TSTP Solution File: LCL805-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL805-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:58:13 EDT 2022
% Result : Unsatisfiable 1.00s 1.39s
% Output : Refutation 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL805-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n015.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 : Mon Jul 4 04:46:16 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.96/1.36 *** allocated 10000 integers for termspace/termends
% 0.96/1.36 *** allocated 10000 integers for clauses
% 0.96/1.36 *** allocated 10000 integers for justifications
% 0.96/1.36 *** allocated 15000 integers for termspace/termends
% 0.96/1.36 *** allocated 22500 integers for termspace/termends
% 0.96/1.36 Bliksem 1.12
% 0.96/1.36
% 0.96/1.36
% 0.96/1.36 Automatic Strategy Selection
% 0.96/1.36
% 0.96/1.36 Clauses:
% 0.96/1.36 [
% 0.96/1.36 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.36 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.96/1.36 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.36 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.96/1.36 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.36 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.36 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.96/1.36 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.36 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.96/1.36 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.96/1.36 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.36 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.96/1.36 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.96/1.36 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.36 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.36 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.96/1.36 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.96/1.36 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.36 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.96/1.36 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.96/1.36 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.96/1.36 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.96/1.36 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.96/1.36 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.36 , X ) ) ],
% 0.96/1.36 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.96/1.36 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.36 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.36 , X ) ) ],
% 0.96/1.36 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), X ), Z ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y
% 0.96/1.37 , 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.96/1.37 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.96/1.37 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 0.96/1.37 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.37 T, X ) ) ],
% 0.96/1.37 [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 0.96/1.37 'tc_nat' ), 'tc_nat' ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.96/1.37 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.96/1.37 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.37 , X ) ) ],
% 0.96/1.37 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.96/1.37 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.96/1.37 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.96/1.37 X ), Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.37 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.96/1.37 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.96/1.37 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.37 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.96/1.37 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.96/1.37 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 0.96/1.37 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.96/1.37 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 0.96/1.37 , Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.96/1.37 ), =( Z, Y ) ],
% 0.96/1.37 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , X ), Y ), 'tc_nat' ) ],
% 0.96/1.37 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , Y ), X ), 'tc_nat' ) ],
% 0.96/1.37 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , X ), Y ), 'tc_nat' ) ],
% 0.96/1.37 [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.96/1.37 ), Y ), X ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), X, 'tc_nat' ), Y ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.37 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.96/1.37 'c_lessequals'( Z, T, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.37 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.96/1.37 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.96/1.37 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.96/1.37 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.96/1.37 'c_lessequals'( Z, T, X ) ) ],
% 0.96/1.37 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.96/1.37 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 0.96/1.37 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.96/1.37 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 0.96/1.37 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y,
% 0.96/1.37 X, 'tc_nat' ) ), X ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), ~( 'c_lessequals'(
% 0.96/1.37 X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ), X ), ~(
% 0.96/1.37 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X,
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( U, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.96/1.37 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, U, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 0.96/1.37 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 0.96/1.37 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 0.96/1.37 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 0.96/1.37 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 0.96/1.37 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 0.96/1.37 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 0.96/1.37 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 0.96/1.37 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 0.96/1.37 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 0.96/1.37 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 0.96/1.37 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 0.96/1.37 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.96/1.37 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 0.96/1.37 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.96/1.37 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.96/1.37 ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.37 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.96/1.37 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.96/1.37 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.96/1.37 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.96/1.37 X ), T, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.96/1.37 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.96/1.37 X ), T, X ) ) ],
% 0.96/1.37 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.96/1.37 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 0.96/1.37 , Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.37 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.96/1.37 ],
% 0.96/1.37 [ ~( =( 'c_Type_Otype_OFun'( X, Y ), 'c_Type_Otype_OFun'( Z, T ) ) ),
% 0.96/1.37 =( Y, T ) ],
% 0.96/1.37 [ ~( =( 'c_Type_Otype_OFun'( X, Y ), 'c_Type_Otype_OFun'( Z, T ) ) ),
% 0.96/1.37 =( X, Z ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.96/1.37 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.96/1.37 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.96/1.37 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 0.96/1.37 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.37 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 0.96/1.37 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.37 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.37 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 0.96/1.37 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.37 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.96/1.37 ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , Z ), Y ), 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 0.96/1.37 ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.37 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.37 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.37 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.37 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.96/1.37 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 0.96/1.37 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.37 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.96/1.37 , X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.37 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.96/1.37 , X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.96/1.37 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 0.96/1.37 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 0.96/1.37 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.96/1.37 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.37 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.96/1.37 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.96/1.37 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.96/1.37 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.96/1.37 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Y ), T ), Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Y ), Z ), T, X ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.96/1.37 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.37 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.37 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.96/1.37 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.37 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.96/1.37 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.37 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.37 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.37 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.96/1.37 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 0.96/1.37 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.96/1.37 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.37 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.96/1.37 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.96/1.37 'c_lessequals'( Z, Y, X ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.96/1.37 , Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.96/1.37 , Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.96/1.37 , X ) ) ],
% 0.96/1.37 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.37 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.37 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.37 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.96/1.37 ) ],
% 0.96/1.37 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.96/1.37 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 0.96/1.37 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.96/1.37 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), Y ) ), ~(
% 0.96/1.37 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.96/1.37 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( 'c_lessequals'( Z
% 0.96/1.37 , Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.96/1.37 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.96/1.37 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.96/1.37 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.96/1.37 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.96/1.37 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.96/1.37 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 0.96/1.37 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.37 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 0.96/1.37 Z, T, X ), X ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.96/1.37 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 0.96/1.37 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.37 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.96/1.37 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.37 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.96/1.37 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 0.96/1.37 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 X, T, 'tc_nat' ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.96/1.37 , X, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.96/1.37 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.96/1.37 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 0.96/1.37 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.96/1.37 ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.96/1.37 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.96/1.37 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.37 Y ) ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 0.96/1.37 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 0.96/1.37 ) ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 0.96/1.37 'tc_nat' ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.37 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.96/1.37 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ),
% 0.96/1.37 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.37 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ),
% 0.96/1.37 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.96/1.37 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 0.96/1.37 Y, X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 0.96/1.37 Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 0.96/1.37 ), Z ), Y ) ],
% 0.96/1.37 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 0.96/1.37 hBOOL( hAPP( X, Z ) ) ],
% 0.96/1.37 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 0.96/1.37 hBOOL( hAPP( X, Z ) ) ],
% 0.96/1.37 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 0.96/1.37 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.96/1.37 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 0.96/1.37 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.96/1.37 Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.96/1.37 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.96/1.37 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.96/1.37 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.96/1.37 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 0.96/1.37 'c_Suc'( X ), 'tc_nat' ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.37 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 0.96/1.37 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.37 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.37 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.96/1.37 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.96/1.37 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.37 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.96/1.37 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.96/1.37 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.96/1.37 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.96/1.37 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.37 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.96/1.37 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, 'c_Suc'( Z ), T, X ),
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, Z, hAPP( Y, T ), X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 0.96/1.37 ), Z ), T, X ) ) ],
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 0.96/1.37 , X ) ), T, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.37 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.96/1.37 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.96/1.37 Y, T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 0.96/1.37 ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.96/1.37 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.96/1.37 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.96/1.37 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 0.96/1.37 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.96/1.37 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.96/1.37 ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.37 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.96/1.37 , T, X ) ) ), =( Y, Z ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.96/1.37 , T, X ) ) ), =( Z, T ) ],
% 0.96/1.37 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.96/1.37 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.96/1.37 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 0.96/1.37 Y ) ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.96/1.37 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.96/1.37 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.96/1.37 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.37 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.96/1.37 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.96/1.37 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.96/1.37 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 0.96/1.37 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.96/1.37 Y, T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 0.96/1.37 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.96/1.37 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.96/1.37 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.96/1.37 , Y, X ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.37 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.96/1.37 'tc_nat' ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T, U, Z ),
% 0.96/1.37 'c_List_Oappend'( X, 'c_List_Olist__update'( Y,
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( T, 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'tc_nat' ), U, Z ), Z ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'tc_nat' ) ],
% 0.96/1.37 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.96/1.37 ), Z ), 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.96/1.37 ), Z ), 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 0.96/1.37 ) ), 'c_Suc'( Z ) ), hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP(
% 0.96/1.37 'c_Lambda_Olift', X ), Z ) ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_List_Orotate'( X, 'c_List_Orev'( Y, Z ), Z ), 'c_List_Orev'(
% 0.96/1.37 'c_List_Orotate'( 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.37 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ),
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( X, 'c_Nat_Osize__class_Osize'( Y,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'tc_nat' ), 'tc_nat' ), Y, Z ), Z ) ) ],
% 0.96/1.37 [ =( 'c_Map_Omap__upds'( X, Y, 'c_List_Olist__update'( Z, T, U, W ), V0
% 0.96/1.37 , W ), 'c_Map_Omap__upds'( X, Y, Z, V0, W ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( Z,
% 0.96/1.37 'tc_List_Olist'( W ) ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 0.96/1.37 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( V0 ) ), T, 'tc_nat' ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.96/1.37 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.37 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.96/1.37 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.96/1.37 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.37 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.37 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.96/1.37 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.37 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.96/1.37 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.37 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.96/1.37 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.37 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.37 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.37 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.37 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.96/1.37 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.96/1.37 , X ), X ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.96/1.37 , X ), X ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.96/1.37 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.96/1.37 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.96/1.37 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.96/1.37 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.96/1.37 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.96/1.37 , 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.96/1.37 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 0.96/1.37 , 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.37 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.37 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.96/1.37 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 'tc_nat' ) ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.37 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.37 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( X, Y, Z ),
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'c_Suc'( 'c_Nat_Osize__class_Osize'( Y,
% 0.96/1.37 'tc_List_Olist'( Z ) ) ) ) ],
% 0.96/1.37 [ =( 'c_Suc'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ) ),
% 0.96/1.37 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( Z, X, Y ),
% 0.96/1.37 'tc_List_Olist'( Y ) ) ) ],
% 0.96/1.37 [ ~( 'c_lessequals'( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( X
% 0.96/1.37 , Y, Z ), 'tc_List_Olist'( Z ) ), 'c_Nat_Osize__class_Osize'( Y,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 0.96/1.37 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.96/1.37 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 0.96/1.37 ), Y, X ) ), =( Z, T ) ],
% 0.96/1.37 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Otake'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 0.96/1.37 'c_List_Olist_OCons'( Y, Z, T ), T ), 'c_List_Olist_OCons'( Y,
% 0.96/1.37 'c_List_Otake'( 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.37 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z, T ), T ) ), =(
% 0.96/1.37 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.96/1.37 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 0.96/1.37 'c_List_Olist_OCons'( Y, Z, T ), T ), 'c_List_Odrop'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 0.96/1.37 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z, T ) ),
% 0.96/1.37 =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_List_Otake'( 'c_Suc'( X ), 'c_List_Olist_OCons'( Y, Z, T ), T )
% 0.96/1.37 , 'c_List_Olist_OCons'( Y, 'c_List_Otake'( X, Z, T ), T ) ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( 'c_Suc'( X ), 'c_List_Olist_OCons'( Y, Z, T ), T )
% 0.96/1.37 , 'c_List_Odrop'( X, Z, T ) ) ],
% 0.96/1.37 [ =( 'c_List_Otake'( X, Y, Z ), Y ), ~( 'c_lessequals'(
% 0.96/1.37 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), X, 'tc_nat' ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'c_lessequals'( 'c_Nat_Osize__class_Osize'( 'c_List_Ofilter'( X, Y, Z
% 0.96/1.37 ), 'tc_List_Olist'( Z ) ), 'c_Nat_Osize__class_Osize'( Y,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'tc_nat' ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Y,
% 0.96/1.37 'c_List_Olist_OCons'( Z, T, X ), X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Y,
% 0.96/1.37 'c_List_Olist_OCons'( Z, T, X ), X ), X ), ~(
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Z, T, X ), X ) )
% 0.96/1.37 , ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.37 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Odrop'( X, Y, Z ),
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.37 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), X, 'tc_nat' ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Olist__update'( 'c_List_Olist_OCons'( X, Y, Z ), 'c_Suc'( T
% 0.96/1.37 ), U, Z ), 'c_List_Olist_OCons'( X, 'c_List_Olist__update'( Y, T, U, Z )
% 0.96/1.37 , Z ) ) ],
% 0.96/1.37 [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T ),
% 0.96/1.37 ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y,
% 0.96/1.37 'c_Type_Otype_OFun'( U, T ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Oreplicate'( 'c_Suc'( X ), Y, Z ), 'c_List_Olist_OCons'( Y
% 0.96/1.37 , 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist__update'( X, Y, Z, T ), X ), ~( 'c_lessequals'(
% 0.96/1.37 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T ) ), Y, 'tc_nat' ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( hAPP( hAPP( hAPP(
% 0.96/1.37 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y ) ],
% 0.96/1.37 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.96/1.37 ), Z ), 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 Z, X, 'tc_nat' ) ],
% 0.96/1.37 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.96/1.37 ), Z ), 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Olist__update'( X, Y, Z, T ), T ),
% 0.96/1.37 'c_List_Olist__update'( 'c_List_Orev'( X, T ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.37 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T ) ), Y, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z, T ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( T ) ), 'tc_nat' ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP(
% 0.96/1.37 'c_Lambda_Osubst', X ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ), 'c_Suc'(
% 0.96/1.37 T ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', U ), Y ), T ) ), Z ), hAPP(
% 0.96/1.37 hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ),
% 0.96/1.37 U ), Z ) ), Y ), T ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 0.96/1.37 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( X, 'c_List_Otake'( Y, Z, T ), T ), 'c_List_Otake'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'c_List_Odrop'( X, Z, T )
% 0.96/1.37 , T ) ) ],
