = 2000
% 1.33/1.69
% 1.33/1.69 prologoutput = 1
% 1.33/1.69 nrgoals = 5000000
% 1.33/1.69 totalproof = 1
% 1.33/1.69
% 1.33/1.69 Symbols occurring in the translation:
% 1.33/1.69
% 1.33/1.69 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.33/1.69 . [1, 2] (w:1, o:144, a:1, s:1, b:0),
% 1.33/1.69 ! [4, 1] (w:0, o:72, a:1, s:1, b:0),
% 1.33/1.69 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.33/1.69 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.33/1.69 'tc_nat' [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.33/1.69 'c_HOL_Ozero__class_Ozero' [40, 1] (w:1, o:77, a:1, s:1, b:0),
% 1.33/1.69 'c_HOL_Oord__class_Oless' [42, 3] (w:1, o:181, a:1, s:1, b:0),
% 1.33/1.69 'c_HOL_Oone__class_Oone' [43, 1] (w:1, o:78, a:1, s:1, b:0),
% 1.33/1.69 'c_HOL_Otimes__class_Otimes' [44, 3] (w:1, o:182, a:1, s:1, b:0),
% 1.33/1.69 'c_Ring__and__Field_Odvd__class_Odvd' [45, 3] (w:1, o:183, a:1, s:1
% 1.33/1.69 , b:0),
% 1.33/1.69 'c_Suc' [47, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.33/1.69 'class_OrderedGroup_Olordered__ab__group__add' [49, 1] (w:1, o:81, a:
% 1.33/1.69 1, s:1, b:0),
% 1.33/1.69 'c_lessequals' [51, 3] (w:1, o:184, a:1, s:1, b:0),
% 1.33/1.69 'c_HOL_Oplus__class_Oplus' [52, 3] (w:1, o:185, a:1, s:1, b:0),
% 1.33/1.69 'tc_bool' [56, 0] (w:1, o:22, a:1, s:1, b:0),
% 1.33/1.69 'tc_fun' [57, 2] (w:1, o:169, a:1, s:1, b:0),
% 1.33/1.69 'c_Lattices_Olower__semilattice__class_Oinf' [58, 3] (w:1, o:186, a:1
% 1.33/1.69 , s:1, b:0),
% 1.33/1.69 'c_Orderings_Obot__class_Obot' [59, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.33/1.69 'c_HOL_Ominus__class_Ominus' [60, 3] (w:1, o:187, a:1, s:1, b:0),
% 1.33/1.69 'class_Ring__and__Field_Ocomm__semiring__1' [61, 1] (w:1, o:85, a:1
% 1.33/1.69 , s:1, b:0),
% 1.33/1.69 'class_OrderedGroup_Opordered__comm__monoid__add' [64, 1] (w:1, o:86
% 1.33/1.69 , a:1, s:1, b:0),
% 1.33/1.69 'class_Divides_Osemiring__div' [66, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.33/1.69 'c_Divides_Odiv__class_Omod' [68, 3] (w:1, o:188, a:1, s:1, b:0),
% 1.33/1.69 'c_Set_Ovimage' [72, 4] (w:1, o:194, a:1, s:1, b:0),
% 1.33/1.69 'c_Finite__Set_Ofinite' [73, 2] (w:1, o:170, a:1, s:1, b:0),
% 1.33/1.69 'c_Orderings_Otop__class_Otop' [74, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.33/1.69 'c_Fun_Oinj__on' [75, 4] (w:1, o:195, a:1, s:1, b:0),
% 1.33/1.69 'class_Orderings_Opreorder' [76, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.33/1.69 'class_Orderings_Oorder' [79, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.33/1.69 'class_OrderedGroup_Oab__group__add' [80, 1] (w:1, o:93, a:1, s:1, b:
% 1.33/1.69 0),
% 1.33/1.69 'class_OrderedGroup_Ocomm__monoid__add' [81, 1] (w:1, o:94, a:1, s:1
% 1.33/1.69 , b:0),
% 1.33/1.69 'class_OrderedGroup_Oab__semigroup__add' [82, 1] (w:1, o:95, a:1, s:1
% 1.33/1.69 , b:0),
% 1.33/1.69 'class_OrderedGroup_Olordered__ab__group__add__meet' [85, 1] (w:1, o:
% 2.11/2.40 96, a:1, s:1, b:0),
% 2.11/2.40 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [86, 1]
% 2.11/2.40 (w:1, o:97, a:1, s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Osemiring__1' [87, 1] (w:1, o:101, a:1, s:1
% 2.11/2.40 , b:0),
% 2.11/2.40 'c_Nat_Osemiring__1__class_Oof__nat' [88, 2] (w:1, o:171, a:1, s:1
% 2.11/2.40 , b:0),
% 2.11/2.40 'class_Ring__and__Field_Ozero__neq__one' [89, 1] (w:1, o:102, a:1, s:
% 2.11/2.40 1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Oidom' [90, 1] (w:1, o:103, a:1, s:1, b:0),
% 2.11/2.40 'class_Int_Onumber__ring' [91, 1] (w:1, o:105, a:1, s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Odvd' [92, 1] (w:1, o:107, a:1, s:1, b:0),
% 2.11/2.40 'class_OrderedGroup_Omonoid__mult' [93, 1] (w:1, o:108, a:1, s:1, b:0
% 2.11/2.40 ),
% 2.11/2.40 'class_OrderedGroup_Ocomm__monoid__mult' [94, 1] (w:1, o:109, a:1, s:
% 2.11/2.40 1, b:0),
% 2.11/2.40 'c_Set_Oinsert' [95, 3] (w:1, o:189, a:1, s:1, b:0),
% 2.11/2.40 'c_in' [96, 3] (w:1, o:190, a:1, s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Oring' [97, 1] (w:1, o:98, a:1, s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Oordered__semiring__strict' [100, 1] (w:1, o:
% 2.11/2.40 115, a:1, s:1, b:0),
% 2.11/2.40 'c_Set_Oimage' [103, 4] (w:1, o:196, a:1, s:1, b:0),
% 2.11/2.40 'c_Hilbert__Choice_Oinv__into' [104, 4] (w:1, o:197, a:1, s:1, b:0),
% 2.11/2.40
% 2.11/2.40 hAPP [105, 2] (w:1, o:172, a:1, s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Oordered__ring__strict' [107, 1] (w:1, o:114
% 2.11/2.40 , a:1, s:1, b:0),
% 2.11/2.40 'class_Lattices_Obounded__lattice' [108, 1] (w:1, o:116, a:1, s:1, b:
% 2.11/2.40 0),
% 2.11/2.40 'c_Finite__Set_Ocard' [110, 2] (w:1, o:173, a:1, s:1, b:0),
% 2.11/2.40 'c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2' [111, 3] (w:1
% 2.11/2.40 , o:191, a:1, s:1, b:0),
% 2.11/2.40 'class_Nat_Osemiring__char__0' [112, 1] (w:1, o:80, a:1, s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Oordered__semiring' [113, 1] (w:1, o:117, a:1
% 2.11/2.40 , s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Opordered__ring' [114, 1] (w:1, o:121, a:1
% 2.11/2.40 , s:1, b:0),
% 2.11/2.40 'class_Orderings_Olinorder' [115, 1] (w:1, o:122, a:1, s:1, b:0),
% 2.11/2.40 'c_Finite__Set_Olinorder__class_OMax' [116, 2] (w:1, o:174, a:1, s:1
% 2.11/2.40 , b:0),
% 2.11/2.40 'class_Lattices_Olower__semilattice' [117, 1] (w:1, o:123, a:1, s:1
% 2.11/2.40 , b:0),
% 2.11/2.40 'class_Lattices_Olattice' [118, 1] (w:1, o:124, a:1, s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Osemiring' [119, 1] (w:1, o:125, a:1, s:1, b:
% 2.11/2.40 0),
% 2.11/2.40 'class_Ring__and__Field_Opordered__cancel__semiring' [120, 1] (w:1
% 2.11/2.40 , o:126, a:1, s:1, b:0),
% 2.11/2.40 'class_OrderedGroup_Ocancel__ab__semigroup__add' [121, 1] (w:1, o:127
% 2.11/2.40 , a:1, s:1, b:0),
% 2.11/2.40 'class_OrderedGroup_Ocancel__semigroup__add' [122, 1] (w:1, o:128, a:
% 2.11/2.40 1, s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Oordered__idom' [123, 1] (w:1, o:118, a:1, s:
% 2.11/2.40 1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Oordered__semidom' [124, 1] (w:1, o:119, a:1
% 2.11/2.40 , s:1, b:0),
% 2.11/2.40 hBOOL [127, 1] (w:1, o:129, a:1, s:1, b:0),
% 2.11/2.40 'c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1' [128, 1] (w:1, o:
% 2.11/2.40 130, a:1, s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Oordered__comm__semiring__strict' [129, 1]
% 2.11/2.40 (w:1, o:120, a:1, s:1, b:0),
% 2.11/2.40 'c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2' [130, 3] (w:
% 2.11/2.40 1, o:192, a:1, s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Oring__no__zero__divisors' [131, 1] (w:1, o:
% 2.11/2.40 99, a:1, s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Ono__zero__divisors' [132, 1] (w:1, o:113, a:
% 2.11/2.40 1, s:1, b:0),
% 2.11/2.40 'c_Fun_Ofun__upd' [133, 5] (w:1, o:198, a:1, s:1, b:0),
% 2.11/2.40 'c_Finite__Set_Olinorder__class_OMin' [137, 2] (w:1, o:175, a:1, s:1
% 2.11/2.40 , b:0),
% 2.11/2.40 'class_Ring__and__Field_Omult__zero' [142, 1] (w:1, o:110, a:1, s:1
% 2.11/2.40 , b:0),
% 2.11/2.40 'c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1' [143, 2] (w:1, o:176
% 2.11/2.40 , a:1, s:1, b:0),
% 2.11/2.40 'class_Ring__and__Field_Opordered__semiring' [144, 1] (w:1, o:131, a:
% 2.11/2.40 1, s:1, b:0),
% 2.11/2.40 'class_OrderedGroup_Omonoid__add' [145, 1] (w:1, o:132, a:1, s:1, b:0