% 0.96/1.37 [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 0.96/1.37 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 0.96/1.37 'c_Suc'( Y ), Z, T ) ) ],
% 0.96/1.37 [ =( 'c_List_Orotate'( X, Y, Z ), 'c_List_Orotate'(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( X, 'c_Nat_Osize__class_Osize'( Y,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'tc_nat' ), Y, Z ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_Nat_Osize__class_Osize'( 'c_List_Oremdups'( X, Y )
% 0.96/1.37 , 'tc_List_Olist'( Y ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'(
% 0.96/1.37 Y ) ), 'tc_nat' ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( X, 'c_List_Oreplicate'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Oreplicate'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, T
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X ) ), Y ),
% 0.96/1.37 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.96/1.37 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( X, Y, Z ),
% 0.96/1.37 'tc_List_Olist'( Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.96/1.37 ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ) ), 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.96/1.37 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 0.96/1.37 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 0.96/1.37 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 0.96/1.37 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 0.96/1.37 'c_lessequals'( Y, Z, X ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 0.96/1.37 'c_lessequals'( Z, Y, X ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'c_Suc'( X ), 'tc_nat' ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'c_Suc'( X ), 'tc_nat' ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 0.96/1.37 'tc_nat' ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.96/1.37 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.96/1.37 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.96/1.37 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.96/1.37 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_Suc'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 0.96/1.37 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.37 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.96/1.37 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.37 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.96/1.37 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.37 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.96/1.37 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 0.96/1.37 , 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.96/1.37 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 0.96/1.37 , X, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 0.96/1.37 'tc_nat' ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 0.96/1.37 'tc_nat' ) ],
% 0.96/1.37 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), Z, 'tc_nat' ), 'tc_nat'
% 0.96/1.37 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.96/1.37 , T, X ), X ), T, X ) ) ],
% 0.96/1.37 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 0.96/1.37 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.96/1.37 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.96/1.37 Z, T, X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.96/1.37 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.96/1.37 T, Z, X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 0.96/1.37 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 0.96/1.37 'c_lessequals'( Z, T, X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.96/1.37 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.96/1.37 Z, T, X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.96/1.37 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.96/1.37 T, Z, X ), X ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.96/1.37 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.37 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.96/1.37 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.96/1.37 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.96/1.37 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.96/1.37 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 0.96/1.37 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.96/1.37 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.37 , Y ), Z ), Z, X ), Y ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 0.96/1.37 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 0.96/1.37 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.96/1.37 Y, T, X ), X ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.96/1.37 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.96/1.37 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.96/1.37 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.37 ) ), =( Y, Z ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.37 ) ), =( Y, Z ) ],
% 0.96/1.37 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'tc_nat' ) ) ) ],
% 0.96/1.37 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 0.96/1.37 , Y ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 'tc_nat' ), Z, X ), Z ) ],
% 0.96/1.37 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.96/1.37 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.96/1.37 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.96/1.37 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.96/1.37 ), 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.96/1.37 ), 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.96/1.37 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 0.96/1.37 ],
% 0.96/1.37 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.96/1.37 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.96/1.37 'tc_nat' ) ],
% 0.96/1.37 [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ), hAPP( hAPP(
% 0.96/1.37 'c_Lambda_Olift', 'c_Lambda_Oliftn'( X, Y, Z ) ), Z ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ), 'tc_nat' ), =( X,
% 0.96/1.37 'c_List_Olist_ONil'( Y ) ) ],
% 0.96/1.37 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ), 'tc_List_Olist'( X
% 0.96/1.37 ) ), 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 'c_List_Odrop'(
% 0.96/1.37 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_List_Olist_OCons'(
% 0.96/1.37 Y, Z, T ), T ), 'c_List_Olist_OCons'( Y, Z, T ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Odrop'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ),
% 0.96/1.37 'c_lessequals'( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), X
% 0.96/1.37 , 'tc_nat' ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ), ~(
% 0.96/1.37 'c_lessequals'( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), X
% 0.96/1.37 , 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, U, Z ) ) ),
% 0.96/1.37 =( 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) )
% 0.96/1.37 , X, Z ), T ), 'c_lessequals'( 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z
% 0.96/1.37 ) ), 'tc_nat' ) ],
% 0.96/1.37 [ =( 'c_List_Otake'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Oappend'( 'c_List_Otake'( X, Y, T ), 'c_List_Otake'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, 'c_Nat_Osize__class_Osize'( Y,
% 0.96/1.37 'tc_List_Olist'( T ) ), 'tc_nat' ), Z, T ), T ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, U, Z ) ) ),
% 0.96/1.37 =( X, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z )
% 0.96/1.37 ), T, Z ) ), ~( 'c_lessequals'( 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z
% 0.96/1.37 ) ), 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, U, Z ) ) ),
% 0.96/1.37 =( Y, 'c_List_Oappend'( 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( Z ) ), T, Z ), U, Z ) ), ~( 'c_lessequals'(
% 0.96/1.37 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) ),
% 0.96/1.37 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, U, Z ) ) ),
% 0.96/1.37 =( 'c_List_Oappend'( 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( T,
% 0.96/1.37 'tc_List_Olist'( Z ) ), X, Z ), Y, Z ), U ), 'c_lessequals'(
% 0.96/1.37 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) ),
% 0.96/1.37 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) ), 'tc_nat' ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Oappend'( 'c_List_Odrop'( X, Y, T ), 'c_List_Odrop'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( X, 'c_Nat_Osize__class_Osize'( Y,
% 0.96/1.37 'tc_List_Olist'( T ) ), 'tc_nat' ), Z, T ), T ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T, U, Z ),
% 0.96/1.37 'c_List_Oappend'( 'c_List_Olist__update'( X, T, U, Z ), Y, Z ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T, U, Z ),
% 0.96/1.37 'c_List_Oappend'( 'c_List_Olist__update'( X, T, U, Z ), Y, Z ) ), ~(
% 0.96/1.37 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist__update'( X, Y, Z, T ), 'c_List_Oappend'(
% 0.96/1.37 'c_List_Otake'( Y, X, T ), 'c_List_Olist_OCons'( Z, 'c_List_Odrop'(
% 0.96/1.37 'c_Suc'( Y ), X, T ), T ), T ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.37 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T ) ), 'tc_nat' ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Nat_Osize__class_Osize'( Y,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.96/1.37 ) ) ), =( 'c_List_Orotate'( X, Y, Z ), Y ) ],
% 0.96/1.37 [ =( 'c_List_Orotate'( X, Y, Z ), Y ), ~( 'c_lessequals'(
% 0.96/1.37 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.96/1.37 'c_List_Olistsum'( 'c_List_Omap'( Y, 'c_List_Ofilter'( Z, T, U ), U, X )
% 0.96/1.37 , X ), 'c_List_Olistsum'( 'c_List_Omap'( Y, T, U, X ), X ) ), ~( hBOOL(
% 0.96/1.37 hAPP( Z, 'c_List_Osko__List__Xlistsum__map__filter__1__1'( Z, Y, T, U, X
% 0.96/1.37 ) ) ) ) ],
% 0.96/1.37 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.96/1.37 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.37 Y ), X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ],
% 0.96/1.37 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 'c_List_Otake'(
% 0.96/1.37 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_List_Olist_OCons'(
% 0.96/1.37 Y, Z, T ), T ), 'c_List_Olist_ONil'( T ) ) ],
% 0.96/1.37 [ =( 'c_List_Otake'( X, 'c_List_Olist_OCons'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Olist_OCons'( Y, 'c_List_Otake'( 'c_HOL_Ominus__class_Ominus'( X
% 0.96/1.37 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z, T ), T ) ), =( X,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.96/1.37 'v_sko__List__Xdistinct__Xinduct__1'( X ),
% 0.96/1.37 'v_sko__List__Xdistinct__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.96/1.37 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.96/1.37 'v_sko__List__Xremove1__Xinduct__1'( X ),
% 0.96/1.37 'v_sko__List__Xremove1__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.96/1.37 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.96/1.37 'v_sko__List__Xlist__Xinduct__1'( X ), 'v_sko__List__Xlist__Xinduct__2'(
% 0.96/1.37 X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_ONil'( 't_a' ) ) ) )
% 0.96/1.37 ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.96/1.37 'v_sko__List__Xmap__Xinduct__1'( X ), 'v_sko__List__Xmap__Xinduct__2'( X
% 0.96/1.37 ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_ONil'( 't_a' ) ) ) )
% 0.96/1.37 ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.96/1.37 'v_sko__List__Xtake__Xinduct__1'( X ), 'v_sko__List__Xtake__Xinduct__2'(
% 0.96/1.37 X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_ONil'( 't_a' ) ) ) )
% 0.96/1.37 ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.96/1.37 'v_sko__List__Xconcat__Xinduct__1'( X ),
% 0.96/1.37 'v_sko__List__Xconcat__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X
% 0.96/1.37 , 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( X, 'c_List_Olist_OCons'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Odrop'( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 0.96/1.37 'tc_nat' ), 'tc_nat' ), Z, T ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 'tc_nat' ) ) ],
% 0.96/1.37 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ),
% 0.96/1.37 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.96/1.37 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( 'c_Lambda_Obeta'(
% 0.96/1.37 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), Z,
% 0.96/1.37 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 0.96/1.37 'c_List_Osko__List__Xlistsum__map__filter__1__1'( Z, Y, T, U, X ) ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_List_Olistsum'( 'c_List_Omap'(
% 0.96/1.37 Y, 'c_List_Ofilter'( Z, T, U ), U, X ), X ), 'c_List_Olistsum'(
% 0.96/1.37 'c_List_Omap'( Y, T, U, X ), X ) ) ],
% 0.96/1.37 [ ~( =( X, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( Y ) ), Z, Y ) ) ), =( 'c_List_Oappend'( X,
% 0.96/1.37 'c_List_Oappend'( 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( Y ) ), Z, Y ), T, Y ), Y ), 'c_List_Oappend'( Z, T, Y )
% 0.96/1.37 ), ~( 'c_lessequals'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y
% 0.96/1.37 ) ), 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( Y ) ), 'tc_nat' ) )
% 0.96/1.37 ],
% 0.96/1.37 [ ~( =( 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'(
% 0.96/1.37 Y ) ), Z, Y ), X ) ), 'c_lessequals'( 'c_Nat_Osize__class_Osize'( Z,
% 0.96/1.37 'tc_List_Olist'( Y ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y
% 0.96/1.37 ) ), 'tc_nat' ), =( 'c_List_Oappend'( Z, T, Y ), 'c_List_Oappend'( X,
% 0.96/1.37 'c_List_Oappend'( 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( Y ) ), Z, Y ), T, Y ), Y ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist_Olist__size'( X, 'c_List_Olist_OCons'( Y, Z, T ), T )
% 0.96/1.37 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( X, Y ) ),
% 0.96/1.37 'c_List_Olist_Olist__size'( X, Z, T ) ) ), 'c_Suc'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Odrop'( X, Y, Z ), Z ), 'c_List_Otake'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( 'c_Nat_Osize__class_Osize'( Y,
% 0.96/1.37 'tc_List_Olist'( Z ) ), X, 'tc_nat' ), 'c_List_Orev'( Y, Z ), Z ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Otake'( X, Y, Z ), Z ), 'c_List_Odrop'(
% 0.96/1.37 'c_HOL_Ominus__class_Ominus'( 'c_Nat_Osize__class_Osize'( Y,
% 0.96/1.37 'tc_List_Olist'( Z ) ), X, 'tc_nat' ), 'c_List_Orev'( Y, Z ), Z ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.96/1.37 X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.96/1.37 'c_Lambda_Olift', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , T ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( hAPP(
% 0.96/1.37 'c_Lambda_Olift', Y ), T ) ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.96/1.37 X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.96/1.37 'c_Lambda_Olift', X ), T ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), T ) ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.37 T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X ) ), Y ),
% 0.96/1.37 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.37 X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ),
% 0.96/1.37 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.96/1.37 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeE__1__1'(
% 0.96/1.37 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeD__1__1'(
% 0.96/1.37 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), 'c_Type_Otype_OFun'( Z
% 0.96/1.37 , T ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( X,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_Type_Otype' ), Y, T ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubstn'(
% 0.96/1.37 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'( X, Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat__aux'( 'c_COMBC'(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ), X, X, X )
% 0.96/1.37 , Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.37 [ =( 'c_List_Otake'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.37 , X ), Y ), Z, T ), 'c_List_Oappend'( 'c_List_Otake'( X, Z, T ),
% 0.96/1.37 'c_List_Otake'( Y, 'c_List_Odrop'( X, Z, T ), T ), T ) ), ~(
% 0.96/1.37 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.37 Y ), 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( T ) ), 'tc_nat' ) )
% 0.96/1.37 ],
% 0.96/1.37 [ =( 'c_List_Orotate'( X, Y, Z ), 'c_List_Oappend'( 'c_List_Odrop'(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( X, 'c_Nat_Osize__class_Osize'( Y,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'tc_nat' ), Y, Z ), 'c_List_Otake'(
% 0.96/1.37 'c_Divides_Odiv__class_Omod'( X, 'c_Nat_Osize__class_Osize'( Y,
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'tc_nat' ), Y, Z ), Z ) ) ],
% 0.96/1.37 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__types__1__1'(
% 0.96/1.37 Z, T, X, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 0.96/1.37 'tc_Lambda_OdB' ), T ) ), ~( 'c_Type_Otypings'( X, W, V0 ) ), ~(
% 0.96/1.37 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.96/1.37 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.96/1.37 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.96/1.37 , Z ) ) ],
% 0.96/1.37 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__typesE__1__1'(
% 0.96/1.37 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB',
% 0.96/1.37 'tc_Lambda_OdB' ), Z ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.96/1.37 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.96/1.37 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.96/1.37 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.96/1.37 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.96/1.37 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.96/1.37 ) ],
% 0.96/1.37 [ =( 'c_List_Oremove1'( X, 'c_List_Olist_OCons'( X, Y, Z ), Z ), Y ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Olist_Olist__case'( X, Y, 'c_List_Olist_OCons'( Z, T, U ),
% 0.96/1.37 W, U ), hAPP( hAPP( Y, Z ), T ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( 'c_List_Ofilter'( X, Y, Z ), Z ), ~(
% 0.96/1.37 'c_List_Odistinct'( Y, Z ) ) ],
% 0.96/1.37 [ =( X, 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'(
% 0.96/1.37 Z ) ), 'c_List_Oappend'( Y, X, Z ), Z ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 0.96/1.37 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 0.96/1.37 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.96/1.37 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.96/1.37 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 0.96/1.37 , Y ) ],
% 0.96/1.37 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Y, Z, X ), X ),
% 0.96/1.37 ~( 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( T,
% 0.96/1.37 'c_List_Olist_OCons'( Y, Z, X ), X ), X ) ) ],
% 0.96/1.37 [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.96/1.37 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.96/1.37 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 0.96/1.37 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.96/1.37 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 0.96/1.37 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_OCons'( Z, T, Y ) ) ), =( X
% 0.96/1.37 , 'c_List_Oappend'( 'c_List_Orev'( T, Y ), 'c_List_Olist_OCons'( Z,
% 0.96/1.37 'c_List_Olist_ONil'( Y ), Y ), Y ) ) ],
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y
% 0.96/1.37 ), Y ), 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 0.96/1.37 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_OCons'( Z, T, U ), W, U ),
% 0.96/1.37 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, W, U ) ) ],
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Olist_OCons'( X, Y, Z ), Z ),
% 0.96/1.37 'c_List_Oappend'( 'c_List_Orev'( Y, Z ), 'c_List_Olist_OCons'( X,
% 0.96/1.37 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Ofilter'( T, U, Z ) ) )
% 0.96/1.37 , hBOOL( hAPP( T, X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.96/1.37 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.96/1.37 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.96/1.37 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.96/1.37 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.96/1.37 [ =( 'c_List_Otake'( X, 'c_List_Odrop'( Y, Z, T ), T ), 'c_List_Odrop'(
% 0.96/1.37 Y, 'c_List_Otake'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.96/1.37 ), Y ), Z, T ), T ) ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_OCons'( X, Y, Z ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.96/1.37 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 X ), Y ), Z ) ), T ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 X ), Y ), Z ) ), T ) ) ],
% 0.96/1.37 [ =( 'c_List_Oremdups'( 'c_List_Ofilter'( X, Y, Z ), Z ),
% 0.96/1.37 'c_List_Ofilter'( X, 'c_List_Oremdups'( Y, Z ), Z ) ) ],
% 0.96/1.37 [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.96/1.37 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.96/1.37 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Odrop'( Y, Z, X ), X ), ~(
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'( Y,
% 0.96/1.37 X ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ) ) ],
% 0.96/1.37 [ =( 'c_List_Ofilter'( X, 'c_List_Olist_OCons'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Olist_OCons'( Y, 'c_List_Ofilter'( X, Z, T ), T ) ), ~( hBOOL(
% 0.96/1.37 hAPP( X, Y ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.96/1.37 'c_List_Orev'( Z, Y ) ) ), =( Z, 'c_List_Olist_OCons'( X,
% 0.96/1.37 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 0.96/1.37 [ =( 'c_List_Otake'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.96/1.37 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_OCons'( X,
% 0.96/1.37 'c_List_Olist_ONil'( Z ), Z ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 0.96/1.37 ), =( X, T ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, Y, Z ) ) ),
% 0.96/1.37 =( X, T ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( X, T, Z ) ) ),
% 0.96/1.37 =( Y, T ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Otake'( Y, Z, X ), X ), ~(
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( Z, X ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Ofilter'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z ) ) )
% 0.96/1.37 , hBOOL( hAPP( X, T ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'( 'c_List_Oappend'( X
% 0.96/1.37 , Z, Y ), Y ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'( 'c_List_Oappend'( Z
% 0.96/1.37 , X, Y ), Y ) ) ],
% 0.96/1.37 [ =( X, 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ) ) ],
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ), X ) ],
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ), X ) ],
% 0.96/1.37 [ ~( =( 'c_Nat_Osize__class_Osize'( 'c_List_Oremdups'( X, Y ),
% 0.96/1.37 'tc_List_Olist'( Y ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y
% 0.96/1.37 ) ) ) ), =( 'c_List_Oremdups'( X, Y ), X ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oremdups'( X, Y ), X ) ), =( 'c_Nat_Osize__class_Osize'(
% 0.96/1.37 'c_List_Oremdups'( X, Y ), 'tc_List_Olist'( Y ) ),
% 0.96/1.37 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ) ) ],
% 0.96/1.37 [ =( X, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'(
% 0.96/1.37 Y ) ), 'c_List_Oappend'( X, Z, Y ), Y ) ) ],
% 0.96/1.37 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 0.96/1.37 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubstn'( X, Y, hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.96/1.37 'tc_nat' ) ) ) ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 0.96/1.37 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.37 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Oreplicate'( X, Y, Z ), Z ),
% 0.96/1.37 'c_List_Oreplicate'( X, Y, Z ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.96/1.37 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.96/1.37 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.96/1.37 'c_List_Olist_OCons'( X, Y, Z ), Z ), Y ) ],
% 0.96/1.37 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.96/1.37 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 0.96/1.37 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( 'c_List_Otake'( X, Y, Z ), 'c_List_Odrop'( X, Y,
% 0.96/1.37 Z ), Z ), Y ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( Y, X ), ~(
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Z, Y, X ), X ) )
% 0.96/1.37 ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.96/1.37 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.96/1.37 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.96/1.37 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.96/1.37 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Oappend'( 'c_List_Orev'( X, Y ),
% 0.96/1.37 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( Y ), Y ), Y ), Y ),
% 0.96/1.37 'c_List_Olist_OCons'( Z, X, Y ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( 'c_List_Odrop'( X, Y, Z ), Z ), ~(
% 0.96/1.37 'c_List_Odistinct'( Y, Z ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( 'c_List_Orev'( X, Y ), Y ), ~( 'c_List_Odistinct'(
% 0.96/1.37 X, Y ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'( 'c_List_Orev'( X, Y
% 0.96/1.37 ), Y ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oremdups'( X, Y ), X ) ), 'c_List_Odistinct'( X, Y ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Oremdups'( X, Y ), X ), ~( 'c_List_Odistinct'( X, Y ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T
% 0.96/1.37 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y, T ) ),
% 0.96/1.37 'c_Lambda_Oliftn'( X, Z, T ) ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.96/1.37 'v_sko__List__Xlistsp__Xinduct__1'( Z, X ),
% 0.96/1.37 'v_sko__List__Xlistsp__Xinduct__2'( Z, X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.96/1.37 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' )
% 0.96/1.37 ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.96/1.37 'v_sko__List__Xlistsp__Xinducts__1'( Z, X ),
% 0.96/1.37 'v_sko__List__Xlistsp__Xinducts__2'( Z, X ), 't_a' ) ) ) ), ~( hBOOL(
% 0.96/1.37 hAPP( X, 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y,
% 0.96/1.37 't_a' ) ) ],
% 0.96/1.37 [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.96/1.37 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.96/1.37 ), 'c_Lambda_OdB_OAbs'( X ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ],