% 2.11/2.40 ),
% 2.11/2.40 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [146, 1]
% 2.11/2.40 (w:1, o:133, a:1, s:1, b:0),
% 2.11/2.40 'class_OrderedGroup_Opordered__ab__group__add' [148, 1] (w:1, o:134
% 2.11/2.40 , a:1, s:1, b:0),
% 2.11/2.40 'class_Complete__Lattice_Ocomplete__lattice' [149, 1] (w:1, o:87, a:1
% 2.11/2.40 , s:1, b:0),
% 14.57/14.85 'c_Inductive_Ocomplete__lattice__class_Ogfp' [150, 2] (w:1, o:177, a:
% 14.57/14.85 1, s:1, b:0),
% 14.57/14.85 'class_Orderings_Otop' [151, 1] (w:1, o:135, a:1, s:1, b:0),
% 14.57/14.85 'class_OrderedGroup_Opordered__ab__semigroup__add' [152, 1] (w:1, o:
% 14.57/14.85 136, a:1, s:1, b:0),
% 14.57/14.85 'c_SetInterval_Oord__class_OatLeast' [153, 2] (w:1, o:178, a:1, s:1
% 14.57/14.85 , b:0),
% 14.57/14.85 'class_OrderedGroup_Oab__semigroup__idem__mult' [154, 1] (w:1, o:137
% 14.57/14.85 , a:1, s:1, b:0),
% 14.57/14.85 'class_Ring__and__Field_Omult__mono' [158, 1] (w:1, o:111, a:1, s:1
% 14.57/14.85 , b:0),
% 14.57/14.85 'class_Ring__and__Field_Omult__mono1' [159, 1] (w:1, o:112, a:1, s:1
% 14.57/14.85 , b:0),
% 14.57/14.85 'class_Orderings_Obot' [160, 1] (w:1, o:138, a:1, s:1, b:0),
% 14.57/14.85 'class_Divides_Oring__div' [163, 1] (w:1, o:88, a:1, s:1, b:0),
% 14.57/14.85 'class_Ring__and__Field_Ocomm__ring__1' [164, 1] (w:1, o:83, a:1, s:1
% 14.57/14.85 , b:0),
% 14.57/14.85 'class_OrderedGroup_Ogroup__add' [165, 1] (w:1, o:139, a:1, s:1, b:0)
% 14.57/14.85 ,
% 14.57/14.85 'class_Finite__Set_Ofinite_Ofinite' [166, 1] (w:1, o:140, a:1, s:1
% 14.57/14.85 , b:0),
% 14.57/14.85 'class_HOL_Oord' [169, 1] (w:1, o:104, a:1, s:1, b:0),
% 14.57/14.85 'class_Ring__and__Field_Ocomm__ring' [171, 1] (w:1, o:84, a:1, s:1
% 14.57/14.85 , b:0),
% 14.57/14.85 'class_OrderedGroup_Oab__semigroup__mult' [174, 1] (w:1, o:141, a:1
% 14.57/14.85 , s:1, b:0),
% 14.57/14.85 'class_Ring__and__Field_Ocomm__semiring' [175, 1] (w:1, o:106, a:1
% 14.57/14.85 , s:1, b:0),
% 14.57/14.85 'c_ATP__Linkup_Osko__Set__Ximage__cong__1__1' [179, 5] (w:1, o:199
% 14.57/14.85 , a:1, s:1, b:0),
% 14.57/14.85 'c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1' [180, 1] (w:1
% 14.57/14.85 , o:142, a:1, s:1, b:0),
% 14.57/14.85 'c_ATP__Linkup_Osko__Set__XimageE__1__1' [181, 5] (w:1, o:200, a:1
% 14.57/14.85 , s:1, b:0),
% 14.57/14.85 'c_ATP__Linkup_Osko__Set__Ximage__iff__1__1' [182, 5] (w:1, o:201, a:
% 14.57/14.85 1, s:1, b:0),
% 14.57/14.85 'c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1' [184, 1] (w:1, o:143, a:
% 14.57/14.85 1, s:1, b:0),
% 14.57/14.85 'c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1' [185, 2] (w:1, o:
% 14.57/14.85 179, a:1, s:1, b:0),
% 14.57/14.85 'c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1' [186, 5] (w:1
% 14.57/14.85 , o:202, a:1, s:1, b:0),
% 14.57/14.85 'c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1' [188
% 14.57/14.85 , 2] (w:1, o:180, a:1, s:1, b:0),
% 14.57/14.85 'c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1' [189, 5] (w:1, o:203
% 14.57/14.85 , a:1, s:1, b:0),
% 14.57/14.85 'c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1' [190, 5] (w:1
% 14.57/14.85 , o:204, a:1, s:1, b:0),
% 14.57/14.85 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1' [191, 5
% 14.57/14.85 ] (w:1, o:205, a:1, s:1, b:0),
% 14.57/14.85 'class_Ring__and__Field_Oring__1' [192, 1] (w:1, o:100, a:1, s:1, b:0
% 14.57/14.85 ),
% 14.57/14.85 'v_U' [195, 0] (w:1, o:62, a:1, s:1, b:0),
% 14.57/14.85 'tc_Com_Opname' [196, 0] (w:1, o:63, a:1, s:1, b:0),
% 14.57/14.85 'v_G' [197, 0] (w:1, o:64, a:1, s:1, b:0),
% 14.57/14.85 'v_mgt__call' [198, 0] (w:1, o:65, a:1, s:1, b:0),
% 14.57/14.85 't_a' [199, 0] (w:1, o:66, a:1, s:1, b:0),