% 0.96/1.37 [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ],
% 0.96/1.37 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Oremdups'( X, Y ),
% 0.96/1.37 'tc_List_Olist'( Y ) ), 'c_List_Olength__unique'( X, Y ) ) ],
% 0.96/1.37 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.96/1.37 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.96/1.37 'tc_Lambda_OdB' ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist__update'( 'c_List_Olist_OCons'( X, Y, Z ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, Z ), 'c_List_Olist_OCons'( T,
% 0.96/1.37 Y, Z ) ) ],
% 0.96/1.37 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist__update'( X, Y, Z, T ),
% 0.96/1.37 'tc_List_Olist'( T ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T
% 0.96/1.37 ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Oappend'(
% 0.96/1.37 'c_List_Olist_ONil'( Z ), 'c_List_Olist_OCons'( X, Y, Z ), Z ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.96/1.37 'c_List_Orev'( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ), Y
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.96/1.37 , 'c_Lambda_OdB_OVar'( Y ) ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.96/1.37 ) ) ) ],
% 0.96/1.37 [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 0.96/1.37 X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'( X, hAPP( hAPP(
% 0.96/1.37 hAPP( 'c_Lambda_Osubst', U ), Y ), T ), W ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 0.96/1.37 'tc_bool' ) ), Y ) ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.96/1.37 'tc_bool' ) ), Y ) ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Y,
% 0.96/1.37 'c_List_Olist_ONil'( X ), X ), X ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y )
% 0.96/1.37 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.96/1.37 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( 'c_List_Otake'( X, Y, Z ), Z ), ~(
% 0.96/1.37 'c_List_Odistinct'( Y, Z ) ) ],
% 0.96/1.37 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.96/1.37 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.96/1.37 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( Z ), Z ), Z ),
% 0.96/1.37 'c_List_Olist_OCons'( Y, 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ],
% 0.96/1.37 [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 0.96/1.37 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X, Z, T ) ),
% 0.96/1.37 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Oappend'( X, Y, Z ), Z ), 'c_List_Oappend'(
% 0.96/1.37 'c_List_Orev'( Y, Z ), 'c_List_Orev'( X, Z ), Z ) ) ],
% 0.96/1.37 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Oappend'( Z, T, U ), W, U ),
% 0.96/1.37 'c_List_Ofoldl'( X, 'c_List_Ofoldl'( X, Y, Z, W, U ), T, W, U ) ) ],
% 0.96/1.37 [ =( 'c_List_Orotate'( X, 'c_List_Orotate'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Orotate'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.96/1.37 , Y ), Z, T ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'(
% 0.96/1.37 'c_List_Olist_OCons'( Z, X, Y ), Y ) ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OVar'(
% 0.96/1.37 Z ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Ofilter'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Oappend'( 'c_List_Ofilter'( X, Y, T ), 'c_List_Ofilter'( X, Z, T
% 0.96/1.37 ), T ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.96/1.37 , 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ),
% 0.96/1.37 ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y, 'tc_Lambda_OdB' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.96/1.37 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.96/1.37 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.96/1.37 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 0.96/1.37 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.96/1.37 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.96/1.37 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.96/1.37 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.96/1.37 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.96/1.37 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.96/1.37 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.96/1.37 Y ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.96/1.37 Y ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.96/1.37 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.96/1.37 Y ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.96/1.37 Y ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.96/1.37 Y ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.96/1.37 Y ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.96/1.37 Y ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.96/1.37 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.96/1.37 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 0.96/1.37 X ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.96/1.37 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 0.96/1.37 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ), X )
% 0.96/1.37 ],
% 0.96/1.37 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 0.96/1.37 , 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, Y ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 0.96/1.37 ), =( Y, U ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.96/1.37 [ =( 'c_List_Otake'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.37 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_ONil'( Z ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_ONil'( X
% 0.96/1.37 ), X ), 'c_List_Olist_ONil'( X ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Orev'( 'c_List_Olist_ONil'( X ),
% 0.96/1.37 X ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oremdups'( 'c_List_Olist_ONil'( X
% 0.96/1.37 ), X ) ) ],
% 0.96/1.37 [ ~( =( X, 'c_List_Oappend'( Y, X, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( X, Y, Z ), Y ) ), =( X, 'c_List_Olist_ONil'( Z
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ ~( =( X, 'c_List_Oappend'( X, Y, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( X, Y, Z ), X ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oremdups'( X, Y ), 'c_List_Olist_ONil'( Y ) ) ), =( X,
% 0.96/1.37 'c_List_Olist_ONil'( Y ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Orotate'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y
% 0.96/1.37 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Orev'( Y, X ) ) ), =( Y,
% 0.96/1.37 'c_List_Olist_ONil'( X ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( 'c_List_Olist_ONil'( X ), X ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y
% 0.96/1.37 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( X
% 0.96/1.37 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Z
% 0.96/1.37 , 'c_List_Olist_ONil'( X ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Y
% 0.96/1.37 , 'c_List_Olist_ONil'( X ) ) ],
% 0.96/1.37 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), Y ) ],
% 0.96/1.37 [ =( 'c_List_Oremdups'( 'c_List_Olist_ONil'( X ), X ),
% 0.96/1.37 'c_List_Olist_ONil'( X ) ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.96/1.37 'c_List_Olist_ONil'( Y ) ) ],
% 0.96/1.37 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), Y, X ), Y ) ],
% 0.96/1.37 [ =( X, 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 0.96/1.37 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ), X ) ],
% 0.96/1.37 [ =( 'c_List_Otake'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.96/1.37 'c_List_Olist_ONil'( Y ) ) ],
% 0.96/1.37 [ ~( hBOOL( hAPP( X, 'c_List_Olist_Olist__case'( Y, Z,
% 0.96/1.37 'c_List_Olist_ONil'( 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X, Y ) )
% 0.96/1.37 ],
% 0.96/1.37 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.96/1.37 [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_OCons'( Z,
% 0.96/1.37 'c_List_Olist_ONil'( Y ), Y ) ) ), =( X, 'c_List_Olist_OCons'( Z,
% 0.96/1.37 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 0.96/1.37 [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y )
% 0.96/1.37 , Z ) ) ],
% 0.96/1.37 [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) )
% 0.96/1.37 ) ],
% 0.96/1.37 [ =( hAPP( X, hAPP( Y, Z ) ), hAPP( 'c_Fun_Ocomp'( X, Y, T, U, W ), Z )
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.96/1.37 X ), Y ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.96/1.37 X ), Y ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.96/1.37 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Ofilter'( X, 'c_List_Oreplicate'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Oreplicate'( Y, Z, T ) ), ~( hBOOL( hAPP( X, Z ) ) ) ],
% 0.96/1.37 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ],
% 0.96/1.37 [ 'c_List_Olistrelp'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 0.96/1.37 'c_List_Olist_OCons'( U, W, T ), T ), ~( 'c_List_Olistrelp'( X, Z, W, T )
% 0.96/1.37 ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.96/1.37 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.96/1.37 'tc_Lambda_OdB' ) ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 0.96/1.37 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.96/1.37 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.96/1.37 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.96/1.37 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.96/1.37 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.96/1.37 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.96/1.37 ) ],
% 0.96/1.37 [ =( 'c_List_Oremove1'( X, 'c_List_Olist_OCons'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Olist_OCons'( Y, 'c_List_Oremove1'( X, Z, T ), T ) ), =( X, Y ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ),
% 0.96/1.37 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( T ) ) ) ), =(
% 0.96/1.37 'c_Map_Omap__upds'( U, 'c_List_Oappend'( X, W, Y ), Z, Y, T ),
% 0.96/1.37 'c_Map_Omap__upds'( U, X, Z, Y, T ) ) ],
% 0.96/1.37 [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ),
% 0.96/1.37 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( T ) ) ) ), =(
% 0.96/1.37 'c_Map_Omap__upds'( U, X, 'c_List_Oappend'( Z, W, T ), Y, T ),
% 0.96/1.37 'c_Map_Omap__upds'( U, X, Z, Y, T ) ) ],
% 0.96/1.37 [ ~( =( X, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( Y ) ), Z, Y ) ) ), =( 'c_List_Oappend'( X,
% 0.96/1.37 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ), Z
% 0.96/1.37 , Y ), Y ), Z ) ],
% 0.96/1.37 [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.96/1.37 Z ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.96/1.37 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.96/1.37 'tc_Lambda_OdB' ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( 'c_List_Oremove1'( X, Y, Z ), Z ), ~(
% 0.96/1.37 'c_List_Odistinct'( Y, Z ) ) ],
% 0.96/1.37 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.96/1.37 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OVar'( X )
% 0.96/1.37 , Y ) ],
% 0.96/1.37 [ 'c_Lambda_Obeta'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.96/1.37 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.96/1.37 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( 'c_Lambda_Obeta'( X, Z )
% 0.96/1.37 ) ],
% 0.96/1.37 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Orotate'( X, Y, Z ),
% 0.96/1.37 'tc_List_Olist'( Z ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z
% 0.96/1.37 ) ) ) ],
% 0.96/1.37 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.96/1.37 X ) ), Y ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Oappend'( X, Y, Z ),
% 0.96/1.37 'tc_List_Olist'( Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.96/1.37 ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) ) ),
% 0.96/1.37 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ) ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 0.96/1.37 'c_List_Olist_OCons'( Y, Z, X ), X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Olistsum'( Z, X ) ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ),
% 0.96/1.37 'c_Lambda_OdB_OAbs'( 'c_Lambda_Oliftn'( X, Y, hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.96/1.37 'tc_nat' ) ) ) ) ) ],
% 0.96/1.37 [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.96/1.37 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.96/1.37 'tc_Lambda_OdB' ), X ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.96/1.37 'c_List_Oreplicate'( T, Y, Z ), Z ), 'c_List_Oappend'(
% 0.96/1.37 'c_List_Oreplicate'( T, Y, Z ), 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 0.96/1.37 [ =( X, 'c_List_Olist_OCons'( 'v_sko__List__Xlistsp__Xcases__1'( Y, X )
% 0.96/1.37 , 'v_sko__List__Xlistsp__Xcases__2'( Y, X ), 't_a' ) ), =( X,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ), ~( 'c_List_Olistsp'( Y, X, 't_a' ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.96/1.37 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.96/1.37 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.96/1.37 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.96/1.37 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.96/1.37 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.96/1.37 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.96/1.37 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.96/1.37 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 0.96/1.37 [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.96/1.37 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.96/1.37 'c_Lambda_OdB_OApp', X ), Y ), Z ) ],
% 0.96/1.37 [ =( 'c_List_Oremove1'( X, 'c_List_Ofilter'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Ofilter'( Y, Z, T ) ), hBOOL( hAPP( Y, X ) ) ],
% 0.96/1.37 [ =( 'c_List_Ofilter'( X, 'c_List_Oreplicate'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Olist_ONil'( T ) ), hBOOL( hAPP( X, Z ) ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( X, 'c_List_Odrop'( Y, Z, T ), T ), 'c_List_Odrop'(
% 0.96/1.37 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, T ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Oreplicate'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 'tc_nat' ), X ), Y ), Z, T ), 'c_List_Oappend'( 'c_List_Oreplicate'( X, Z
% 0.96/1.37 , T ), 'c_List_Oreplicate'( Y, Z, T ), T ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Orev'( Z, Y ) ) ), =( X, Z ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.96/1.37 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.96/1.37 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'( 'c_List_Orotate'( Z
% 0.96/1.37 , X, Y ), Y ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( 'c_List_Orotate'( X, Y, Z ), Z ), ~(
% 0.96/1.37 'c_List_Odistinct'( Y, Z ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.96/1.37 'c_List_Olistsum'( 'c_List_Orev'( Y, X ), X ), 'c_List_Olistsum'( Y, X )
% 0.96/1.37 ) ],
% 0.96/1.37 [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Ocomp'( Y, Z, T, U, W ), U, V0, W ),
% 0.96/1.37 'c_Fun_Ocomp'( 'c_Fun_Ocomp'( X, Y, U, V0, T ), Z, T, V0, W ) ) ],
% 0.96/1.37 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.96/1.37 'tc_List_Olist'( Z ) ), X ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 0.96/1.37 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.96/1.37 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.96/1.37 'tc_bool' ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, 'c_List_Olist_OCons'(
% 0.96/1.37 Y, Z, T ), T ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T ) ), U
% 0.96/1.37 , T ), 'c_List_Oappend'( X, 'c_List_Olist_OCons'( U, Z, T ), T ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y
% 0.96/1.37 , Z, X ), X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( 'c_List_Oremdups'( X, Y ), Y ) ],
% 0.96/1.37 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.96/1.37 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 0.96/1.37 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 0.96/1.37 'tc_bool' ) ), X ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X
% 0.96/1.37 , 'tc_List_Olist'( Y ) ), Z, Y ), 'c_List_Oappend'( 'c_List_Odrop'(
% 0.96/1.37 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( Y ) ), X, Y ), T, Y ), Y
% 0.96/1.37 ), T ) ), ~( =( 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X,
% 0.96/1.37 'tc_List_Olist'( Y ) ), Z, Y ), X ) ), ~( =( Z, 'c_List_Otake'(
% 0.96/1.37 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( Y ) ), X, Y ) ) ), =(
% 0.96/1.37 'c_List_Oappend'( Z, 'c_List_Oappend'( 'c_List_Odrop'(
% 0.96/1.37 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( Y ) ), X, Y ), T, Y ), Y
% 0.96/1.37 ), 'c_List_Oappend'( X, T, Y ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 0.96/1.37 ) ), =( X, T ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 0.96/1.37 ) ), =( Y, U ) ],
% 0.96/1.37 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.96/1.37 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.96/1.37 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.96/1.37 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.96/1.37 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.96/1.37 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.96/1.37 [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Lambda_Obeta'( T, Y ) ), ~(
% 0.96/1.37 'c_Type_Otyping'( X, T, Z ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( Y, X ), ~(
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Oappend'( Y, Z, X ), X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( Y, X ), ~(
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Oappend'( Z, Y, X ), X ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.96/1.37 Z ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist__update'( 'c_List_Olist__update'( X, Y, Z, T ), U, W
% 0.96/1.37 , T ), 'c_List_Olist__update'( 'c_List_Olist__update'( X, U, W, T ), Y, Z
% 0.96/1.37 , T ) ), =( Y, U ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Oremdups'( Y, X ), X ), ~(
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( Y, X ) ) ],
% 0.96/1.37 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 0.96/1.37 Z ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.96/1.37 'c_List_Olist_OCons'( Y, T, Z ), Z ), 'c_List_Olist_OCons'( Y,
% 0.96/1.37 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ), T, Z ), Z ) ) ],
% 0.96/1.37 [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( W, V0, V1, T, U )
% 0.96/1.37 ) ), =( hAPP( X, hAPP( Y, V2 ) ), hAPP( W, hAPP( V0, V2 ) ) ) ],
% 0.96/1.37 [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( U, W ) ) ) ), =( hAPP(
% 0.96/1.37 'c_Fun_Ocomp'( X, Y, V0, V1, V2 ), Z ), hAPP( 'c_Fun_Ocomp'( T, U, V3, V1
% 0.96/1.37 , V4 ), W ) ) ],
% 0.96/1.37 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Orev'( X, Y ), 'tc_List_Olist'(
% 0.96/1.37 Y ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Ofilter'( X, 'c_List_Olist_OCons'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Ofilter'( X, Z, T ) ), hBOOL( hAPP( X, Y ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.96/1.37 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 0.96/1.37 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 0.96/1.37 hAPP( X, T ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Ofilter'( X, Y, Z ), Z ), 'c_List_Ofilter'(
% 0.96/1.37 X, 'c_List_Orev'( Y, Z ), Z ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 0.96/1.37 'c_List_Oappend'( Y, Z, X ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.37 X ), 'c_List_Olistsum'( Y, X ) ), 'c_List_Olistsum'( Z, X ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.96/1.37 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.96/1.37 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( X, T
% 0.96/1.37 ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.96/1.37 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.96/1.37 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( Y, U
% 0.96/1.37 ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.96/1.37 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OAbs'( X ) ), Y ),
% 0.96/1.37 'c_Lambda_OdB_OAbs'( hAPP( hAPP( 'c_Lambda_Olift', X ), hAPP( hAPP(
% 0.96/1.37 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.96/1.37 'tc_nat' ) ) ) ) ) ],
% 0.96/1.37 [ ~( hBOOL( hAPP( X, 'c_List_Olist_Olist__case'( Y, Z,
% 0.96/1.37 'c_List_Olist_OCons'( T, U, 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X
% 0.96/1.37 , hAPP( hAPP( Z, T ), U ) ) ) ],
% 0.96/1.37 [ ~( hBOOL( hAPP( X, 'c_List_Olist_Olist__case'( Y, Z,
% 0.96/1.37 'c_List_Olist_OCons'( T, U, 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X
% 0.96/1.37 , hAPP( hAPP( Z, T ), U ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist__update'( 'c_List_Olist__update'( X, Y, Z, T ), Y, U
% 0.96/1.37 , T ), 'c_List_Olist__update'( X, Y, U, T ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.96/1.37 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.96/1.37 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.96/1.37 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.96/1.37 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Oremove1'( Y, Z, X ), X ), ~(
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( Z, X ) ) ],
% 0.96/1.37 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ), hAPP(
% 0.96/1.37 hAPP( 'c_Lambda_Olift', T ), Y ), U ), ~( 'c_Type_Otyping'( X, T, U ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.96/1.37 'v_sko__List__Xtake__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.96/1.37 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.96/1.37 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_ONil'( X ), X ) ],
% 0.96/1.37 [ =( 'c_List_Ofiltermap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 0.96/1.37 'c_List_Olist_ONil'( Z ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oremdups'( Y, X ) ) ), =( Y,
% 0.96/1.37 'c_List_Olist_ONil'( X ) ) ],
% 0.96/1.37 [ =( 'c_List_Ofilter'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.96/1.37 'c_List_Olist_ONil'( Y ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z, X ),
% 0.96/1.37 'c_List_Olist_ONil'( X ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z, X ),
% 0.96/1.37 'c_List_Olist_ONil'( X ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z, X ),
% 0.96/1.37 'c_List_Olist_ONil'( X ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.96/1.37 'v_sko__List__Xconcat__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Oremove1'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.96/1.37 'c_List_Olist_ONil'( Y ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.96/1.37 'v_sko__List__Xdistinct__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.96/1.37 [ =( 'c_Map_Omap__upds'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), X ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_Map_Omap__upds'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T ), X ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.96/1.37 'v_sko__List__Xremove1__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist_Olist__case'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z )
% 0.96/1.37 , X ) ],
% 0.96/1.37 [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_ONil'( Y ) ) ), =( X,
% 0.96/1.37 'c_List_Olist_ONil'( Y ) ) ],
% 0.96/1.37 [ =( 'c_List_Orotate'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.96/1.37 'c_List_Olist_ONil'( Y ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.96/1.37 'v_sko__List__Xlist__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( 'c_List_Olist_ONil'( X
% 0.96/1.37 ), 'c_List_Olist_ONil'( X ), X ) ) ],
% 0.96/1.37 [ 'c_List_Olistrelp'( X, 'c_List_Olist_ONil'( Y ), 'c_List_Olist_ONil'(
% 0.96/1.37 Y ), Y ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__List__Xmap__Xinduct__2'(
% 0.96/1.37 X ) ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Olist_ONil'( X ), X ), 'c_List_Olist_ONil'(
% 0.96/1.37 X ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist__update'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) )
% 0.96/1.37 ), =( X, 'c_List_Olist_ONil'( T ) ) ],
% 0.96/1.37 [ =( 'c_Lambda_Osubstn'( X, Y, Z ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.96/1.37 , X ), 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.96/1.37 ), Z ) ) ],
% 0.96/1.37 [ =( 'c_List_Odrop'( X, 'c_List_Omap'( Y, Z, T, U ), U ), 'c_List_Omap'(
% 0.96/1.37 Y, 'c_List_Odrop'( X, Z, T ), T, U ) ) ],
% 0.96/1.37 [ ~( =( hAPP( X, 'c_List_Osko__List__Xmap__idI__1__1'( X, Y, Z ) ),
% 0.96/1.37 'c_List_Osko__List__Xmap__idI__1__1'( X, Y, Z ) ) ), =( 'c_List_Omap'( X
% 0.96/1.37 , Y, Z, Z ), Y ) ],
% 0.96/1.37 [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'( 'c_List_Omap'( Z, X
% 0.96/1.37 , Y, T ), T ) ) ],
% 0.96/1.37 [ =( 'c_List_Omap'( X, 'c_List_Oappend'( Y, Z, T ), T, U ),
% 0.96/1.37 'c_List_Oappend'( 'c_List_Omap'( X, Y, T, U ), 'c_List_Omap'( X, Z, T, U
% 0.96/1.37 ), U ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Omap'( X, U, Z, T ) ) ),
% 0.96/1.37 =( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ),
% 0.96/1.37 'c_Nat_Osize__class_Osize'( U, 'tc_List_Olist'( Z ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Omap'( X, 'c_List_Oreplicate'( Y, Z, T ), T, U ),
% 0.96/1.37 'c_List_Oreplicate'( Y, hAPP( X, Z ), U ) ) ],
% 0.96/1.37 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Omap'( X, Y, Z, T ),
% 0.96/1.37 'tc_List_Olist'( T ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z
% 0.96/1.37 ) ) ) ],
% 0.96/1.37 [ =( 'c_List_Orotate'( X, 'c_List_Omap'( Y, Z, T, U ), U ),
% 0.96/1.37 'c_List_Omap'( Y, 'c_List_Orotate'( X, Z, T ), T, U ) ) ],
% 0.96/1.37 [ =( 'c_List_Orev'( 'c_List_Omap'( X, Y, Z, T ), T ), 'c_List_Omap'( X,
% 0.96/1.37 'c_List_Orev'( Y, Z ), Z, T ) ) ],
% 0.96/1.37 [ ~( =( hAPP( X, 'c_List_Osko__List__Xmap__ext__1__1'( X, Y, Z, T, U ) )
% 0.96/1.37 , hAPP( Y, 'c_List_Osko__List__Xmap__ext__1__1'( X, Y, Z, T, U ) ) ) ),
% 0.96/1.37 =( 'c_List_Omap'( X, Z, T, U ), 'c_List_Omap'( Y, Z, T, U ) ) ],
% 0.96/1.37 [ =( 'c_List_Otake'( X, 'c_List_Omap'( Y, Z, T, U ), U ), 'c_List_Omap'(
% 0.96/1.37 Y, 'c_List_Otake'( X, Z, T ), T, U ) ) ],
% 0.96/1.37 [ =( 'c_List_Omap'( X, 'c_List_Omap'( Y, Z, T, U ), U, W ),
% 0.96/1.37 'c_List_Omap'( 'c_Fun_Ocomp'( X, Y, U, W, T ), Z, T, W ) ) ],
% 0.96/1.37 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 0.96/1.37 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U
% 0.96/1.37 ), 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ) ) ],
% 0.96/1.37 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 0.96/1.37 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ ~( =( hAPP( X, 'c_List_Osko__List__Xmap__cong__1__1'( X, Y, Z, T, U )
% 0.96/1.37 ), hAPP( Y, 'c_List_Osko__List__Xmap__cong__1__1'( X, Y, Z, T, U ) ) ) )
% 0.96/1.37 , =( 'c_List_Omap'( X, Z, T, U ), 'c_List_Omap'( Y, Z, T, U ) ) ],
% 0.96/1.37 [ ~( =( hAPP( X, 'c_List_Osko__List__Xmap__eq__conv__1__1'( X, Y, Z, T,
% 0.96/1.37 U ) ), hAPP( Y, 'c_List_Osko__List__Xmap__eq__conv__1__1'( X, Y, Z, T, U
% 0.96/1.37 ) ) ) ), =( 'c_List_Omap'( X, Z, T, U ), 'c_List_Omap'( Y, Z, T, U ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Omap'( X, 'c_List_Olist__update'( Y, Z, T, U ), U, W ),
% 0.96/1.37 'c_List_Olist__update'( 'c_List_Omap'( X, Y, U, W ), Z, hAPP( X, T ), W )
% 0.96/1.37 ) ],
% 0.96/1.37 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.96/1.37 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.96/1.37 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.96/1.37 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.96/1.37 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.96/1.37 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB'
% 0.96/1.37 , 'tc_Lambda_OdB' ) ) ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.96/1.37 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), T ), hAPP( hAPP(
% 0.96/1.37 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Z ), T ) )
% 0.96/1.37 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', Y ), Z ), T ) ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.96/1.37 ), X ), Y ) ],
% 0.96/1.37 [ 'c_Lambda_Obeta'( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ), Z ),
% 0.96/1.37 hAPP( hAPP( hAPP( 'c_Lambda_Osubst', T ), Y ), Z ) ), ~( 'c_Lambda_Obeta'(
% 0.96/1.37 X, T ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OAbs'( X ) ), Y
% 0.96/1.37 ), Z ), 'c_Lambda_OdB_OAbs'( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ),
% 0.96/1.37 hAPP( hAPP( 'c_Lambda_Olift', Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.96/1.37 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.96/1.37 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X ) ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_ua______' ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X ) ) ), ~(
% 0.96/1.37 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.96/1.37 [ 'c_List_Olistsp'( X, 'c_List_Oappend'( Y, Z, T ), T ), ~(
% 0.96/1.37 'c_List_Olistsp'( X, Z, T ) ), ~( 'c_List_Olistsp'( X, Y, T ) ) ],
% 0.96/1.37 [ 'c_List_Olistsp'( X, Y, Z ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_List_Osko__List__Xin__listsp__conv__set__1__1'( X, Y, Z ) ) ) ) ],
% 0.96/1.37 [ 'c_List_Olistsp'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 0.96/1.37 'tc_fun'( Z, 'tc_bool' ) ), T, Z ), ~( 'c_List_Olistsp'( Y, T, Z ) ), ~(
% 0.96/1.37 'c_List_Olistsp'( X, T, Z ) ) ],
% 0.96/1.37 [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X, 'c_List_Oappend'(
% 0.96/1.37 T, Y, Z ), Z ) ) ],
% 0.96/1.37 [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X, 'c_List_Oappend'(
% 0.96/1.37 Y, T, Z ), Z ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.96/1.37 , Y ) ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.96/1.37 'c_Lambda_Olift', X ), Z ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ) )
% 0.96/1.37 ],
% 0.96/1.37 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_Olift', X ), Y ), hAPP( hAPP(
% 0.96/1.37 'c_Lambda_Olift', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.96/1.37 [ =( 'v_n____', 'v_i____' ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.96/1.37 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.96/1.37 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.96/1.37 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.96/1.37 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.96/1.37 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.37 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.96/1.37 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.96/1.37 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.96/1.37 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.96/1.37 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.96/1.37 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.37 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.37 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 0.96/1.37 'c_List_Olist_ONil'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist_Olist__size'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist_Olist__size'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_List_Olist_ONil'( Y
% 0.96/1.37 ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'( Y, Z, X ) ) ),
% 0.96/1.37 =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ),
% 0.96/1.37 =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_List_Otake'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 0.96/1.37 'c_List_Olist_ONil'( Y ) ) ],
% 0.96/1.37 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'(
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, X ) ) ],
% 0.96/1.37 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ),
% 0.96/1.37 'tc_List_Olist'( X ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Otake'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y,
% 0.96/1.37 'c_List_Olist_ONil'( Z ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.96/1.37 ) ],
% 0.96/1.37 [ =( 'c_List_Olength__unique'( 'c_List_Olist_ONil'( X ), X ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.37 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 0.96/1.37 , 'c_List_Olist_ONil'( Y ) ) ],
% 0.96/1.37 [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.96/1.37 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.96/1.37 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z,
% 0.96/1.37 'v_sko__List__Xlistsp__Xinducts__1'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' ) )
% 0.96/1.37 ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.96/1.37 'v_sko__List__Xlistsp__Xinducts__2'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' ) )
% 0.96/1.37 ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z,
% 0.96/1.37 'v_sko__List__Xlistsp__Xinduct__1'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' ) )
% 0.96/1.37 ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.96/1.37 'v_sko__List__Xlistsp__Xinduct__2'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' ) )
% 0.96/1.37 ],
% 0.96/1.37 [ 'c_List_Olistsp'( X, 'v_sko__List__Xlistsp__Xcases__2'( X, Y ), 't_a'
% 0.96/1.37 ), =( Y, 'c_List_Olist_ONil'( 't_a' ) ), ~( 'c_List_Olistsp'( X, Y,
% 0.96/1.37 't_a' ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( X, 'v_sko__List__Xlistsp__Xcases__1'( X, Y ) ) ), =( Y,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ), ~( 'c_List_Olistsp'( X, Y, 't_a' ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), 'c_List_Olistsp'( Z,
% 0.96/1.37 'v_sko__List__Xlistsp__Xinducts__2'( Z, X ), 't_a' ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' ) )
% 0.96/1.37 ],
% 0.96/1.37 [ hBOOL( hAPP( X, Y ) ), 'c_List_Olistsp'( Z,
% 0.96/1.37 'v_sko__List__Xlistsp__Xinduct__2'( Z, X ), 't_a' ), ~( hBOOL( hAPP( X,
% 0.96/1.37 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' ) )
% 0.96/1.37 ],
% 0.96/1.37 [ 'c_Type_Otypings'( X, 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.96/1.37 'c_Lambda_Osubst', Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.96/1.37 'tc_nat', 'tc_Lambda_OdB' ) ), Z, 'tc_Lambda_OdB', 'tc_nat',
% 0.96/1.37 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 0.96/1.37 'c_Type_Otypings'( 'c_Type_Oshift'( X, Z, W, 'tc_Type_Otype' ), T, U ) )
% 0.96/1.37 , ~( 'c_Type_Otyping'( X, Y, W ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.96/1.37 , X ), 'c_Lambda_OdB_OVar'( Y ) ), Z ) ) ), ~( hBOOL( hAPP(
% 0.96/1.37 'c_InductTermi_OIT', X ) ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.96/1.37 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_Olift', X ), Z ),
% 0.96/1.37 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Z, 'tc_Lambda_OdB', 'tc_nat'
% 0.96/1.37 , 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.96/1.37 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.96/1.37 [ 'c_Type_Otypings'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ),
% 0.96/1.37 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Y, 'tc_Lambda_OdB', 'tc_nat'
% 0.96/1.37 , 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 0.96/1.37 'c_Type_Otypings'( X, T, U ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_List_Ofoldl'(
% 0.96/1.37 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), T )
% 0.96/1.37 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP(
% 0.96/1.37 'c_Lambda_Osubst', X ), Z ), T ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.96/1.37 'c_Lambda_Osubst', Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.96/1.37 'tc_nat', 'tc_Lambda_OdB' ) ), T, 'tc_Lambda_OdB', 'tc_nat',
% 0.96/1.37 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB'
% 0.96/1.37 , 'tc_Lambda_OdB' ) ) ],
% 0.96/1.37 [ 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'( 'c_COMBC'(
% 0.96/1.37 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_Lambda_OdB'
% 0.96/1.37 , 'tc_nat', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.96/1.37 'tc_Lambda_OdB' ), ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', X,
% 0.96/1.37 'tc_Lambda_OdB' ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) ) ), =( Y
% 0.96/1.37 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 0.96/1.37 ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.96/1.37 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X ) ) ), =( Z
% 0.96/1.37 , 'c_List_Olist_ONil'( T ) ) ],
% 0.96/1.37 [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ],
% 0.96/1.37 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 0.96/1.37 'c_List_Olist_ONil'( Z ) ) ],
% 0.96/1.37 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ],
% 0.96/1.37 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( 'c_Lambda_Olift',
% 0.96/1.37 X ), Y ) ), Z ), Y ), X ) ],
% 0.96/1.37 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, 'c_List_Olist_ONil'( Z
% 0.96/1.37 ), Z, X ) ) ],
% 0.96/1.37 [ ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'( 'c_COMBC'(
% 0.96/1.37 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_Lambda_OdB'
% 0.96/1.37 , 'tc_nat', 'tc_Lambda_OdB' ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.96/1.37 'c_Lambda_Osubst', 'v_u____', 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.96/1.37 'tc_nat', 'tc_Lambda_OdB' ) ), 'v_i____', 'tc_Lambda_OdB', 'tc_nat',
% 0.96/1.37 'tc_Lambda_OdB' ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.96/1.37 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.96/1.37 'tc_Lambda_OdB' ) ) ],
% 0.96/1.37 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 0.96/1.37 'class_Lattices_Olattice'( Y ) ) ],
% 0.96/1.37 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.96/1.37 'class_Orderings_Opreorder'( Y ) ) ],
% 0.96/1.37 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 0.96/1.37 'class_Lattices_Olattice'( Y ) ) ],
% 0.96/1.37 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.96/1.37 'class_Orderings_Oorder'( Y ) ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.96/1.37 ],
% 0.96/1.37 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.96/1.37 ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 0.96/1.37 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 0.96/1.37 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 0.96/1.37 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 0.96/1.37 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.96/1.37 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 0.96/1.37 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Olordered__ab__group__add__meet'( 'tc_Int_Oint' )
% 0.96/1.37 ],
% 0.96/1.37 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 0.96/1.37 ],
% 0.96/1.37 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Lattices_Olower__semilattice'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Lattices_Olattice'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 0.96/1.37 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.96/1.37 ,
% 0.96/1.37 [ =( 'c_COMBB'( X, Y, Z, T, U, W ), hAPP( X, hAPP( Y, Z ) ) ) ],
% 0.96/1.37 [ 'c_fequal'( X, X, Y ) ],
% 0.96/1.37 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 0.96/1.37 ] .
% 0.96/1.37
% 0.96/1.37
% 0.96/1.37 percentage equality = 0.361159, percentage horn = 0.915375
% 0.96/1.37 This is a problem with some equality
% 0.96/1.37
% 0.96/1.37
% 0.96/1.37
% 0.96/1.37 Options Used:
% 0.96/1.37
% 0.96/1.37 useres = 1
% 0.96/1.37 useparamod = 1
% 0.96/1.37 useeqrefl = 1
% 0.96/1.37 useeqfact = 1
% 0.96/1.37 usefactor = 1
% 0.96/1.37 usesimpsplitting = 0
% 0.96/1.37 usesimpdemod = 5
% 0.96/1.37 usesimpres = 3
% 0.96/1.37
% 0.96/1.37 resimpinuse = 1000
% 0.96/1.38 resimpclauses = 20000
% 0.96/1.38 substype = eqrewr
% 0.96/1.38 backwardsubs = 1
% 0.96/1.38 selectoldest = 5
% 0.96/1.38
% 0.96/1.38 litorderings [0] = split
% 0.96/1.38 litorderings [1] = extend the termordering, first sorting on arguments
% 0.96/1.38
% 0.96/1.38 termordering = kbo
% 0.96/1.38
% 0.96/1.38 litapriori = 0
% 0.96/1.38 termapriori = 1
% 0.96/1.38 litaposteriori = 0
% 0.96/1.38 termaposteriori = 0
% 0.96/1.38 demodaposteriori = 0
% 0.96/1.38 ordereqreflfact = 0
% 0.96/1.38
% 0.96/1.38 litselect = negord
% 0.96/1.38
% 0.96/1.38 maxweight = 15
% 0.96/1.38 maxdepth = 30000
% 0.96/1.38 maxlength = 115
% 0.96/1.38 maxnrvars = 195
% 0.96/1.38 excuselevel = 1
% 0.96/1.38 increasemaxweight = 1
% 0.96/1.38
% 0.96/1.38 maxselected = 10000000
% 0.96/1.38 maxnrclauses = 10000000
% 0.96/1.38
% 0.96/1.38 showgenerated = 0
% 0.96/1.38 showkept = 0
% 0.96/1.38 showselected = 0
% 0.96/1.38 showdeleted = 0
% 0.96/1.38 showresimp = 1
% 0.96/1.38 showstatus = 2000
% 0.96/1.38
% 0.96/1.38 prologoutput = 1
% 0.96/1.38 nrgoals = 5000000
% 0.96/1.38 totalproof = 1
% 0.96/1.38
% 0.96/1.38 Symbols occurring in the translation:
% 0.96/1.38
% 0.96/1.38 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.96/1.38 . [1, 2] (w:1, o:175, a:1, s:1, b:0),
% 0.96/1.38 ! [4, 1] (w:0, o:110, a:1, s:1, b:0),
% 0.96/1.38 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.38 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.38 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [40, 1]
% 0.96/1.38 (w:1, o:116, a:1, s:1, b:0),
% 0.96/1.38 'c_lessequals' [43, 3] (w:1, o:219, a:1, s:1, b:0),
% 0.96/1.38 'c_HOL_Oplus__class_Oplus' [44, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.96/1.38 hAPP [45, 2] (w:1, o:200, a:1, s:1, b:0),
% 0.96/1.38 'c_Suc' [48, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.96/1.38 'tc_nat' [50, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.96/1.38 'c_HOL_Oord__class_Oless' [51, 3] (w:1, o:220, a:1, s:1, b:0),
% 0.96/1.38 'class_Ring__and__Field_Oordered__semidom' [55, 1] (w:1, o:122, a:1
% 0.96/1.38 , s:1, b:0),
% 0.96/1.38 'c_Nat_Osemiring__1__class_Oof__nat' [57, 2] (w:1, o:201, a:1, s:1
% 0.96/1.38 , b:0),
% 0.96/1.38 'class_OrderedGroup_Opordered__ab__group__add' [58, 1] (w:1, o:123
% 0.96/1.38 , a:1, s:1, b:0),
% 0.96/1.38 'c_HOL_Ominus__class_Ominus' [59, 3] (w:1, o:221, a:1, s:1, b:0),
% 0.96/1.38 'c_HOL_Ozero__class_Ozero' [60, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.96/1.38 'c_HOL_Oone__class_Oone' [61, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.96/1.38 'c_Power_Opower__class_Opower' [62, 3] (w:1, o:222, a:1, s:1, b:0),
% 0.96/1.38 'class_Orderings_Opreorder' [63, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.96/1.38 'class_Orderings_Oorder' [65, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.96/1.38 'class_Lattices_Olower__semilattice' [66, 1] (w:1, o:127, a:1, s:1
% 0.96/1.38 , b:0),
% 0.96/1.38 'c_Lattices_Olower__semilattice__class_Oinf' [67, 3] (w:1, o:223, a:1
% 0.96/1.38 , s:1, b:0),
% 0.96/1.38 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [69, 1]
% 0.96/1.38 (w:1, o:128, a:1, s:1, b:0),
% 0.96/1.38 'class_Divides_Oring__div' [71, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.96/1.38 'c_Divides_Odiv__class_Omod' [72, 3] (w:1, o:224, a:1, s:1, b:0),
% 0.96/1.38 'class_Orderings_Olinorder' [75, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.96/1.38 hBOOL [77, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.96/1.38 'class_Ring__and__Field_Oordered__idom' [78, 1] (w:1, o:132, a:1, s:1
% 0.96/1.38 , b:0),
% 0.96/1.38 'class_OrderedGroup_Opordered__ab__semigroup__add' [79, 1] (w:1, o:
% 0.96/1.38 133, a:1, s:1, b:0),
% 0.96/1.38 'c_Type_Oshift' [82, 4] (w:1, o:243, a:1, s:1, b:0),
% 0.96/1.38 'class_Int_Onumber' [83, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.96/1.38 'c_Int_Onumber__class_Onumber__of' [85, 2] (w:1, o:202, a:1, s:1, b:0
% 0.96/1.38 ),
% 0.96/1.38 'class_Lattices_Olattice' [87, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.96/1.38 'class_Divides_Osemiring__div' [89, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.96/1.38 'class_Ring__and__Field_Oring__1' [91, 1] (w:1, o:137, a:1, s:1, b:0)
% 0.96/1.38 ,
% 0.96/1.38 'c_Type_Otype_OFun' [94, 2] (w:1, o:203, a:1, s:1, b:0),
% 0.96/1.38 'class_OrderedGroup_Opordered__comm__monoid__add' [99, 1] (w:1, o:138
% 0.96/1.38 , a:1, s:1, b:0),
% 0.96/1.38 'class_OrderedGroup_Ocomm__monoid__add' [102, 1] (w:1, o:139, a:1, s:
% 0.96/1.38 1, b:0),
% 0.96/1.38 'class_OrderedGroup_Ogroup__add' [103, 1] (w:1, o:140, a:1, s:1, b:0)
% 0.96/1.38 ,
% 0.96/1.38 'class_Ring__and__Field_Osemiring__1' [104, 1] (w:1, o:143, a:1, s:1
% 0.96/1.38 , b:0),
% 0.96/1.38 'c_Nat_Osemiring__1__class_Oof__nat__aux' [106, 4] (w:1, o:244, a:1
% 0.96/1.38 , s:1, b:0),
% 0.96/1.38 'class_OrderedGroup_Oab__group__add' [107, 1] (w:1, o:144, a:1, s:1
% 0.96/1.38 , b:0),
% 0.96/1.38 'c_List_Oappend' [111, 3] (w:1, o:225, a:1, s:1, b:0),
% 0.96/1.38 'c_List_Olist__update' [112, 4] (w:1, o:245, a:1, s:1, b:0),
% 0.96/1.38 'tc_List_Olist' [113, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.00/1.39 'c_Nat_Osize__class_Osize' [114, 2] (w:1, o:204, a:1, s:1, b:0),
% 1.00/1.39 'c_Lambda_Osubst' [115, 0] (w:1, o:72, a:1, s:1, b:0),
% 1.00/1.39 'c_Lambda_OdB_OVar' [116, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.00/1.39 'c_Lambda_Olift' [119, 0] (w:1, o:73, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Orev' [121, 2] (w:1, o:205, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Orotate' [122, 3] (w:1, o:226, a:1, s:1, b:0),
% 1.00/1.39 'c_Map_Omap__upds' [124, 5] (w:1, o:259, a:1, s:1, b:0),
% 1.00/1.39 'c_Lambda_Osubstn' [125, 3] (w:1, o:227, a:1, s:1, b:0),
% 1.00/1.39 'class_OrderedGroup_Olordered__ab__group__add' [126, 1] (w:1, o:147
% 1.00/1.39 , a:1, s:1, b:0),
% 1.00/1.39 'class_Ring__and__Field_Osemiring__0' [127, 1] (w:1, o:142, a:1, s:1
% 1.00/1.39 , b:0),
% 1.00/1.39 'class_Power_Opower' [128, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Olist_OCons' [129, 3] (w:1, o:228, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Otake' [130, 3] (w:1, o:231, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Odrop' [131, 3] (w:1, o:232, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Ofilter' [132, 3] (w:1, o:233, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Olinorder__class_Osorted' [134, 2] (w:1, o:206, a:1, s:1, b:0
% 1.00/1.39 ),
% 1.00/1.39 'c_Lambda_OdB_OApp' [136, 0] (w:1, o:77, a:1, s:1, b:0),
% 1.00/1.39 'c_Type_Otyping' [138, 3] (w:1, o:234, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Oreplicate' [139, 3] (w:1, o:235, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Oremdups' [140, 2] (w:1, o:207, a:1, s:1, b:0),
% 1.00/1.39 'c_Lambda_Oliftn' [141, 3] (w:1, o:236, a:1, s:1, b:0),
% 1.00/1.39 'class_Int_Oring__char__0' [143, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.00/1.39 'class_Int_Onumber__ring' [144, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.00/1.39 'class_Ring__and__Field_Oidom' [145, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.00/1.39
% 1.00/1.39 'c_List_Olist_ONil' [146, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Omap' [152, 4] (w:1, o:247, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Olistsum' [153, 2] (w:1, o:208, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Osko__List__Xlistsum__map__filter__1__1' [154, 5] (w:1, o:253
% 1.00/1.39 , a:1, s:1, b:0),
% 1.00/1.39 'v_sko__List__Xdistinct__Xinduct__1' [155, 1] (w:1, o:162, a:1, s:1
% 1.00/1.39 , b:0),
% 1.00/1.39 'v_sko__List__Xdistinct__Xinduct__2' [156, 1] (w:1, o:163, a:1, s:1
% 1.00/1.39 , b:0),
% 1.00/1.39 't_a' [157, 0] (w:1, o:82, a:1, s:1, b:0),
% 1.00/1.39 'v_sko__List__Xremove1__Xinduct__1' [158, 1] (w:1, o:164, a:1, s:1
% 1.00/1.39 , b:0),
% 1.00/1.39 'v_sko__List__Xremove1__Xinduct__2' [159, 1] (w:1, o:165, a:1, s:1
% 1.00/1.39 , b:0),
% 1.00/1.39 'v_sko__List__Xlist__Xinduct__1' [160, 1] (w:1, o:166, a:1, s:1, b:0)
% 1.00/1.39 ,
% 1.00/1.39 'v_sko__List__Xlist__Xinduct__2' [161, 1] (w:1, o:167, a:1, s:1, b:0)
% 1.00/1.39 ,
% 1.00/1.39 'v_sko__List__Xmap__Xinduct__1' [162, 1] (w:1, o:168, a:1, s:1, b:0)
% 1.00/1.39 ,
% 1.00/1.39 'v_sko__List__Xmap__Xinduct__2' [163, 1] (w:1, o:169, a:1, s:1, b:0)
% 1.00/1.39 ,
% 1.00/1.39 'v_sko__List__Xtake__Xinduct__1' [164, 1] (w:1, o:170, a:1, s:1, b:0)
% 1.00/1.39 ,
% 1.00/1.39 'v_sko__List__Xtake__Xinduct__2' [165, 1] (w:1, o:171, a:1, s:1, b:0)
% 1.00/1.39 ,
% 1.00/1.39 'v_sko__List__Xconcat__Xinduct__1' [166, 1] (w:1, o:160, a:1, s:1, b:
% 1.00/1.39 0),
% 1.00/1.39 'v_sko__List__Xconcat__Xinduct__2' [167, 1] (w:1, o:161, a:1, s:1, b:
% 1.00/1.39 0),
% 1.00/1.39 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1' [169, 3] (w:
% 1.00/1.39 1, o:237, a:1, s:1, b:0),
% 1.00/1.39 'tc_Lambda_OdB' [170, 0] (w:1, o:83, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Ofoldl' [171, 5] (w:1, o:254, a:1, s:1, b:0),
% 1.00/1.39 'c_Lambda_Obeta' [172, 2] (w:1, o:209, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Olist_Olist__size' [174, 3] (w:1, o:238, a:1, s:1, b:0),
% 1.00/1.39 'c_Type_Osko__Type__Xlist__app__typeE__1__1' [176, 4] (w:1, o:249, a:
% 1.00/1.39 1, s:1, b:0),
% 1.00/1.39 'c_Type_Otypings' [177, 3] (w:1, o:239, a:1, s:1, b:0),
% 1.00/1.39 'c_Type_Osko__Type__Xlist__app__typeD__1__1' [178, 4] (w:1, o:248, a:
% 1.00/1.39 1, s:1, b:0),
% 1.00/1.39 'c_Lambda_OdB_OAbs' [179, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.00/1.39 'tc_Type_Otype' [180, 0] (w:1, o:85, a:1, s:1, b:0),
% 1.00/1.39 'c_COMBC' [181, 5] (w:1, o:260, a:1, s:1, b:0),
% 1.00/1.39 'c_Type_Osko__Type__Xvar__app__types__1__1' [183, 4] (w:1, o:250, a:1
% 1.00/1.39 , s:1, b:0),
% 1.00/1.39 'c_Type_Osko__Type__Xvar__app__typesE__1__1' [185, 4] (w:1, o:251, a:
% 1.00/1.39 1, s:1, b:0),
% 1.00/1.39 'class_OrderedGroup_Ocancel__semigroup__add' [186, 1] (w:1, o:148, a:
% 1.00/1.39 1, s:1, b:0),
% 1.00/1.39 'class_OrderedGroup_Ocancel__ab__semigroup__add' [187, 1] (w:1, o:149
% 1.00/1.39 , a:1, s:1, b:0),
% 1.00/1.39 'c_List_Oremove1' [188, 3] (w:1, o:240, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Olist_Olist__case' [191, 5] (w:1, o:255, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Odistinct' [192, 2] (w:1, o:210, a:1, s:1, b:0),
% 1.00/1.39 'tc_bool' [197, 0] (w:1, o:90, a:1, s:1, b:0),
% 1.00/1.39 'tc_fun' [198, 2] (w:1, o:211, a:1, s:1, b:0),
% 1.00/1.39 'class_OrderedGroup_Olordered__ab__group__add__meet' [199, 1] (w:1
% 1.00/1.39 , o:150, a:1, s:1, b:0),
% 1.00/1.39 'class_OrderedGroup_Omonoid__mult' [200, 1] (w:1, o:151, a:1, s:1, b:
% 1.00/1.39 0),
% 1.00/1.39 'class_Ring__and__Field_Ocomm__semiring__1' [201, 1] (w:1, o:173, a:1
% 1.00/1.39 , s:1, b:0),
% 1.00/1.39 'class_OrderedGroup_Oab__semigroup__add' [202, 1] (w:1, o:152, a:1
% 1.00/1.39 , s:1, b:0),
% 1.00/1.39 'class_OrderedGroup_Omonoid__add' [203, 1] (w:1, o:153, a:1, s:1, b:0
% 1.00/1.39 ),
% 1.00/1.39 'class_OrderedGroup_Osemigroup__add' [204, 1] (w:1, o:154, a:1, s:1
% 1.00/1.39 , b:0),
% 1.00/1.39 'v_sko__List__Xlistsp__Xinduct__1' [206, 2] (w:1, o:212, a:1, s:1, b:
% 1.00/1.39 0),
% 1.00/1.39 'v_sko__List__Xlistsp__Xinduct__2' [207, 2] (w:1, o:213, a:1, s:1, b:
% 1.00/1.39 0),
% 1.00/1.39 'c_List_Olistsp' [208, 3] (w:1, o:241, a:1, s:1, b:0),
% 1.00/1.39 'v_sko__List__Xlistsp__Xinducts__1' [209, 2] (w:1, o:214, a:1, s:1
% 1.00/1.39 , b:0),
% 1.00/1.39 'v_sko__List__Xlistsp__Xinducts__2' [210, 2] (w:1, o:215, a:1, s:1
% 1.00/1.39 , b:0),
% 1.00/1.39 'c_List_Olength__unique' [211, 2] (w:1, o:216, a:1, s:1, b:0),
% 1.00/1.39 'c_InductTermi_OIT' [212, 0] (w:1, o:91, a:1, s:1, b:0),
% 1.00/1.39 'class_Ring__and__Field_Ozero__neq__one' [216, 1] (w:1, o:174, a:1
% 1.00/1.39 , s:1, b:0),
% 1.00/1.39 'class_Ring__and__Field_Ono__zero__divisors' [217, 1] (w:1, o:121, a:
% 1.00/1.39 1, s:1, b:0),
% 1.00/1.39 'class_Ring__and__Field_Omult__zero' [218, 1] (w:1, o:120, a:1, s:1
% 1.00/1.39 , b:0),
% 1.00/1.39 'class_Ring__and__Field_Oring__1__no__zero__divisors' [219, 1] (w:1
% 1.00/1.39 , o:141, a:1, s:1, b:0),
% 1.00/1.39 't_b' [221, 0] (w:1, o:92, a:1, s:1, b:0),
% 1.00/1.39 'class_Nat_Osemiring__char__0' [222, 1] (w:1, o:115, a:1, s:1, b:0),
% 1.00/1.39
% 1.00/1.39 'c_Fun_Ocomp' [225, 5] (w:1, o:261, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Olistrelp' [227, 4] (w:1, o:246, a:1, s:1, b:0),
% 1.00/1.39 'v_sko__List__Xlistsp__Xcases__1' [232, 2] (w:1, o:217, a:1, s:1, b:0
% 1.00/1.39 ),
% 1.00/1.39 'v_sko__List__Xlistsp__Xcases__2' [233, 2] (w:1, o:218, a:1, s:1, b:0
% 1.00/1.39 ),
% 1.00/1.39 'c_List_Ofiltermap' [242, 4] (w:1, o:252, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Osko__List__Xmap__idI__1__1' [245, 3] (w:1, o:229, a:1, s:1
% 1.00/1.39 , b:0),
% 1.00/1.39 'c_List_Osko__List__Xmap__ext__1__1' [246, 5] (w:1, o:256, a:1, s:1
% 1.00/1.39 , b:0),
% 1.00/1.39 'c_List_Osko__List__Xmap__cong__1__1' [247, 5] (w:1, o:257, a:1, s:1
% 1.00/1.39 , b:0),
% 1.00/1.39 'c_List_Osko__List__Xmap__eq__conv__1__1' [248, 5] (w:1, o:258, a:1