% 14.57/14.85 'v_na' [200, 0] (w:1, o:67, a:1, s:1, b:0),
% 14.57/14.85 'v_pn' [201, 0] (w:1, o:68, a:1, s:1, b:0),
% 14.57/14.85 'c_fequal' [204, 3] (w:1, o:193, a:1, s:1, b:0).
% 14.57/14.85
% 14.57/14.85
% 14.57/14.85 Starting Search:
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 14.57/14.85 Done
% 14.57/14.85
% 14.57/14.85
% 14.57/14.85 Intermediate Status:
% 14.57/14.85 Generated: 4758
% 14.57/14.85 Kept: 2004
% 14.57/14.85 Inuse: 200
% 14.57/14.85 Deleted: 11
% 14.57/14.85 Deletedinuse: 0
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 14.57/14.85 Done
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 14.57/14.85 Done
% 14.57/14.85
% 14.57/14.85
% 14.57/14.85 Intermediate Status:
% 14.57/14.85 Generated: 10067
% 14.57/14.85 Kept: 4005
% 14.57/14.85 Inuse: 329
% 14.57/14.85 Deleted: 16
% 14.57/14.85 Deletedinuse: 0
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 14.57/14.85 Done
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 14.57/14.85 Done
% 14.57/14.85
% 14.57/14.85
% 14.57/14.85 Intermediate Status:
% 14.57/14.85 Generated: 16715
% 14.57/14.85 Kept: 6008
% 14.57/14.85 Inuse: 415
% 14.57/14.85 Deleted: 16
% 14.57/14.85 Deletedinuse: 0
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 14.57/14.85 Done
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 14.57/14.85 Done
% 14.57/14.85
% 14.57/14.85
% 14.57/14.85 Intermediate Status:
% 14.57/14.85 Generated: 24344
% 14.57/14.85 Kept: 8017
% 14.57/14.85 Inuse: 553
% 14.57/14.85 Deleted: 23
% 14.57/14.85 Deletedinuse: 4
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 14.57/14.85 Done
% 14.57/14.85
% 14.57/14.85
% 14.57/14.85 Intermediate Status:
% 14.57/14.85 Generated: 31326
% 14.57/14.85 Kept: 10282
% 14.57/14.85 Inuse: 566
% 14.57/14.85 Deleted: 25
% 14.57/14.85 Deletedinuse: 5
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 14.57/14.85 Done
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 14.57/14.85 Done
% 14.57/14.85
% 14.57/14.85
% 14.57/14.85 Intermediate Status:
% 14.57/14.85 Generated: 47090
% 14.57/14.85 Kept: 12499
% 14.57/14.85 Inuse: 606
% 14.57/14.85 Deleted: 25
% 14.57/14.85 Deletedinuse: 5
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 14.57/14.85 Done
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 14.57/14.85 Done
% 14.57/14.85
% 14.57/14.85
% 14.57/14.85 Intermediate Status:
% 14.57/14.85 Generated: 56028
% 14.57/14.85 Kept: 14787
% 14.57/14.85 Inuse: 636
% 14.57/14.85 Deleted: 25
% 14.57/14.85 Deletedinuse: 5
% 14.57/14.85
% 14.57/14.85 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09
% 50.76/51.09 Intermediate Status:
% 50.76/51.09 Generated: 64514
% 50.76/51.09 Kept: 16790
% 50.76/51.09 Inuse: 660
% 50.76/51.09 Deleted: 25
% 50.76/51.09 Deletedinuse: 5
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09
% 50.76/51.09 Intermediate Status:
% 50.76/51.09 Generated: 73395
% 50.76/51.09 Kept: 18854
% 50.76/51.09 Inuse: 732
% 50.76/51.09 Deleted: 54
% 50.76/51.09 Deletedinuse: 30
% 50.76/51.09
% 50.76/51.09
% 50.76/51.09 Intermediate Status:
% 50.76/51.09 Generated: 83417
% 50.76/51.09 Kept: 21031
% 50.76/51.09 Inuse: 769
% 50.76/51.09 Deleted: 55
% 50.76/51.09 Deletedinuse: 30
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09 Resimplifying clauses:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09
% 50.76/51.09 Intermediate Status:
% 50.76/51.09 Generated: 90536
% 50.76/51.09 Kept: 23361
% 50.76/51.09 Inuse: 786
% 50.76/51.09 Deleted: 1014
% 50.76/51.09 Deletedinuse: 35
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09
% 50.76/51.09 Intermediate Status:
% 50.76/51.09 Generated: 98740
% 50.76/51.09 Kept: 25409
% 50.76/51.09 Inuse: 826
% 50.76/51.09 Deleted: 1014
% 50.76/51.09 Deletedinuse: 35
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09
% 50.76/51.09 Intermediate Status:
% 50.76/51.09 Generated: 113954
% 50.76/51.09 Kept: 28373
% 50.76/51.09 Inuse: 856
% 50.76/51.09 Deleted: 1014
% 50.76/51.09 Deletedinuse: 35
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09
% 50.76/51.09 Intermediate Status:
% 50.76/51.09 Generated: 130887
% 50.76/51.09 Kept: 30375
% 50.76/51.09 Inuse: 873
% 50.76/51.09 Deleted: 1014
% 50.76/51.09 Deletedinuse: 35
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09
% 50.76/51.09 Intermediate Status:
% 50.76/51.09 Generated: 148517
% 50.76/51.09 Kept: 32653
% 50.76/51.09 Inuse: 901
% 50.76/51.09 Deleted: 1014
% 50.76/51.09 Deletedinuse: 35
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09
% 50.76/51.09 Intermediate Status:
% 50.76/51.09 Generated: 160653
% 50.76/51.09 Kept: 35539
% 50.76/51.09 Inuse: 936
% 50.76/51.09 Deleted: 1014
% 50.76/51.09 Deletedinuse: 35
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09
% 50.76/51.09 Intermediate Status:
% 50.76/51.09 Generated: 171539
% 50.76/51.09 Kept: 37546
% 50.76/51.09 Inuse: 982
% 50.76/51.09 Deleted: 1014
% 50.76/51.09 Deletedinuse: 35
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09
% 50.76/51.09 Intermediate Status:
% 50.76/51.09 Generated: 182133
% 50.76/51.09 Kept: 39573
% 50.76/51.09 Inuse: 1021
% 50.76/51.09 Deleted: 1016
% 50.76/51.09 Deletedinuse: 37
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09 Resimplifying clauses:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.09
% 50.76/51.09 Intermediate Status:
% 50.76/51.09 Generated: 200423
% 50.76/51.09 Kept: 42824
% 50.76/51.09 Inuse: 1051
% 50.76/51.09 Deleted: 1385
% 50.76/51.09 Deletedinuse: 37
% 50.76/51.09
% 50.76/51.09 Resimplifying inuse:
% 50.76/51.09 Done
% 50.76/51.09
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 222494
% 50.76/51.10 Kept: 45559
% 50.76/51.10 Inuse: 1061
% 50.76/51.10 Deleted: 1385
% 50.76/51.10 Deletedinuse: 37
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 242618
% 50.76/51.10 Kept: 47659
% 50.76/51.10 Inuse: 1096
% 50.76/51.10 Deleted: 1385
% 50.76/51.10 Deletedinuse: 37
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 275148
% 50.76/51.10 Kept: 50304
% 50.76/51.10 Inuse: 1135
% 50.76/51.10 Deleted: 1386
% 50.76/51.10 Deletedinuse: 37
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 288940
% 50.76/51.10 Kept: 52471
% 50.76/51.10 Inuse: 1180
% 50.76/51.10 Deleted: 1386
% 50.76/51.10 Deletedinuse: 37
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 318695
% 50.76/51.10 Kept: 55199
% 50.76/51.10 Inuse: 1195
% 50.76/51.10 Deleted: 1386
% 50.76/51.10 Deletedinuse: 37
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 346796
% 50.76/51.10 Kept: 57441
% 50.76/51.10 Inuse: 1200
% 50.76/51.10 Deleted: 1386
% 50.76/51.10 Deletedinuse: 37
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 365479
% 50.76/51.10 Kept: 59543
% 50.76/51.10 Inuse: 1225
% 50.76/51.10 Deleted: 1386
% 50.76/51.10 Deletedinuse: 37
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10 Resimplifying clauses:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 385928
% 50.76/51.10 Kept: 62460
% 50.76/51.10 Inuse: 1235
% 50.76/51.10 Deleted: 1744
% 50.76/51.10 Deletedinuse: 37
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 398035
% 50.76/51.10 Kept: 64487
% 50.76/51.10 Inuse: 1254
% 50.76/51.10 Deleted: 1744
% 50.76/51.10 Deletedinuse: 37
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 411011
% 50.76/51.10 Kept: 66761
% 50.76/51.10 Inuse: 1285
% 50.76/51.10 Deleted: 1744
% 50.76/51.10 Deletedinuse: 37