% 1.00/1.39 , s:1, b:0),
% 1.00/1.39 'v_ua______' [249, 0] (w:1, o:99, a:1, s:1, b:0),
% 1.00/1.39 'c_List_Osko__List__Xin__listsp__conv__set__1__1' [250, 3] (w:1, o:
% 1.00/1.39 230, a:1, s:1, b:0),
% 1.00/1.39 'v_n____' [251, 0] (w:1, o:100, a:1, s:1, b:0),
% 1.00/1.39 'v_i____' [252, 0] (w:1, o:101, a:1, s:1, b:0),
% 1.00/1.39 'v_u____' [255, 0] (w:1, o:104, a:1, s:1, b:0),
% 1.00/1.39 'tc_Int_Oint' [258, 0] (w:1, o:107, a:1, s:1, b:0),
% 1.00/1.39 'c_COMBB' [259, 6] (w:1, o:262, a:1, s:1, b:0),
% 1.00/1.39 'c_fequal' [260, 3] (w:1, o:242, a:1, s:1, b:0).
% 1.00/1.39
% 1.00/1.39
% 1.00/1.39 Starting Search:
% 1.00/1.39
% 1.00/1.39
% 1.00/1.39 Bliksems!, er is een bewijs:
% 1.00/1.39 % SZS status Unsatisfiable
% 1.00/1.39 % SZS output start Refutation
% 1.00/1.39
% 1.00/1.39 clause( 689, [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ] )
% 1.00/1.39 .
% 1.00/1.39 clause( 691, [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 1.00/1.39 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.39 .
% 1.00/1.39 clause( 694, [] )
% 1.00/1.39 .
% 1.00/1.39
% 1.00/1.39
% 1.00/1.39 % SZS output end Refutation
% 1.00/1.39 found a proof!
% 1.00/1.39
% 1.00/1.39 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.00/1.39
% 1.00/1.39 initialclauses(
% 1.00/1.39 [ clause( 696, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 1.00/1.39 , clause( 697, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.00/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.00/1.39 'c_lessequals'( Y, T, X ) ) ] )
% 1.00/1.39 , clause( 698, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.00/1.39 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 699, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 700, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 701, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 1.00/1.39 , clause( 702, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 703, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.00/1.39 , X ) ) ] )
% 1.00/1.39 , clause( 704, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.39 , X ) ) ] )
% 1.00/1.39 , clause( 705, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Z ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y
% 1.00/1.39 , 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 706, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 707, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 1.00/1.39 Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 708, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z,
% 1.00/1.39 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 709, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 710, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 711, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.39 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.00/1.39 , clause( 712, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.39 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.00/1.39 , clause( 713, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 714, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.00/1.39 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.00/1.39 T, X ) ) ] )
% 1.00/1.39 , clause( 715, [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.00/1.39 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.00/1.39 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 716, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.00/1.39 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.00/1.39 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 717, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 718, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.39 , X ) ) ] )
% 1.00/1.39 , clause( 719, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.00/1.39 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.00/1.39 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.00/1.39 X ), Z, X ) ) ] )
% 1.00/1.39 , clause( 720, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 721, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 1.00/1.39 , clause( 722, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.00/1.39 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.00/1.39 , clause( 723, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.00/1.39 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 724, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.00/1.39 ), =( Z, Y ) ] )
% 1.00/1.39 , clause( 725, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.00/1.39 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 726, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 1.00/1.39 , clause( 727, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), =( Z, Y ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 728, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 1.00/1.39 , clause( 729, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.00/1.39 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 730, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 731, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.00/1.39 ), =( Z, Y ) ] )
% 1.00/1.39 , clause( 732, [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Y ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 733, [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), Y ), X ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 734, [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Y ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 735, [ ~( 'c_lessequals'( X, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ), =(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), Y ), X ), X, 'tc_nat' ), Y ) ] )
% 1.00/1.39 , clause( 736, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.00/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.00/1.39 'c_lessequals'( Z, T, X ) ) ] )
% 1.00/1.39 , clause( 737, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 1.00/1.39 , clause( 738, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 1.00/1.39 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.00/1.39 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.00/1.39 'c_lessequals'( Y, T, X ) ) ] )
% 1.00/1.39 , clause( 739, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 1.00/1.39 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.00/1.39 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.00/1.39 'c_lessequals'( Z, T, X ) ) ] )
% 1.00/1.39 , clause( 740, [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , Z ), Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 741, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 742, [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , X ), Z ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 743, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y,
% 1.00/1.39 X, 'tc_nat' ) ), X ) ) ] )
% 1.00/1.39 , clause( 744, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 1.00/1.39 , 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), ~(
% 1.00/1.39 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 745, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ), X ), ~(
% 1.00/1.39 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 746, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X,
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( U, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.00/1.39 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, U, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 747, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 1.00/1.39 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.00/1.39 ) ) ] )
% 1.00/1.39 , clause( 748, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 1.00/1.39 ) ) ] )
% 1.00/1.39 , clause( 749, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 X ), Z, X ) ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 1.00/1.39 'c_Suc'( T ), X ), 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ),
% 1.00/1.39 X ) ) ] )
% 1.00/1.39 , clause( 750, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.00/1.39 'class_Int_Onumber'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ] )
% 1.00/1.39 , clause( 751, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.00/1.39 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ] )
% 1.00/1.39 , clause( 752, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ] )
% 1.00/1.39 , clause( 753, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ] )
% 1.00/1.39 , clause( 754, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X
% 1.00/1.39 ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 755, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X
% 1.00/1.39 ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 756, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X
% 1.00/1.39 ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 757, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.00/1.39 Z, X ) ] )
% 1.00/1.39 , clause( 758, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.00/1.39 Y, X ) ] )
% 1.00/1.39 , clause( 759, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 760, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 1.00/1.39 , clause( 761, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U )
% 1.00/1.39 ), ~( 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 762, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.00/1.39 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 763, [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.00/1.39 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 764, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 765, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.00/1.39 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.00/1.39 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 766, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 1.00/1.39 , Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat'
% 1.00/1.39 ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.00/1.39 Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 767, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 768, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.00/1.39 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.00/1.39 X ), T, X ) ) ] )
% 1.00/1.39 , clause( 769, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 770, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.00/1.39 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.00/1.39 X ), T, X ) ) ] )
% 1.00/1.39 , clause( 771, [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 772, [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 773, [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.00/1.39 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 1.00/1.39 , Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 774, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.00/1.39 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 775, [ ~( =( 'c_Type_Otype_OFun'( X, Y ), 'c_Type_Otype_OFun'( Z
% 1.00/1.39 , T ) ) ), =( Y, T ) ] )
% 1.00/1.39 , clause( 776, [ ~( =( 'c_Type_Otype_OFun'( X, Y ), 'c_Type_Otype_OFun'( Z
% 1.00/1.39 , T ) ) ), =( X, Z ) ] )
% 1.00/1.39 , clause( 777, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 1.00/1.39 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 778, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 779, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 1.00/1.39 , clause( 780, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 1.00/1.39 , clause( 781, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat'
% 1.00/1.39 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'(
% 1.00/1.39 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 782, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.00/1.39 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.00/1.39 , clause( 783, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.00/1.39 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.00/1.39 , clause( 784, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 1.00/1.39 , clause( 785, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.00/1.39 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.00/1.39 , clause( 786, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.00/1.39 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.00/1.39 , clause( 787, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 1.00/1.39 , clause( 788, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 789, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , Z ), Y ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 790, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 791, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z,
% 1.00/1.39 X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 1.00/1.39 , clause( 792, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 1.00/1.39 , clause( 793, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.00/1.39 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 1.00/1.39 , clause( 794, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 1.00/1.39 Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 795, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 796, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y
% 1.00/1.39 , 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 797, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 798, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y,
% 1.00/1.39 X ) ] )
% 1.00/1.39 , clause( 799, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 1.00/1.39 Y, X ) ] )
% 1.00/1.39 , clause( 800, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 1.00/1.39 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.00/1.39 , clause( 801, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.00/1.39 , clause( 802, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.00/1.39 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ] )
% 1.00/1.39 , clause( 803, [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )
% 1.00/1.39 , ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ] )
% 1.00/1.39 , clause( 804, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ),
% 1.00/1.39 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 805, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 806, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 1.00/1.39 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 807, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 808, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.00/1.39 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 809, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.00/1.39 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 810, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 1.00/1.39 , Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.00/1.39 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 811, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.00/1.39 ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 1.00/1.39 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.00/1.39 , clause( 812, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.00/1.39 ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 1.00/1.39 ~( 'c_lessequals'( U, T, X ) ) ] )
% 1.00/1.39 , clause( 813, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.00/1.39 ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 1.00/1.39 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 814, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.00/1.39 ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 1.00/1.39 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 1.00/1.39 , clause( 815, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , Y ), T ), Z, X ) ) ] )
% 1.00/1.39 , clause( 816, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , Y ), Z ), T, X ) ) ] )
% 1.00/1.39 , clause( 817, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 1.00/1.39 , 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 818, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 1.00/1.39 , 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 819, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 1.00/1.39 , X ) ) ] )
% 1.00/1.39 , clause( 820, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 1.00/1.39 Z, Y ) ] )
% 1.00/1.39 , clause( 821, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 1.00/1.39 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 822, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 1.00/1.39 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 823, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 1.00/1.39 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 824, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 825, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.00/1.39 , X ) ) ] )
% 1.00/1.39 , clause( 826, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.00/1.39 , X ) ) ] )
% 1.00/1.39 , clause( 827, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 1.00/1.39 Y, Z ) ] )
% 1.00/1.39 , clause( 828, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 1.00/1.39 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 1.00/1.39 , clause( 829, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 830, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.00/1.39 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 831, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ),
% 1.00/1.39 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 832, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.00/1.39 Y, X ) ) ] )
% 1.00/1.39 , clause( 833, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.00/1.39 Y, X ) ) ] )
% 1.00/1.39 , clause( 834, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.00/1.39 'tc_nat' ) ] )
% 1.00/1.39 , clause( 835, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.00/1.39 Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.00/1.39 , clause( 836, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.00/1.39 , clause( 837, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.00/1.39 , clause( 838, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.00/1.39 , clause( 839, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 840, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 841, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 1.00/1.39 'c_lessequals'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 842, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ),
% 1.00/1.39 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 843, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 1.00/1.39 , Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.00/1.39 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 844, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 845, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.00/1.39 ) ) ] )
% 1.00/1.39 , clause( 846, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), Y ) ), ~(
% 1.00/1.39 'c_lessequals'( Z, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 847, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( 'c_lessequals'( Z
% 1.00/1.39 , Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 848, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ),
% 1.00/1.39 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 849, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ),
% 1.00/1.39 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 850, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 1.00/1.39 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 851, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.00/1.39 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.00/1.39 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z
% 1.00/1.39 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.00/1.39 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 852, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.00/1.39 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.00/1.39 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.00/1.39 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 853, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y
% 1.00/1.39 ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 854, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.00/1.39 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 855, [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 856, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.00/1.39 Z, T, X ), X ) ) ] )
% 1.00/1.39 , clause( 857, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 858, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.00/1.39 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ] )
% 1.00/1.39 , clause( 859, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.00/1.39 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 860, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 1.00/1.39 , clause( 861, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 1.00/1.39 , clause( 862, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 1.00/1.39 , Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.00/1.39 ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 863, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.00/1.39 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 864, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) )
% 1.00/1.39 ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, T, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 865, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat'
% 1.00/1.39 ), 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~(
% 1.00/1.39 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 866, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 1.00/1.39 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 1.00/1.39 , clause( 867, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 868, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 869, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 870, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 871, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 872, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 873, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 874, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 875, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 876, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.00/1.39 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 1.00/1.39 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 877, [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.00/1.39 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 878, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 879, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 880, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 881, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 'c_Suc'( X ) ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Y ) ) ) ] )
% 1.00/1.39 , clause( 882, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 1.00/1.39 , 'c_Suc'( Y ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Y ) ) ) ] )
% 1.00/1.39 , clause( 883, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.00/1.39 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 884, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.00/1.39 'tc_nat' ) ] )
% 1.00/1.39 , clause( 885, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ), ~(
% 1.00/1.39 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 886, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.00/1.39 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.00/1.39 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.00/1.39 , clause( 887, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 1.00/1.39 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 888, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.00/1.39 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 889, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 1.00/1.39 , clause( 890, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 1.00/1.39 Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 891, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 892, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.00/1.39 ), Z ), Y ) ] )
% 1.00/1.39 , clause( 893, [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) )
% 1.00/1.39 ), hBOOL( hAPP( X, Z ) ) ] )
% 1.00/1.39 , clause( 894, [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) )
% 1.00/1.39 ), hBOOL( hAPP( X, Z ) ) ] )
% 1.00/1.39 , clause( 895, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat'
% 1.00/1.39 ), 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.00/1.39 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ] )
% 1.00/1.39 , clause( 896, [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , Z ), T ), 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~(
% 1.00/1.39 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 897, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 1.00/1.39 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.00/1.39 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.00/1.39 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.00/1.39 , clause( 898, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.00/1.39 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 899, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 900, [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 901, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 1.00/1.39 , Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 902, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.00/1.39 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ] )
% 1.00/1.39 , clause( 903, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 1.00/1.39 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.00/1.39 , clause( 904, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.00/1.39 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 1.00/1.39 , clause( 905, [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 906, [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 907, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 908, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 909, [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 910, [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 911, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.00/1.39 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 1.00/1.39 , clause( 912, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.00/1.39 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 1.00/1.39 , clause( 913, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X
% 1.00/1.39 , Y, 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 914, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.00/1.39 , clause( 915, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 1.00/1.39 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.00/1.39 , clause( 916, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 1.00/1.39 , clause( 917, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 918, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.00/1.39 Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 1.00/1.39 , clause( 919, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 1.00/1.39 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 1.00/1.39 , clause( 920, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.00/1.39 , clause( 921, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 1.00/1.39 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 1.00/1.39 , clause( 922, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, 'c_Suc'( Z ), T, X ),
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, Z, hAPP( Y, T ), X ) ) ] )
% 1.00/1.39 , clause( 923, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.00/1.39 ), Z ), T, X ) ) ] )
% 1.00/1.39 , clause( 924, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.00/1.39 , X ) ), T, X ) ) ] )
% 1.00/1.39 , clause( 925, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.00/1.39 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.00/1.39 , clause( 926, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 1.00/1.39 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 927, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.00/1.39 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.00/1.39 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 928, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.00/1.39 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.00/1.39 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 929, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.00/1.39 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.00/1.39 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat'
% 1.00/1.39 ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 930, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.00/1.39 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 931, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 932, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.00/1.39 , T, X ) ) ), =( Y, Z ) ] )
% 1.00/1.39 , clause( 933, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.00/1.39 , T, X ) ) ), =( Z, T ) ] )
% 1.00/1.39 , clause( 934, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.00/1.39 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ] )
% 1.00/1.39 , clause( 935, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 X ), 'c_Suc'( Y ) ) ) ] )
% 1.00/1.39 , clause( 936, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.00/1.39 Y, X ) ) ] )
% 1.00/1.39 , clause( 937, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.00/1.39 Y, X ) ) ] )
% 1.00/1.39 , clause( 938, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.00/1.39 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 939, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.00/1.39 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.39 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 1.00/1.39 , clause( 940, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.00/1.39 =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( T, Z, X ) ) ), =( Y, T ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.00/1.39 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.00/1.39 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 941, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 1.00/1.39 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 942, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 943, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.00/1.39 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 1.00/1.39 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 944, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.00/1.39 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.00/1.39 , Y, X ) ) ] )
% 1.00/1.39 , clause( 945, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 1.00/1.39 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.00/1.39 'tc_nat' ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 946, [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T
% 1.00/1.39 , U, Z ), 'c_List_Oappend'( X, 'c_List_Olist__update'( Y,
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( T, 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( Z ) ), 'tc_nat' ), U, Z ), Z ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( Z ) ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 947, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 1.00/1.39 'c_Lambda_OdB_OVar'( X ) ), Y ), Z ), 'c_Lambda_OdB_OVar'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.00/1.39 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 948, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 1.00/1.39 'c_Lambda_OdB_OVar'( X ) ), Y ), Z ), 'c_Lambda_OdB_OVar'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.00/1.39 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 949, [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Olift', X ), Y ) ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_Olift', X ), Z ) ), Y ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 950, [ =( 'c_List_Orotate'( X, 'c_List_Orev'( Y, Z ), Z ),
% 1.00/1.39 'c_List_Orev'( 'c_List_Orotate'( 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ),
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( X, 'c_Nat_Osize__class_Osize'( Y,
% 1.00/1.39 'tc_List_Olist'( Z ) ), 'tc_nat' ), 'tc_nat' ), Y, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 951, [ =( 'c_Map_Omap__upds'( X, Y, 'c_List_Olist__update'( Z, T
% 1.00/1.39 , U, W ), V0, W ), 'c_Map_Omap__upds'( X, Y, Z, V0, W ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( Z,
% 1.00/1.39 'tc_List_Olist'( W ) ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( V0 ) ), T, 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 952, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 1.00/1.39 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.00/1.39 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 953, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 954, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 1.00/1.39 , clause( 955, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.00/1.39 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.00/1.39 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 956, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.00/1.39 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 957, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.00/1.39 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.00/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.00/1.39 , clause( 958, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 959, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.00/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 1.00/1.39 , clause( 960, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.00/1.39 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.00/1.39 Y, T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 961, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.00/1.39 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.00/1.39 Y, Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 962, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.00/1.39 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.00/1.39 , clause( 963, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.00/1.39 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.00/1.39 , clause( 964, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.00/1.39 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 965, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.00/1.39 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 966, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.00/1.39 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 967, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.00/1.39 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 968, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.00/1.39 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 969, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.00/1.39 , clause( 970, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 971, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.00/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 972, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.00/1.39 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.00/1.39 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 973, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 974, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'(
% 1.00/1.39 X ), X ) ] )
% 1.00/1.39 , clause( 975, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.00/1.39 , clause( 976, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.00/1.39 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 X ), X ) ) ] )
% 1.00/1.39 , clause( 977, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.00/1.39 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 1.00/1.39 , clause( 978, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ] )
% 1.00/1.39 , clause( 979, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 1.00/1.39 , clause( 980, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 1.00/1.39 , clause( 981, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 982, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 983, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 984, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.00/1.39 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.00/1.39 , clause( 985, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 986, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.00/1.39 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 987, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.00/1.39 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 988, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 989, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y,
% 1.00/1.39 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 990, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 991, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.00/1.39 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 992, [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 993, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 1.00/1.39 , clause( 994, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 995, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 996, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.00/1.39 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 997, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 998, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 999, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 1000, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y,
% 1.00/1.39 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 1001, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1002, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( X, Y
% 1.00/1.39 , Z ), 'tc_List_Olist'( Z ) ), 'c_Suc'( 'c_Nat_Osize__class_Osize'( Y,
% 1.00/1.39 'tc_List_Olist'( Z ) ) ) ) ] )
% 1.00/1.39 , clause( 1003, [ =( 'c_Suc'( 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( Y ) ) ), 'c_Nat_Osize__class_Osize'(
% 1.00/1.39 'c_List_Olist_OCons'( Z, X, Y ), 'tc_List_Olist'( Y ) ) ) ] )
% 1.00/1.39 , clause( 1004, [ ~( 'c_lessequals'( 'c_Nat_Osize__class_Osize'(
% 1.00/1.39 'c_List_Olist_OCons'( X, Y, Z ), 'tc_List_Olist'( Z ) ),
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1005, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 1006, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.00/1.39 =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.00/1.39 , T ) ] )
% 1.00/1.39 , clause( 1007, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 1008, [ =( 'c_List_Otake'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.00/1.39 , 'tc_nat' ), 'c_List_Olist_OCons'( Y, Z, T ), T ), 'c_List_Olist_OCons'(
% 1.00/1.39 Y, 'c_List_Otake'( 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z, T ), T ) ), =(
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1009, [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 1010, [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ] )
% 1.00/1.39 , clause( 1011, [ =( 'c_List_Odrop'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.00/1.39 , 'tc_nat' ), 'c_List_Olist_OCons'( Y, Z, T ), T ), 'c_List_Odrop'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.00/1.39 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z, T ) ),
% 1.00/1.39 =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1012, [ =( 'c_List_Otake'( 'c_Suc'( X ), 'c_List_Olist_OCons'( Y
% 1.00/1.39 , Z, T ), T ), 'c_List_Olist_OCons'( Y, 'c_List_Otake'( X, Z, T ), T ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1013, [ =( 'c_List_Odrop'( 'c_Suc'( X ), 'c_List_Olist_OCons'( Y
% 1.00/1.39 , Z, T ), T ), 'c_List_Odrop'( X, Z, T ) ) ] )
% 1.00/1.39 , clause( 1014, [ =( 'c_List_Otake'( X, Y, Z ), Y ), ~( 'c_lessequals'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), X, 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1015, [ 'c_lessequals'( 'c_Nat_Osize__class_Osize'(
% 1.00/1.39 'c_List_Ofilter'( X, Y, Z ), 'tc_List_Olist'( Z ) ),
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1016, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.00/1.39 , Z, X ), ~( 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Y,
% 1.00/1.39 'c_List_Olist_OCons'( Z, T, X ), X ), X ) ) ] )
% 1.00/1.39 , clause( 1017, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Y,
% 1.00/1.39 'c_List_Olist_OCons'( Z, T, X ), X ), X ), ~(
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Z, T, X ), X ) )
% 1.00/1.39 , ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 1018, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Odrop'( X, Y, Z )
% 1.00/1.39 , 'tc_List_Olist'( Z ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), X, 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1019, [ =( 'c_List_Olist__update'( 'c_List_Olist_OCons'( X, Y, Z
% 1.00/1.39 ), 'c_Suc'( T ), U, Z ), 'c_List_Olist_OCons'( X, 'c_List_Olist__update'(
% 1.00/1.39 Y, T, U, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1020, [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y )
% 1.00/1.39 , Z ), T ), ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y,
% 1.00/1.39 'c_Type_Otype_OFun'( U, T ) ) ) ] )
% 1.00/1.39 , clause( 1021, [ =( 'c_List_Oreplicate'( 'c_Suc'( X ), Y, Z ),
% 1.00/1.39 'c_List_Olist_OCons'( Y, 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1022, [ =( 'c_List_Olist__update'( X, Y, Z, T ), X ), ~(
% 1.00/1.39 'c_lessequals'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T ) ), Y
% 1.00/1.39 , 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1023, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( hAPP(
% 1.00/1.39 hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1024, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 1.00/1.39 'c_Lambda_OdB_OVar'( X ) ), Y ), Z ), 'c_Lambda_OdB_OVar'( X ) ), =( X, Z
% 1.00/1.39 ), 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1025, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 1.00/1.39 'c_Lambda_OdB_OVar'( X ) ), Y ), Z ), 'c_Lambda_OdB_OVar'( X ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1026, [ =( 'c_List_Orev'( 'c_List_Olist__update'( X, Y, Z, T ), T
% 1.00/1.39 ), 'c_List_Olist__update'( 'c_List_Orev'( X, T ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T ) ), Y, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z, T ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( T ) ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1027, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Osubst', X ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ), 'c_Suc'(
% 1.00/1.39 T ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', U ), Y ), T ) ), Z ), hAPP(
% 1.00/1.39 hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ),
% 1.00/1.39 U ), Z ) ), Y ), T ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 1.00/1.39 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1028, [ =( 'c_List_Odrop'( X, 'c_List_Otake'( Y, Z, T ), T ),
% 1.00/1.39 'c_List_Otake'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.00/1.39 'c_List_Odrop'( X, Z, T ), T ) ) ] )
% 1.00/1.39 , clause( 1029, [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 1.00/1.39 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 1.00/1.39 'c_Suc'( Y ), Z, T ) ) ] )
% 1.00/1.39 , clause( 1030, [ =( 'c_List_Orotate'( X, Y, Z ), 'c_List_Orotate'(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( X, 'c_Nat_Osize__class_Osize'( Y,
% 1.00/1.39 'tc_List_Olist'( Z ) ), 'tc_nat' ), Y, Z ) ) ] )
% 1.00/1.39 , clause( 1031, [ 'c_lessequals'( 'c_Nat_Osize__class_Osize'(
% 1.00/1.39 'c_List_Oremdups'( X, Y ), 'tc_List_Olist'( Y ) ),
% 1.00/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1032, [ =( 'c_List_Odrop'( X, 'c_List_Oreplicate'( Y, Z, T ), T )
% 1.00/1.39 , 'c_List_Oreplicate'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z
% 1.00/1.39 , T ) ) ] )
% 1.00/1.39 , clause( 1033, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X )
% 1.00/1.39 ), Y ), 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.00/1.39 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1034, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 1.00/1.39 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 1.00/1.39 ) ) ] )
% 1.00/1.39 , clause( 1035, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( X, Y
% 1.00/1.39 , Z ), 'tc_List_Olist'( Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ) ),
% 1.00/1.39 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 1.00/1.39 , clause( 1036, [ ~( 'class_Int_Oring__char__0'( X ) ), ~(
% 1.00/1.39 'class_Int_Onumber__ring'( X ) ), ~( =(
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ] )
% 1.00/1.39 , clause( 1037, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1038, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1039, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 1.00/1.39 'c_lessequals'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 1040, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 1.00/1.39 'c_lessequals'( Y, Z, X ) ] )
% 1.00/1.39 , clause( 1041, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 1.00/1.39 'c_lessequals'( Z, Y, X ) ) ] )
% 1.00/1.39 , clause( 1042, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1043, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1044, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.00/1.39 'tc_nat' ), X, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1045, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.00/1.39 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.00/1.39 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.00/1.39 , clause( 1046, [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.00/1.39 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'(
% 1.00/1.39 X, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1047, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.00/1.39 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1048, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 1.00/1.39 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1049, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.00/1.39 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.00/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 1050, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.00/1.39 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 1051, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 1.00/1.39 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1052, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.00/1.39 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1053, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.00/1.39 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1054, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.00/1.39 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1055, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.00/1.39 'tc_nat' ), X, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1056, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), Z, 'tc_nat' ),
% 1.00/1.39 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1057, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.00/1.39 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.00/1.39 , T, X ), X ), T, X ) ) ] )
% 1.00/1.39 , clause( 1058, [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.00/1.39 'tc_nat' ) ), Y ) ), =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 1.00/1.39 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1059, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.00/1.39 , clause( 1060, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, X ), X ) ) ] )
% 1.00/1.39 , clause( 1061, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.00/1.39 T, X ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.00/1.39 , clause( 1062, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.00/1.39 T, X ), ~( 'c_lessequals'( Z, T, X ) ) ] )
% 1.00/1.39 , clause( 1063, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.00/1.39 , clause( 1064, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, X ), X ) ) ] )
% 1.00/1.39 , clause( 1065, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 1.00/1.39 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 1.00/1.39 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1066, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ),
% 1.00/1.39 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 1.00/1.39 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1067, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1068, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 1.00/1.39 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1069, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ),
% 1.00/1.39 ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1070, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1071, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1072, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1073, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.00/1.39 =( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 1.00/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.00/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.00/1.39 , clause( 1074, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ] )
% 1.00/1.39 , clause( 1075, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ] )
% 1.00/1.39 , clause( 1076, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.39 , Y ), Z ), Z, X ), Y ) ] )
% 1.00/1.39 , clause( 1077, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.00/1.39 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.00/1.39 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.00/1.39 X ), T, X ) ) ] )
% 1.00/1.39 , clause( 1078, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.00/1.39 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.00/1.39 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.00/1.39 X ), T, X ) ) ] )
% 1.00/1.39 , clause( 1079, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T,
% 1.00/1.39 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.00/1.39 , Y, X ) ) ] )
% 1.00/1.39 , clause( 1080, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.00/1.39 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1081, [ ~(
% 1.00/1.39 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.00/1.39 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.00/1.39 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1082, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 1.00/1.39 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1083, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1084, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 1.00/1.39 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1085, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.00/1.39 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 1.00/1.39 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.00/1.39 , clause( 1086, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1087, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1088, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1089, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1090, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1091, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1092, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.00/1.39 , clause( 1093, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.00/1.39 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.00/1.39 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 1.00/1.39 , clause( 1094, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.39 ) ), =( Y, Z ) ] )
% 1.00/1.39 , clause( 1095, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.39 ) ), =( Y, Z ) ] )
% 1.00/1.39 , clause( 1096, [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.00/1.39 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.00/1.39 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 1097, [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.00/1.39 , Y ) ) ] )