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 426702
% 50.76/51.10 Kept: 68841
% 50.76/51.10 Inuse: 1310
% 50.76/51.10 Deleted: 1745
% 50.76/51.10 Deletedinuse: 38
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 443806
% 50.76/51.10 Kept: 70850
% 50.76/51.10 Inuse: 1363
% 50.76/51.10 Deleted: 1745
% 50.76/51.10 Deletedinuse: 38
% 50.76/51.10
% 50.76/51.10 Resimplifying inuse:
% 50.76/51.10 Done
% 50.76/51.10
% 50.76/51.10
% 50.76/51.10 Intermediate Status:
% 50.76/51.10 Generated: 467486
% 114.79/115.21 Kept: 73625
% 114.79/115.21 Inuse: 1380
% 114.79/115.21 Deleted: 1745
% 114.79/115.21 Deletedinuse: 38
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 484744
% 114.79/115.21 Kept: 75626
% 114.79/115.21 Inuse: 1407
% 114.79/115.21 Deleted: 1746
% 114.79/115.21 Deletedinuse: 39
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 499437
% 114.79/115.21 Kept: 77736
% 114.79/115.21 Inuse: 1430
% 114.79/115.21 Deleted: 1747
% 114.79/115.21 Deletedinuse: 40
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 512754
% 114.79/115.21 Kept: 79912
% 114.79/115.21 Inuse: 1440
% 114.79/115.21 Deleted: 1747
% 114.79/115.21 Deletedinuse: 40
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying clauses:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 523911
% 114.79/115.21 Kept: 81918
% 114.79/115.21 Inuse: 1463
% 114.79/115.21 Deleted: 2265
% 114.79/115.21 Deletedinuse: 40
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 538578
% 114.79/115.21 Kept: 84137
% 114.79/115.21 Inuse: 1520
% 114.79/115.21 Deleted: 2266
% 114.79/115.21 Deletedinuse: 41
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 547483
% 114.79/115.21 Kept: 86284
% 114.79/115.21 Inuse: 1555
% 114.79/115.21 Deleted: 2266
% 114.79/115.21 Deletedinuse: 41
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 564572
% 114.79/115.21 Kept: 88298
% 114.79/115.21 Inuse: 1579
% 114.79/115.21 Deleted: 2271
% 114.79/115.21 Deletedinuse: 46
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 579399
% 114.79/115.21 Kept: 91174
% 114.79/115.21 Inuse: 1595
% 114.79/115.21 Deleted: 2271
% 114.79/115.21 Deletedinuse: 46
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 591639
% 114.79/115.21 Kept: 93356
% 114.79/115.21 Inuse: 1600
% 114.79/115.21 Deleted: 2274
% 114.79/115.21 Deletedinuse: 49
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 603745
% 114.79/115.21 Kept: 95489
% 114.79/115.21 Inuse: 1635
% 114.79/115.21 Deleted: 2274
% 114.79/115.21 Deletedinuse: 49
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 615365
% 114.79/115.21 Kept: 97696
% 114.79/115.21 Inuse: 1673
% 114.79/115.21 Deleted: 2276
% 114.79/115.21 Deletedinuse: 49
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 634905
% 114.79/115.21 Kept: 100273
% 114.79/115.21 Inuse: 1703
% 114.79/115.21 Deleted: 2276
% 114.79/115.21 Deletedinuse: 49
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying clauses:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 663425
% 114.79/115.21 Kept: 104160
% 114.79/115.21 Inuse: 1713
% 114.79/115.21 Deleted: 2543
% 114.79/115.21 Deletedinuse: 49
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 680493
% 114.79/115.21 Kept: 106296
% 114.79/115.21 Inuse: 1742
% 114.79/115.21 Deleted: 2585
% 114.79/115.21 Deletedinuse: 90
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 690648
% 114.79/115.21 Kept: 108310
% 114.79/115.21 Inuse: 1774
% 114.79/115.21 Deleted: 2585
% 114.79/115.21 Deletedinuse: 90
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 706821
% 114.79/115.21 Kept: 110596
% 114.79/115.21 Inuse: 1787
% 114.79/115.21 Deleted: 2585
% 114.79/115.21 Deletedinuse: 90
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 718543