% 1.00/1.39 , clause( 1098, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1099, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), Z, X ), Z ) ] )
% 1.00/1.39 , clause( 1100, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1101, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1102, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.00/1.39 ) ) ) ] )
% 1.00/1.39 , clause( 1103, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.00/1.39 ) ) ) ] )
% 1.00/1.39 , clause( 1104, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 1.00/1.39 , clause( 1105, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.00/1.39 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1106, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 1.00/1.39 , clause( 1107, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1108, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 1.00/1.39 ) ) ) ] )
% 1.00/1.39 , clause( 1109, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 1.00/1.39 ) ) ) ] )
% 1.00/1.39 , clause( 1110, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1111, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1112, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1113, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.00/1.39 , 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1114, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 1.00/1.39 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 1.00/1.39 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1115, [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ), hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Olift', 'c_Lambda_Oliftn'( X, Y, Z ) ), Z ) ) ] )
% 1.00/1.39 , clause( 1116, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.00/1.39 'c_HOL_Oone__class_Oone'( X ) ), X ) ] )
% 1.00/1.39 , clause( 1117, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ] )
% 1.00/1.39 , clause( 1118, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ),
% 1.00/1.39 'tc_nat' ), =( X, 'c_List_Olist_ONil'( Y ) ) ] )
% 1.00/1.39 , clause( 1119, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ),
% 1.00/1.39 'tc_List_Olist'( X ) ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1120, [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 'c_List_Odrop'(
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_List_Olist_OCons'(
% 1.00/1.39 Y, Z, T ), T ), 'c_List_Olist_OCons'( Y, Z, T ) ) ] )
% 1.00/1.39 , clause( 1121, [ ~( =( 'c_List_Odrop'( X, Y, Z ), 'c_List_Olist_ONil'( Z )
% 1.00/1.39 ) ), 'c_lessequals'( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z )
% 1.00/1.39 ), X, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1122, [ =( 'c_List_Odrop'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) )
% 1.00/1.39 , ~( 'c_lessequals'( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z )
% 1.00/1.39 ), X, 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1123, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, U
% 1.00/1.39 , Z ) ) ), =( 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( T,
% 1.00/1.39 'tc_List_Olist'( Z ) ), X, Z ), T ), 'c_lessequals'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) ),
% 1.00/1.39 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1124, [ =( 'c_List_Otake'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 1.00/1.39 'c_List_Oappend'( 'c_List_Otake'( X, Y, T ), 'c_List_Otake'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, 'c_Nat_Osize__class_Osize'( Y,
% 1.00/1.39 'tc_List_Olist'( T ) ), 'tc_nat' ), Z, T ), T ) ) ] )
% 1.00/1.39 , clause( 1125, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, U
% 1.00/1.39 , Z ) ) ), =( X, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( Z ) ), T, Z ) ), ~( 'c_lessequals'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) ),
% 1.00/1.39 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1126, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, U
% 1.00/1.39 , Z ) ) ), =( Y, 'c_List_Oappend'( 'c_List_Odrop'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) ), T, Z ), U, Z ) ),
% 1.00/1.39 ~( 'c_lessequals'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) )
% 1.00/1.39 , 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1127, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, U
% 1.00/1.39 , Z ) ) ), =( 'c_List_Oappend'( 'c_List_Odrop'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) ), X, Z ), Y, Z ), U
% 1.00/1.39 ), 'c_lessequals'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) )
% 1.00/1.39 , 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) ), 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1128, [ =( 'c_List_Odrop'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 1.00/1.39 'c_List_Oappend'( 'c_List_Odrop'( X, Y, T ), 'c_List_Odrop'(
% 1.00/1.39 'c_HOL_Ominus__class_Ominus'( X, 'c_Nat_Osize__class_Osize'( Y,
% 1.00/1.39 'tc_List_Olist'( T ) ), 'tc_nat' ), Z, T ), T ) ) ] )
% 1.00/1.39 , clause( 1129, [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T
% 1.00/1.39 , U, Z ), 'c_List_Oappend'( 'c_List_Olist__update'( X, T, U, Z ), Y, Z )
% 1.00/1.39 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1130, [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T
% 1.00/1.39 , U, Z ), 'c_List_Oappend'( 'c_List_Olist__update'( X, T, U, Z ), Y, Z )
% 1.00/1.39 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1131, [ =( 'c_List_Olist__update'( X, Y, Z, T ), 'c_List_Oappend'(
% 1.00/1.39 'c_List_Otake'( Y, X, T ), 'c_List_Olist_OCons'( Z, 'c_List_Odrop'(
% 1.00/1.39 'c_Suc'( Y ), X, T ), T ), T ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.00/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T ) ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1132, [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 'c_List_Orotate'( X, Y, Z
% 1.00/1.39 ), Y ) ] )
% 1.00/1.39 , clause( 1133, [ =( 'c_List_Orotate'( X, Y, Z ), Y ), ~( 'c_lessequals'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ),
% 1.00/1.39 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1134, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.39 'c_List_Olistsum'( 'c_List_Omap'( Y, 'c_List_Ofilter'( Z, T, U ), U, X )
% 1.00/1.39 , X ), 'c_List_Olistsum'( 'c_List_Omap'( Y, T, U, X ), X ) ), ~( hBOOL(
% 1.00/1.39 hAPP( Z, 'c_List_Osko__List__Xlistsum__map__filter__1__1'( Z, Y, T, U, X
% 1.00/1.39 ) ) ) ) ] )
% 1.00/1.39 , clause( 1135, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 1.00/1.39 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 Y ), X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1136, [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 'c_List_Otake'(
% 1.00/1.39 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_List_Olist_OCons'(
% 1.00/1.39 Y, Z, T ), T ), 'c_List_Olist_ONil'( T ) ) ] )
% 1.00/1.39 , clause( 1137, [ =( 'c_List_Otake'( X, 'c_List_Olist_OCons'( Y, Z, T ), T
% 1.00/1.39 ), 'c_List_Olist_OCons'( Y, 'c_List_Otake'( 'c_HOL_Ominus__class_Ominus'(
% 1.00/1.39 X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z, T ), T ) ), =( X
% 1.00/1.39 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1138, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_OCons'( 'v_sko__List__Xdistinct__Xinduct__1'( X ),
% 1.00/1.39 'v_sko__List__Xdistinct__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 1.00/1.39 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 1.00/1.39 , clause( 1139, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_OCons'( 'v_sko__List__Xremove1__Xinduct__1'( X ),
% 1.00/1.39 'v_sko__List__Xremove1__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 1.00/1.39 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 1.00/1.39 , clause( 1140, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_OCons'( 'v_sko__List__Xlist__Xinduct__1'( X ),
% 1.00/1.39 'v_sko__List__Xlist__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 1.00/1.39 , clause( 1141, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_OCons'( 'v_sko__List__Xmap__Xinduct__1'( X ),
% 1.00/1.39 'v_sko__List__Xmap__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 1.00/1.39 , clause( 1142, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_OCons'( 'v_sko__List__Xtake__Xinduct__1'( X ),
% 1.00/1.39 'v_sko__List__Xtake__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 1.00/1.39 , clause( 1143, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_OCons'( 'v_sko__List__Xconcat__Xinduct__1'( X ),
% 1.00/1.39 'v_sko__List__Xconcat__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X
% 1.00/1.39 , 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 1.00/1.39 , clause( 1144, [ =( 'c_List_Odrop'( X, 'c_List_Olist_OCons'( Y, Z, T ), T
% 1.00/1.39 ), 'c_List_Odrop'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.00/1.39 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z, T ) ), =( X,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1145, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.00/1.39 'c_Lambda_OdB_OVar'( Y ),
% 1.00/1.39 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( 'c_Lambda_Obeta'(
% 1.00/1.39 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), Z,
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ) ] )
% 1.00/1.39 , clause( 1146, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =(
% 1.00/1.39 hAPP( Y, 'c_List_Osko__List__Xlistsum__map__filter__1__1'( Z, Y, T, U, X
% 1.00/1.39 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_List_Olistsum'(
% 1.00/1.39 'c_List_Omap'( Y, 'c_List_Ofilter'( Z, T, U ), U, X ), X ),
% 1.00/1.39 'c_List_Olistsum'( 'c_List_Omap'( Y, T, U, X ), X ) ) ] )
% 1.00/1.39 , clause( 1147, [ ~( =( X, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( Y ) ), Z, Y ) ) ), =( 'c_List_Oappend'( X,
% 1.00/1.39 'c_List_Oappend'( 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( Y ) ), Z, Y ), T, Y ), Y ), 'c_List_Oappend'( Z, T, Y )
% 1.00/1.39 ), ~( 'c_lessequals'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y
% 1.00/1.39 ) ), 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( Y ) ), 'tc_nat' ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1148, [ ~( =( 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( Y ) ), Z, Y ), X ) ), 'c_lessequals'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( Y ) ),
% 1.00/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ), 'tc_nat' ), =(
% 1.00/1.39 'c_List_Oappend'( Z, T, Y ), 'c_List_Oappend'( X, 'c_List_Oappend'(
% 1.00/1.39 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ), Z
% 1.00/1.39 , Y ), T, Y ), Y ) ) ] )
% 1.00/1.39 , clause( 1149, [ =( 'c_List_Olist_Olist__size'( X, 'c_List_Olist_OCons'( Y
% 1.00/1.39 , Z, T ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( X, Y ) ),
% 1.00/1.39 'c_List_Olist_Olist__size'( X, Z, T ) ) ), 'c_Suc'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 1.00/1.39 , clause( 1150, [ =( 'c_List_Orev'( 'c_List_Odrop'( X, Y, Z ), Z ),
% 1.00/1.39 'c_List_Otake'( 'c_HOL_Ominus__class_Ominus'( 'c_Nat_Osize__class_Osize'(
% 1.00/1.39 Y, 'tc_List_Olist'( Z ) ), X, 'tc_nat' ), 'c_List_Orev'( Y, Z ), Z ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1151, [ =( 'c_List_Orev'( 'c_List_Otake'( X, Y, Z ), Z ),
% 1.00/1.39 'c_List_Odrop'( 'c_HOL_Ominus__class_Ominus'( 'c_Nat_Osize__class_Osize'(
% 1.00/1.39 Y, 'tc_List_Olist'( Z ) ), X, 'tc_nat' ), 'c_List_Orev'( Y, Z ), Z ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1152, [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Osubst', X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Osubst', hAPP( hAPP( 'c_Lambda_Olift', X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 1.00/1.39 'tc_nat' ) ) ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), T ) ), Z ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1153, [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Osubst', X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Osubst', hAPP( hAPP( 'c_Lambda_Olift', X ), T ) ), hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Olift', Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~(
% 1.00/1.39 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1154, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X )
% 1.00/1.39 ), Y ), 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ),
% 1.00/1.39 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1155, [ 'c_Type_Otypings'( X, Y,
% 1.00/1.39 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X, T, Y ) ), ~(
% 1.00/1.39 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', T, Y,
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 1.00/1.39 , clause( 1156, [ 'c_Type_Otypings'( X, Y,
% 1.00/1.39 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X, T, Y ) ), ~(
% 1.00/1.39 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', T, Y,
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 1.00/1.39 , clause( 1157, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ),
% 1.00/1.39 'c_Type_Otype_OFun'( Z, T ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( X,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_Type_Otype' ), Y, T ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1158, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 1.00/1.39 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'(
% 1.00/1.39 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 1159, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat__aux'( 'c_COMBC'(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ), X, X, X )
% 1.00/1.39 , Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.00/1.39 , clause( 1160, [ =( 'c_List_Otake'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Y ), Z, T ), 'c_List_Oappend'( 'c_List_Otake'( X, Z, T )
% 1.00/1.39 , 'c_List_Otake'( Y, 'c_List_Odrop'( X, Z, T ), T ), T ) ), ~(
% 1.00/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.00/1.39 Y ), 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( T ) ), 'tc_nat' ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1161, [ =( 'c_List_Orotate'( X, Y, Z ), 'c_List_Oappend'(
% 1.00/1.39 'c_List_Odrop'( 'c_Divides_Odiv__class_Omod'( X,
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), 'tc_nat' ), Y, Z )
% 1.00/1.39 , 'c_List_Otake'( 'c_Divides_Odiv__class_Omod'( X,
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), 'tc_nat' ), Y, Z )
% 1.00/1.39 , Z ) ) ] )
% 1.00/1.39 , clause( 1162, [ 'c_Type_Otypings'( X, Y,
% 1.00/1.39 'c_Type_Osko__Type__Xvar__app__types__1__1'( Z, T, X, Y ) ), ~(
% 1.00/1.39 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.00/1.39 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ) ),
% 1.00/1.39 ~( 'c_Type_Otypings'( X, W, V0 ) ), ~( 'c_Type_Otyping'( X,
% 1.00/1.39 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 1.00/1.39 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 1.00/1.39 , clause( 1163, [ 'c_Type_Otypings'( X, Y,
% 1.00/1.39 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X, T, Y ) ), ~(
% 1.00/1.39 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.00/1.39 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1164, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 1.00/1.39 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ] )
% 1.00/1.39 , clause( 1165, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 1.00/1.39 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 1.00/1.39 , clause( 1166, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 1.00/1.39 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 1.00/1.39 , clause( 1167, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.00/1.39 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 1.00/1.39 , clause( 1168, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z )
% 1.00/1.39 ) ), =( Y, Z ) ] )
% 1.00/1.39 , clause( 1169, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y )
% 1.00/1.39 ) ), =( X, Z ) ] )
% 1.00/1.39 , clause( 1170, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z )
% 1.00/1.39 ) ), =( Y, Z ) ] )
% 1.00/1.39 , clause( 1171, [ =( 'c_List_Oremove1'( X, 'c_List_Olist_OCons'( X, Y, Z )
% 1.00/1.39 , Z ), Y ) ] )
% 1.00/1.39 , clause( 1172, [ =( 'c_List_Olist_Olist__case'( X, Y, 'c_List_Olist_OCons'(
% 1.00/1.39 Z, T, U ), W, U ), hAPP( hAPP( Y, Z ), T ) ) ] )
% 1.00/1.39 , clause( 1173, [ 'c_List_Odistinct'( 'c_List_Ofilter'( X, Y, Z ), Z ), ~(
% 1.00/1.39 'c_List_Odistinct'( Y, Z ) ) ] )
% 1.00/1.39 , clause( 1174, [ =( X, 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( Y,
% 1.00/1.39 'tc_List_Olist'( Z ) ), 'c_List_Oappend'( Y, X, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1175, [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T,
% 1.00/1.39 Z ), 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1176, [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T,
% 1.00/1.39 Z ), 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1177, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 1.00/1.39 'c_Lambda_OdB_OAbs'( X ), Y ) ] )
% 1.00/1.39 , clause( 1178, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y
% 1.00/1.39 ) ) ] )
% 1.00/1.39 , clause( 1179, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Y, Z, X ), X ),
% 1.00/1.39 ~( 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( T,
% 1.00/1.39 'c_List_Olist_OCons'( Y, Z, X ), X ), X ) ) ] )
% 1.00/1.39 , clause( 1180, [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'(
% 1.00/1.39 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.39 , clause( 1181, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ] )
% 1.00/1.39 , clause( 1182, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ] )
% 1.00/1.39 , clause( 1183, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.00/1.39 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.39 Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.00/1.39 , clause( 1184, [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_OCons'( Z, T,
% 1.00/1.39 Y ) ) ), =( X, 'c_List_Oappend'( 'c_List_Orev'( T, Y ),
% 1.00/1.39 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( Y ), Y ), Y ) ) ] )
% 1.00/1.39 , clause( 1185, [ =( 'c_List_Orev'( 'c_List_Olist_OCons'( X,
% 1.00/1.39 'c_List_Olist_ONil'( Y ), Y ), Y ), 'c_List_Olist_OCons'( X,
% 1.00/1.39 'c_List_Olist_ONil'( Y ), Y ) ) ] )
% 1.00/1.39 , clause( 1186, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_OCons'( Z, T, U )
% 1.00/1.39 , W, U ), 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, W, U ) ) ] )
% 1.00/1.39 , clause( 1187, [ =( 'c_List_Orev'( 'c_List_Olist_OCons'( X, Y, Z ), Z ),
% 1.00/1.39 'c_List_Oappend'( 'c_List_Orev'( Y, Z ), 'c_List_Olist_OCons'( X,
% 1.00/1.39 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1188, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Ofilter'(
% 1.00/1.39 T, U, Z ) ) ), hBOOL( hAPP( T, X ) ) ] )
% 1.00/1.39 , clause( 1189, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.00/1.39 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.00/1.39 , clause( 1190, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.00/1.39 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 1.00/1.39 , clause( 1191, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.00/1.39 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ] )
% 1.00/1.39 , clause( 1192, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'(
% 1.00/1.39 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 1.00/1.39 , clause( 1193, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'(
% 1.00/1.39 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ] )
% 1.00/1.39 , clause( 1194, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.00/1.39 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.00/1.39 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.00/1.39 , clause( 1195, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ] )
% 1.00/1.39 , clause( 1196, [ =( 'c_List_Otake'( X, 'c_List_Odrop'( Y, Z, T ), T ),
% 1.00/1.39 'c_List_Odrop'( Y, 'c_List_Otake'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), X ), Y ), Z, T ), T ) ) ] )
% 1.00/1.39 , clause( 1197, [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.00/1.39 , 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_OCons'( X, Y, Z ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1198, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.00/1.39 , clause( 1199, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.00/1.39 , clause( 1200, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 X ), Y ), T ) ), Z ) ) ] )
% 1.00/1.39 , clause( 1201, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 X ), Y ), Z ) ), T ) ) ] )
% 1.00/1.39 , clause( 1202, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.00/1.39 , clause( 1203, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.00/1.39 , clause( 1204, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.00/1.39 , clause( 1205, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ] )
% 1.00/1.39 , clause( 1206, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.00/1.39 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ] )
% 1.00/1.39 , clause( 1207, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.00/1.39 , clause( 1208, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 X ), Y ), Z ) ), T ) ) ] )
% 1.00/1.39 , clause( 1209, [ =( 'c_List_Oremdups'( 'c_List_Ofilter'( X, Y, Z ), Z ),
% 1.00/1.39 'c_List_Ofilter'( X, 'c_List_Oremdups'( Y, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1210, [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'(
% 1.00/1.39 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.39 , clause( 1211, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( 'c_List_Odrop'( Y, Z, X ), X ), ~(
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( Z, X ) ) ] )
% 1.00/1.39 , clause( 1212, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.00/1.39 'c_List_Olistsum'( Y, X ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X
% 1.00/1.39 ), 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ) ) ] )
% 1.00/1.39 , clause( 1213, [ =( 'c_List_Ofilter'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 1.00/1.39 T ), 'c_List_Olist_OCons'( Y, 'c_List_Ofilter'( X, Z, T ), T ) ), ~(
% 1.00/1.39 hBOOL( hAPP( X, Y ) ) ) ] )
% 1.00/1.39 , clause( 1214, [ ~( =( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ),
% 1.00/1.39 Y ), 'c_List_Orev'( Z, Y ) ) ), =( Z, 'c_List_Olist_OCons'( X,
% 1.00/1.39 'c_List_Olist_ONil'( Y ), Y ) ) ] )
% 1.00/1.39 , clause( 1215, [ =( 'c_List_Otake'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.00/1.39 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_OCons'( X,
% 1.00/1.39 'c_List_Olist_ONil'( Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1216, [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'(
% 1.00/1.39 T, U, Z ) ) ), =( X, T ) ] )
% 1.00/1.39 , clause( 1217, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, Y
% 1.00/1.39 , Z ) ) ), =( X, T ) ] )
% 1.00/1.39 , clause( 1218, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( X, T
% 1.00/1.39 , Z ) ) ), =( Y, T ) ] )
% 1.00/1.39 , clause( 1219, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( 'c_List_Otake'( Y, Z, X ), X ), ~(
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( Z, X ) ) ] )
% 1.00/1.39 , clause( 1220, [ ~( =( 'c_List_Ofilter'( X, Y, Z ), 'c_List_Olist_OCons'(
% 1.00/1.39 T, U, Z ) ) ), hBOOL( hAPP( X, T ) ) ] )
% 1.00/1.39 , clause( 1221, [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'(
% 1.00/1.39 'c_List_Oappend'( X, Z, Y ), Y ) ) ] )
% 1.00/1.39 , clause( 1222, [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'(
% 1.00/1.39 'c_List_Oappend'( Z, X, Y ), Y ) ) ] )
% 1.00/1.39 , clause( 1223, [ =( X, 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ) ) ] )
% 1.00/1.39 , clause( 1224, [ =( 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ), X ) ] )
% 1.00/1.39 , clause( 1225, [ =( 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ), X ) ] )
% 1.00/1.39 , clause( 1226, [ ~( =( 'c_Nat_Osize__class_Osize'( 'c_List_Oremdups'( X, Y
% 1.00/1.39 ), 'tc_List_Olist'( Y ) ), 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( Y ) ) ) ), =( 'c_List_Oremdups'( X, Y ), X ) ] )
% 1.00/1.39 , clause( 1227, [ ~( =( 'c_List_Oremdups'( X, Y ), X ) ), =(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( 'c_List_Oremdups'( X, Y ), 'tc_List_Olist'( Y
% 1.00/1.39 ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ) ) ] )
% 1.00/1.39 , clause( 1228, [ =( X, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( Y ) ), 'c_List_Oappend'( X, Z, Y ), Y ) ) ] )
% 1.00/1.39 , clause( 1229, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 1.00/1.39 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubstn'( X, Y, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.00/1.39 'tc_nat' ) ) ) ) ) ] )
% 1.00/1.39 , clause( 1230, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 1.00/1.39 , clause( 1231, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 1.00/1.39 , clause( 1232, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.00/1.39 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1233, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 1.00/1.39 , clause( 1234, [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =(
% 1.00/1.39 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), T, X, X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ] )
% 1.00/1.39 , clause( 1235, [ =( 'c_List_Orev'( 'c_List_Oreplicate'( X, Y, Z ), Z ),
% 1.00/1.39 'c_List_Oreplicate'( X, Y, Z ) ) ] )
% 1.00/1.39 , clause( 1236, [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ),
% 1.00/1.39 T ), 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ] )
% 1.00/1.39 , clause( 1237, [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ),
% 1.00/1.39 T ), 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ] )
% 1.00/1.39 , clause( 1238, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 1.00/1.39 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.39 , clause( 1239, [ =( 'c_List_Odrop'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.00/1.39 'c_List_Olist_OCons'( X, Y, Z ), Z ), Y ) ] )