% 114.79/115.21 Kept: 112702
% 114.79/115.21 Inuse: 1817
% 114.79/115.21 Deleted: 2585
% 114.79/115.21 Deletedinuse: 90
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21 Resimplifying inuse:
% 114.79/115.21 Done
% 114.79/115.21
% 114.79/115.21
% 114.79/115.21 Intermediate Status:
% 114.79/115.21 Generated: 732445
% 114.79/115.21 Kept: 115046
% 114.79/115.22 Inuse: 1839
% 114.79/115.22 Deleted: 2596
% 114.79/115.22 Deletedinuse: 98
% 114.79/115.22
% 114.79/115.22 Resimplifying inuse:
% 114.79/115.22 Done
% 114.79/115.22
% 114.79/115.22
% 114.79/115.22 Intermediate Status:
% 114.79/115.22 Generated: 742943
% 114.79/115.22 Kept: 118178
% 114.79/115.22 Inuse: 1849
% 114.79/115.22 Deleted: 2596
% 114.79/115.22 Deletedinuse: 98
% 114.79/115.22
% 114.79/115.22 Resimplifying inuse:
% 114.79/115.22 Done
% 114.79/115.22
% 114.79/115.22 Resimplifying inuse:
% 114.79/115.22 Done
% 114.79/115.22
% 114.79/115.22
% 114.79/115.22 Intermediate Status:
% 114.79/115.22 Generated: 760273
% 114.79/115.22 Kept: 120369
% 114.79/115.22 Inuse: 1874
% 114.79/115.22 Deleted: 2596
% 114.79/115.22 Deletedinuse: 98
% 114.79/115.22
% 114.79/115.22 Resimplifying inuse:
% 114.79/115.22 Done
% 114.79/115.22
% 114.79/115.22 Resimplifying inuse:
% 114.79/115.22 Done
% 114.79/115.22
% 114.79/115.22 Resimplifying clauses:
% 114.79/115.22 Done
% 114.79/115.22
% 114.79/115.22
% 114.79/115.22 Intermediate Status:
% 114.79/115.22 Generated: 783342
% 114.79/115.22 Kept: 122525
% 114.79/115.22 Inuse: 1909
% 114.79/115.22 Deleted: 4700
% 114.79/115.22 Deletedinuse: 98
% 114.79/115.22
% 114.79/115.22 Resimplifying inuse:
% 114.79/115.22 Done
% 114.79/115.22
% 114.79/115.22 Resimplifying inuse:
% 114.79/115.22 Done
% 114.79/115.22
% 114.79/115.22
% 114.79/115.22 Intermediate Status:
% 114.79/115.22 Generated: 810213
% 114.79/115.22 Kept: 124625
% 114.79/115.22 Inuse: 1949
% 114.79/115.22 Deleted: 4701
% 114.79/115.22 Deletedinuse: 99
% 114.79/115.22
% 114.79/115.22 Resimplifying inuse:
% 114.79/115.22 Done
% 114.79/115.22
% 114.79/115.22 Resimplifying inuse:
% 114.79/115.22 Done
% 114.79/115.22
% 114.79/115.22
% 114.79/115.22 Intermediate Status:
% 114.79/115.22 Generated: 828105
% 114.79/115.22 Kept: 126625
% 114.79/115.22 Inuse: 1970
% 114.79/115.22 Deleted: 4702
% 114.79/115.22 Deletedinuse: 100
% 114.79/115.22
% 114.79/115.22 Resimplifying inuse:
% 114.79/115.22 Done
% 114.79/115.22
% 114.79/115.22 Resimplifying inuse:
% 114.79/115.22 Done
% 114.79/115.22
% 114.79/115.22
% 114.79/115.22 Intermediate Status:
% 114.79/115.22 Generated: 873693
% 206.80/207.28 Kept: 130253
% 206.80/207.28 Inuse: 1989
% 206.80/207.28 Deleted: 4702
% 206.80/207.28 Deletedinuse: 100
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 908390
% 206.80/207.28 Kept: 132587
% 206.80/207.28 Inuse: 1994
% 206.80/207.28 Deleted: 4702
% 206.80/207.28 Deletedinuse: 100
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 931900
% 206.80/207.28 Kept: 135674
% 206.80/207.28 Inuse: 2004
% 206.80/207.28 Deleted: 4702
% 206.80/207.28 Deletedinuse: 100
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 945650
% 206.80/207.28 Kept: 137713
% 206.80/207.28 Inuse: 2029
% 206.80/207.28 Deleted: 4702
% 206.80/207.28 Deletedinuse: 100
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 976163
% 206.80/207.28 Kept: 145489
% 206.80/207.28 Inuse: 2068
% 206.80/207.28 Deleted: 4702
% 206.80/207.28 Deletedinuse: 100
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying clauses:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 984448
% 206.80/207.28 Kept: 147545
% 206.80/207.28 Inuse: 2084
% 206.80/207.28 Deleted: 5123
% 206.80/207.28 Deletedinuse: 100
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 999345
% 206.80/207.28 Kept: 150480
% 206.80/207.28 Inuse: 2099
% 206.80/207.28 Deleted: 5123
% 206.80/207.28 Deletedinuse: 100
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1013790
% 206.80/207.28 Kept: 152489
% 206.80/207.28 Inuse: 2111
% 206.80/207.28 Deleted: 5124
% 206.80/207.28 Deletedinuse: 101
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1045460
% 206.80/207.28 Kept: 156799
% 206.80/207.28 Inuse: 2151
% 206.80/207.28 Deleted: 5133
% 206.80/207.28 Deletedinuse: 102
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1060446
% 206.80/207.28 Kept: 160153
% 206.80/207.28 Inuse: 2153
% 206.80/207.28 Deleted: 5136
% 206.80/207.28 Deletedinuse: 102
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1076568
% 206.80/207.28 Kept: 163583
% 206.80/207.28 Inuse: 2158
% 206.80/207.28 Deleted: 5136
% 206.80/207.28 Deletedinuse: 102
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1095683
% 206.80/207.28 Kept: 165602
% 206.80/207.28 Inuse: 2169
% 206.80/207.28 Deleted: 5140
% 206.80/207.28 Deletedinuse: 102
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying clauses:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1121196
% 206.80/207.28 Kept: 167625
% 206.80/207.28 Inuse: 2192
% 206.80/207.28 Deleted: 5500
% 206.80/207.28 Deletedinuse: 106
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1138651
% 206.80/207.28 Kept: 169682
% 206.80/207.28 Inuse: 2209
% 206.80/207.28 Deleted: 5504
% 206.80/207.28 Deletedinuse: 107
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1163015
% 206.80/207.28 Kept: 173178
% 206.80/207.28 Inuse: 2224
% 206.80/207.28 Deleted: 5504
% 206.80/207.28 Deletedinuse: 107
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1193260
% 206.80/207.28 Kept: 178696
% 206.80/207.28 Inuse: 2249
% 206.80/207.28 Deleted: 5504
% 206.80/207.28 Deletedinuse: 107
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1216093
% 206.80/207.28 Kept: 182042
% 206.80/207.28 Inuse: 2269
% 206.80/207.28 Deleted: 5504
% 206.80/207.28 Deletedinuse: 107
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1234092
% 206.80/207.28 Kept: 184056
% 206.80/207.28 Inuse: 2291
% 206.80/207.28 Deleted: 5504
% 206.80/207.28 Deletedinuse: 107
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1297266
% 206.80/207.28 Kept: 190022
% 206.80/207.28 Inuse: 2299
% 206.80/207.28 Deleted: 5504
% 206.80/207.28 Deletedinuse: 107
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying clauses:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1360342
% 206.80/207.28 Kept: 195589
% 206.80/207.28 Inuse: 2304
% 206.80/207.28 Deleted: 6082
% 206.80/207.28 Deletedinuse: 107
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1391468
% 206.80/207.28 Kept: 198354
% 206.80/207.28 Inuse: 2319
% 206.80/207.28 Deleted: 6082
% 206.80/207.28 Deletedinuse: 107
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1425328
% 206.80/207.28 Kept: 202603
% 206.80/207.28 Inuse: 2339
% 206.80/207.28 Deleted: 6082
% 206.80/207.28 Deletedinuse: 107
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1442368
% 206.80/207.28 Kept: 204618
% 206.80/207.28 Inuse: 2358
% 206.80/207.28 Deleted: 6082
% 206.80/207.28 Deletedinuse: 107
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 1458195
% 206.80/207.28 Kept: 206627
% 206.80/207.28 Inuse: 2374
% 206.80/207.28 Deleted: 6082
% 206.80/207.28 Deletedinuse: 107
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28 Resimplifying inuse:
% 206.80/207.28 Done
% 206.80/207.28
% 206.80/207.28
% 206.80/207.28 Intermediate Status:
% 206.80/207.28 Generated: 14Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------