% 1.00/1.39 , clause( 1240, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 1.00/1.39 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 1.00/1.39 , clause( 1241, [ =( 'c_List_Oappend'( 'c_List_Otake'( X, Y, Z ),
% 1.00/1.39 'c_List_Odrop'( X, Y, Z ), Z ), Y ) ] )
% 1.00/1.39 , clause( 1242, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( Y, X ), ~(
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Z, Y, X ), X ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1243, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1244, [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y
% 1.00/1.39 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ), ~( 'c_Lambda_Obeta'( Y,
% 1.00/1.39 Z ) ) ] )
% 1.00/1.39 , clause( 1245, [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y
% 1.00/1.39 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X,
% 1.00/1.39 Z ) ) ] )
% 1.00/1.39 , clause( 1246, [ =( 'c_List_Orev'( 'c_List_Oappend'( 'c_List_Orev'( X, Y )
% 1.00/1.39 , 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( Y ), Y ), Y ), Y ),
% 1.00/1.39 'c_List_Olist_OCons'( Z, X, Y ) ) ] )
% 1.00/1.39 , clause( 1247, [ 'c_List_Odistinct'( 'c_List_Odrop'( X, Y, Z ), Z ), ~(
% 1.00/1.39 'c_List_Odistinct'( Y, Z ) ) ] )
% 1.00/1.39 , clause( 1248, [ 'c_List_Odistinct'( 'c_List_Orev'( X, Y ), Y ), ~(
% 1.00/1.39 'c_List_Odistinct'( X, Y ) ) ] )
% 1.00/1.39 , clause( 1249, [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'(
% 1.00/1.39 'c_List_Orev'( X, Y ), Y ) ) ] )
% 1.00/1.39 , clause( 1250, [ ~( =( 'c_List_Oremdups'( X, Y ), X ) ),
% 1.00/1.39 'c_List_Odistinct'( X, Y ) ] )
% 1.00/1.39 , clause( 1251, [ =( 'c_List_Oremdups'( X, Y ), X ), ~( 'c_List_Odistinct'(
% 1.00/1.39 X, Y ) ) ] )
% 1.00/1.39 , clause( 1252, [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp'
% 1.00/1.39 , Y ), Z ), T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y
% 1.00/1.39 , T ) ), 'c_Lambda_Oliftn'( X, Z, T ) ) ) ] )
% 1.00/1.39 , clause( 1253, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_OCons'( 'v_sko__List__Xlistsp__Xinduct__1'( Z, X ),
% 1.00/1.39 'v_sko__List__Xlistsp__Xinduct__2'( Z, X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 1.00/1.39 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1254, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_OCons'( 'v_sko__List__Xlistsp__Xinducts__1'( Z, X ),
% 1.00/1.39 'v_sko__List__Xlistsp__Xinducts__2'( Z, X ), 't_a' ) ) ) ), ~( hBOOL(
% 1.00/1.39 hAPP( X, 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y,
% 1.00/1.39 't_a' ) ) ] )
% 1.00/1.39 , clause( 1255, [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.00/1.39 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ) ] )
% 1.00/1.39 , clause( 1256, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ] )
% 1.00/1.39 , clause( 1257, [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ] )
% 1.00/1.39 , clause( 1258, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Oremdups'( X, Y )
% 1.00/1.39 , 'tc_List_Olist'( Y ) ), 'c_List_Olength__unique'( X, Y ) ) ] )
% 1.00/1.39 , clause( 1259, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 1.00/1.39 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.39 , clause( 1260, [ =( 'c_List_Olist__update'( 'c_List_Olist_OCons'( X, Y, Z
% 1.00/1.39 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, Z ), 'c_List_Olist_OCons'(
% 1.00/1.39 T, Y, Z ) ) ] )
% 1.00/1.39 , clause( 1261, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist__update'( X
% 1.00/1.39 , Y, Z, T ), 'tc_List_Olist'( T ) ), 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( T ) ) ) ] )
% 1.00/1.39 , clause( 1262, [ =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Oappend'(
% 1.00/1.39 'c_List_Olist_ONil'( Z ), 'c_List_Olist_OCons'( X, Y, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1263, [ =( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y )
% 1.00/1.39 , 'c_List_Orev'( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.00/1.39 Y ) ) ] )
% 1.00/1.39 , clause( 1264, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 1.00/1.39 'c_Lambda_OdB_OApp', X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ), ~( hBOOL( hAPP(
% 1.00/1.39 'c_InductTermi_OIT', X ) ) ) ] )
% 1.00/1.39 , clause( 1265, [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'(
% 1.00/1.39 'c_Type_Oshift'( X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'(
% 1.00/1.39 X, hAPP( hAPP( hAPP( 'c_Lambda_Osubst', U ), Y ), T ), W ) ] )
% 1.00/1.39 , clause( 1266, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 1.00/1.39 'tc_bool' ) ), Y ) ) ) ] )
% 1.00/1.39 , clause( 1267, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.00/1.39 'tc_bool' ) ), Y ) ) ) ] )
% 1.00/1.39 , clause( 1268, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Y,
% 1.00/1.39 'c_List_Olist_ONil'( X ), X ), X ) ] )
% 1.00/1.39 , clause( 1269, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 1.00/1.39 'c_Lambda_OdB_OAbs'( X ) ), Y ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.00/1.39 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 1.00/1.39 , clause( 1270, [ 'c_List_Odistinct'( 'c_List_Otake'( X, Y, Z ), Z ), ~(
% 1.00/1.39 'c_List_Odistinct'( Y, Z ) ) ] )
% 1.00/1.39 , clause( 1271, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ),
% 1.00/1.39 'c_Lambda_OdB_OAbs'( Y ) ), ~( 'c_Lambda_Obeta'( X, Y ) ) ] )
% 1.00/1.39 , clause( 1272, [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 1.00/1.39 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( Z ), Z ), Z ),
% 1.00/1.39 'c_List_Olist_OCons'( Y, 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1273, [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 1.00/1.39 ), Y ), Z, T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X,
% 1.00/1.39 Z, T ) ), 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ] )
% 1.00/1.39 , clause( 1274, [ =( 'c_List_Orev'( 'c_List_Oappend'( X, Y, Z ), Z ),
% 1.00/1.39 'c_List_Oappend'( 'c_List_Orev'( Y, Z ), 'c_List_Orev'( X, Z ), Z ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1275, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Oappend'( Z, T, U ), W
% 1.00/1.39 , U ), 'c_List_Ofoldl'( X, 'c_List_Ofoldl'( X, Y, Z, W, U ), T, W, U ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1276, [ =( 'c_List_Orotate'( X, 'c_List_Orotate'( Y, Z, T ), T )
% 1.00/1.39 , 'c_List_Orotate'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.00/1.39 ), Y ), Z, T ) ) ] )
% 1.00/1.39 , clause( 1277, [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'(
% 1.00/1.39 'c_List_Olist_OCons'( Z, X, Y ), Y ) ) ] )
% 1.00/1.39 , clause( 1278, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 1.00/1.39 'c_Lambda_OdB_OVar'( Z ) ) ) ] )
% 1.00/1.39 , clause( 1279, [ =( 'c_List_Ofilter'( X, 'c_List_Oappend'( Y, Z, T ), T )
% 1.00/1.39 , 'c_List_Oappend'( 'c_List_Ofilter'( X, Y, T ), 'c_List_Ofilter'( X, Z,
% 1.00/1.39 T ), T ) ) ] )
% 1.00/1.39 , clause( 1280, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB',
% 1.00/1.39 'tc_Lambda_OdB' ) ) ), ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y,
% 1.00/1.39 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.39 , clause( 1281, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.00/1.39 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.00/1.39 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.00/1.39 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.39 ) ) ] )
% 1.00/1.39 , clause( 1282, [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.00/1.39 X ) ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.39 ) ) ] )
% 1.00/1.39 , clause( 1283, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.00/1.39 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1284, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.00/1.39 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.39 ) ) ] )
% 1.00/1.39 , clause( 1285, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.00/1.39 'class_Int_Onumber__ring'( X ) ), ~( =( Y, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), =( Z,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.00/1.39 , clause( 1286, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.00/1.39 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.00/1.39 , clause( 1287, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.00/1.39 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1288, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y ) ] )
% 1.00/1.39 , clause( 1289, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 X ) ), Y ), Y ) ] )
% 1.00/1.39 , clause( 1290, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.00/1.39 'class_Int_Onumber__ring'( X ) ), =( Y, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1291, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 1.00/1.39 , clause( 1292, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.00/1.39 , Y ), Y ) ] )
% 1.00/1.39 , clause( 1293, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.39 ) ), Y ) ] )
% 1.00/1.39 , clause( 1294, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 1.00/1.39 , clause( 1295, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y ) ] )
% 1.00/1.39 , clause( 1296, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.00/1.39 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.00/1.39 X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.00/1.39 , clause( 1297, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), X, Y ), X ) ] )
% 1.00/1.39 , clause( 1298, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1299, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1300, [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.00/1.39 ), X ), Y ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1301, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , X ), Y ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1302, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1303, [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.00/1.39 , X, Y ), X ) ] )
% 1.00/1.39 , clause( 1304, [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), X, Y ), 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), Z, Y ) ) ] )
% 1.00/1.39 , clause( 1305, [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'(
% 1.00/1.39 T, U, Z ) ) ), =( Y, U ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1306, [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.00/1.39 , X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 1307, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ] )
% 1.00/1.39 , clause( 1308, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.00/1.39 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ] )
% 1.00/1.39 , clause( 1309, [ =( 'c_List_Otake'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.00/1.39 , 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.39 , clause( 1310, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ),
% 1.00/1.39 'c_List_Olist_ONil'( X ), X ), 'c_List_Olist_ONil'( X ) ) ] )
% 1.00/1.39 , clause( 1311, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Orev'(
% 1.00/1.39 'c_List_Olist_ONil'( X ), X ) ) ] )
% 1.00/1.39 , clause( 1312, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oremdups'(
% 1.00/1.39 'c_List_Olist_ONil'( X ), X ) ) ] )
% 1.00/1.39 , clause( 1313, [ ~( =( X, 'c_List_Oappend'( Y, X, Z ) ) ), =( Y,
% 1.00/1.39 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.39 , clause( 1314, [ ~( =( 'c_List_Oappend'( X, Y, Z ), Y ) ), =( X,
% 1.00/1.39 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.39 , clause( 1315, [ ~( =( X, 'c_List_Oappend'( X, Y, Z ) ) ), =( Y,
% 1.00/1.39 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.39 , clause( 1316, [ ~( =( 'c_List_Oappend'( X, Y, Z ), X ) ), =( Y,
% 1.00/1.39 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.39 , clause( 1317, [ ~( =( 'c_List_Oremdups'( X, Y ), 'c_List_Olist_ONil'( Y )
% 1.00/1.39 ) ), =( X, 'c_List_Olist_ONil'( Y ) ) ] )
% 1.00/1.39 , clause( 1318, [ ~( =( 'c_List_Orotate'( X, Y, Z ), 'c_List_Olist_ONil'( Z
% 1.00/1.39 ) ) ), =( Y, 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.39 , clause( 1319, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Orev'( Y, X ) ) )
% 1.00/1.39 , =( Y, 'c_List_Olist_ONil'( X ) ) ] )
% 1.00/1.39 , clause( 1320, [ 'c_List_Odistinct'( 'c_List_Olist_ONil'( X ), X ) ] )
% 1.00/1.39 , clause( 1321, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y,
% 1.00/1.39 Z, X ) ) ) ] )
% 1.00/1.39 , clause( 1322, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z
% 1.00/1.39 ) ) ), =( Y, 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.39 , clause( 1323, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z
% 1.00/1.39 ) ) ), =( X, 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.39 , clause( 1324, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X
% 1.00/1.39 ) ) ), =( Z, 'c_List_Olist_ONil'( X ) ) ] )
% 1.00/1.39 , clause( 1325, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X
% 1.00/1.39 ) ) ), =( Y, 'c_List_Olist_ONil'( X ) ) ] )
% 1.00/1.39 , clause( 1326, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z
% 1.00/1.39 ), Y ) ] )
% 1.00/1.39 , clause( 1327, [ =( 'c_List_Oremdups'( 'c_List_Olist_ONil'( X ), X ),
% 1.00/1.39 'c_List_Olist_ONil'( X ) ) ] )
% 1.00/1.39 , clause( 1328, [ =( 'c_List_Odrop'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.00/1.39 'c_List_Olist_ONil'( Y ) ) ] )
% 1.00/1.39 , clause( 1329, [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1330, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), Y, X ), Y
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1331, [ =( X, 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1332, [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1333, [ =( 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ), X
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1334, [ =( 'c_List_Otake'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.00/1.39 'c_List_Olist_ONil'( Y ) ) ] )
% 1.00/1.39 , clause( 1335, [ ~( hBOOL( hAPP( X, 'c_List_Olist_Olist__case'( Y, Z,
% 1.00/1.39 'c_List_Olist_ONil'( 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X, Y ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1336, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 1.00/1.39 , clause( 1337, [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_OCons'( Z,
% 1.00/1.39 'c_List_Olist_ONil'( Y ), Y ) ) ), =( X, 'c_List_Olist_OCons'( Z,
% 1.00/1.39 'c_List_Olist_ONil'( Y ), Y ) ) ] )
% 1.00/1.39 , clause( 1338, [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X,
% 1.00/1.39 'c_Lambda_OdB_OVar'( Y ), Z ) ) ] )
% 1.00/1.39 , clause( 1339, [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W ), hAPP( X,
% 1.00/1.39 hAPP( Y, W ) ) ) ] )
% 1.00/1.39 , clause( 1340, [ =( hAPP( X, hAPP( Y, Z ) ), hAPP( 'c_Fun_Ocomp'( X, Y, T
% 1.00/1.39 , U, W ), Z ) ) ] )
% 1.00/1.39 , clause( 1341, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 1.00/1.39 ) ) ] )
% 1.00/1.39 , clause( 1342, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.00/1.39 ), X ), Y ) ] )
% 1.00/1.39 , clause( 1343, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.00/1.39 X ), Y ) ] )
% 1.00/1.39 , clause( 1344, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 1.00/1.39 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1345, [ =( 'c_List_Ofilter'( X, 'c_List_Oreplicate'( Y, Z, T ), T
% 1.00/1.39 ), 'c_List_Oreplicate'( Y, Z, T ) ), ~( hBOOL( hAPP( X, Z ) ) ) ] )
% 1.00/1.39 , clause( 1346, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ] )
% 1.00/1.39 , clause( 1347, [ 'c_List_Olistrelp'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 1.00/1.39 'c_List_Olist_OCons'( U, W, T ), T ), ~( 'c_List_Olistrelp'( X, Z, W, T )
% 1.00/1.39 ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ) ] )
% 1.00/1.39 , clause( 1348, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.00/1.39 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 1.00/1.39 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 1.00/1.39 , clause( 1349, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.00/1.39 , clause( 1350, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 1.00/1.39 , clause( 1351, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 1.00/1.39 , clause( 1352, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.00/1.39 , clause( 1353, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.00/1.39 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.00/1.39 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.00/1.39 , clause( 1354, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.00/1.39 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.00/1.39 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.00/1.39 , clause( 1355, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 1.00/1.39 ) ), =( X, Y ) ] )
% 1.00/1.39 , clause( 1356, [ =( 'c_List_Oremove1'( X, 'c_List_Olist_OCons'( Y, Z, T )
% 1.00/1.39 , T ), 'c_List_Olist_OCons'( Y, 'c_List_Oremove1'( X, Z, T ), T ) ), =( X
% 1.00/1.39 , Y ) ] )
% 1.00/1.39 , clause( 1357, [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y )
% 1.00/1.39 ), 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( T ) ) ) ), =(
% 1.00/1.39 'c_Map_Omap__upds'( U, 'c_List_Oappend'( X, W, Y ), Z, Y, T ),
% 1.00/1.39 'c_Map_Omap__upds'( U, X, Z, Y, T ) ) ] )
% 1.00/1.39 , clause( 1358, [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y )
% 1.00/1.39 ), 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( T ) ) ) ), =(
% 1.00/1.39 'c_Map_Omap__upds'( U, X, 'c_List_Oappend'( Z, W, T ), Y, T ),
% 1.00/1.39 'c_Map_Omap__upds'( U, X, Z, Y, T ) ) ] )
% 1.00/1.39 , clause( 1359, [ ~( =( X, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( Y ) ), Z, Y ) ) ), =( 'c_List_Oappend'( X,
% 1.00/1.39 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ), Z
% 1.00/1.39 , Y ), Y ), Z ) ] )
% 1.00/1.39 , clause( 1360, [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP(
% 1.00/1.39 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 1.00/1.39 , clause( 1361, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 1.00/1.39 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.39 , clause( 1362, [ 'c_List_Odistinct'( 'c_List_Oremove1'( X, Y, Z ), Z ),
% 1.00/1.39 ~( 'c_List_Odistinct'( Y, Z ) ) ] )
% 1.00/1.39 , clause( 1363, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 1.00/1.39 'c_Lambda_OdB_OVar'( X ), Y ) ] )
% 1.00/1.39 , clause( 1364, [ 'c_Lambda_Obeta'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X
% 1.00/1.39 , Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~(
% 1.00/1.39 'c_Lambda_Obeta'( X, Z ) ) ] )
% 1.00/1.39 , clause( 1365, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Orotate'( X, Y, Z
% 1.00/1.39 ), 'tc_List_Olist'( Z ) ), 'c_Nat_Osize__class_Osize'( Y,
% 1.00/1.39 'tc_List_Olist'( Z ) ) ) ] )
% 1.00/1.39 , clause( 1366, [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 1.00/1.39 'c_Lambda_OdB_OAbs'( X ) ), Y ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X )
% 1.00/1.39 , Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 1367, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Oappend'( X, Y, Z
% 1.00/1.39 ), 'tc_List_Olist'( Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.39 'tc_nat' ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) ) ),
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ) ) ) ] )
% 1.00/1.39 , clause( 1368, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.00/1.39 'c_List_Olistsum'( 'c_List_Olist_OCons'( Y, Z, X ), X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Olistsum'( Z, X ) ) ) ] )
% 1.00/1.39 , clause( 1369, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ),
% 1.00/1.39 'c_Lambda_OdB_OAbs'( 'c_Lambda_Oliftn'( X, Y, hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.00/1.39 'tc_nat' ) ) ) ) ) ] )
% 1.00/1.39 , clause( 1370, [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 1.00/1.39 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 1.00/1.39 'tc_Lambda_OdB' ), X ) ) ] )
% 1.00/1.39 , clause( 1371, [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 1.00/1.39 'c_List_Oreplicate'( T, Y, Z ), Z ), 'c_List_Oappend'(
% 1.00/1.39 'c_List_Oreplicate'( T, Y, Z ), 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1372, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 1.00/1.39 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ] )
% 1.00/1.39 , clause( 1373, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 1.00/1.39 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ] )
% 1.00/1.39 , clause( 1374, [ =( X, 'c_List_Olist_OCons'(
% 1.00/1.39 'v_sko__List__Xlistsp__Xcases__1'( Y, X ),
% 1.00/1.39 'v_sko__List__Xlistsp__Xcases__2'( Y, X ), 't_a' ) ), =( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ), ~( 'c_List_Olistsp'( Y, X, 't_a' ) ) ] )
% 1.00/1.39 , clause( 1375, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.00/1.39 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 1.00/1.39 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 1.00/1.39 , clause( 1376, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.00/1.39 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 1.00/1.39 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 1.00/1.39 , clause( 1377, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 1.00/1.39 'c_Lambda_OdB_OAbs'( Z ) ) ] )
% 1.00/1.39 , clause( 1378, [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ] )
% 1.00/1.39 , clause( 1379, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 1.00/1.39 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'(
% 1.00/1.39 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 1.00/1.39 'c_Lambda_OdB_OApp', X ), Y ), Z ) ] )
% 1.00/1.39 , clause( 1380, [ =( 'c_List_Oremove1'( X, 'c_List_Ofilter'( Y, Z, T ), T )
% 1.00/1.39 , 'c_List_Ofilter'( Y, Z, T ) ), hBOOL( hAPP( Y, X ) ) ] )
% 1.00/1.39 , clause( 1381, [ =( 'c_List_Ofilter'( X, 'c_List_Oreplicate'( Y, Z, T ), T
% 1.00/1.39 ), 'c_List_Olist_ONil'( T ) ), hBOOL( hAPP( X, Z ) ) ] )
% 1.00/1.39 , clause( 1382, [ =( 'c_List_Odrop'( X, 'c_List_Odrop'( Y, Z, T ), T ),
% 1.00/1.39 'c_List_Odrop'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.00/1.39 Y ), Z, T ) ) ] )
% 1.00/1.39 , clause( 1383, [ =( 'c_List_Oreplicate'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, T ),
% 1.00/1.39 'c_List_Oappend'( 'c_List_Oreplicate'( X, Z, T ), 'c_List_Oreplicate'( Y
% 1.00/1.39 , Z, T ), T ) ) ] )
% 1.00/1.39 , clause( 1384, [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Orev'( Z, Y ) ) ),
% 1.00/1.39 =( X, Z ) ] )
% 1.00/1.39 , clause( 1385, [ ~( 'class_Power_Opower'( X ) ), =(
% 1.00/1.39 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.00/1.39 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.00/1.39 , clause( 1386, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.00/1.39 =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.00/1.39 , clause( 1387, [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'(
% 1.00/1.39 'c_List_Orotate'( Z, X, Y ), Y ) ) ] )
% 1.00/1.39 , clause( 1388, [ 'c_List_Odistinct'( 'c_List_Orotate'( X, Y, Z ), Z ), ~(
% 1.00/1.39 'c_List_Odistinct'( Y, Z ) ) ] )
% 1.00/1.39 , clause( 1389, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.39 'c_List_Olistsum'( 'c_List_Orev'( Y, X ), X ), 'c_List_Olistsum'( Y, X )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1390, [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Ocomp'( Y, Z, T, U, W ), U,
% 1.00/1.39 V0, W ), 'c_Fun_Ocomp'( 'c_Fun_Ocomp'( X, Y, U, V0, T ), Z, T, V0, W ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1391, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Oreplicate'( X, Y
% 1.00/1.39 , Z ), 'tc_List_Olist'( Z ) ), X ) ] )
% 1.00/1.39 , clause( 1392, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 1393, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ] )
% 1.00/1.39 , clause( 1394, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.00/1.39 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.00/1.39 'tc_bool' ) ) ) ] )
% 1.00/1.39 , clause( 1395, [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X,
% 1.00/1.39 'c_List_Olist_OCons'( Y, Z, T ), T ), 'c_Nat_Osize__class_Osize'( X,
% 1.00/1.39 'tc_List_Olist'( T ) ), U, T ), 'c_List_Oappend'( X, 'c_List_Olist_OCons'(
% 1.00/1.39 U, Z, T ), T ) ) ] )
% 1.00/1.39 , clause( 1396, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ),
% 1.00/1.39 'c_List_Olist_OCons'( Y, Z, X ), X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1397, [ 'c_List_Odistinct'( 'c_List_Oremdups'( X, Y ), Y ) ] )
% 1.00/1.39 , clause( 1398, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ] )
% 1.00/1.39 , clause( 1399, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X,
% 1.00/1.39 'tc_fun'( Y, 'tc_bool' ) ), X ) ] )
% 1.00/1.39 , clause( 1400, [ ~( =( 'c_List_Oappend'( 'c_List_Odrop'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ), Z, Y ),
% 1.00/1.39 'c_List_Oappend'( 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( Z,
% 1.00/1.39 'tc_List_Olist'( Y ) ), X, Y ), T, Y ), Y ), T ) ), ~( =( 'c_List_Otake'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ), Z, Y ), X ) ), ~(
% 1.00/1.39 =( Z, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( Y )
% 1.00/1.39 ), X, Y ) ) ), =( 'c_List_Oappend'( Z, 'c_List_Oappend'( 'c_List_Odrop'(
% 1.00/1.39 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( Y ) ), X, Y ), T, Y ), Y
% 1.00/1.39 ), 'c_List_Oappend'( X, T, Y ) ) ] )
% 1.00/1.39 , clause( 1401, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 1.00/1.39 'c_List_Olist_OCons'( T, U, Z ) ) ), =( X, T ) ] )
% 1.00/1.39 , clause( 1402, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 1.00/1.39 'c_List_Olist_OCons'( T, U, Z ) ) ), =( Y, U ) ] )
% 1.00/1.39 , clause( 1403, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.00/1.39 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 1.00/1.39 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 1.00/1.39 , clause( 1404, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.00/1.39 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 1.00/1.39 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 1.00/1.39 , clause( 1405, [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Lambda_Obeta'( T, Y )
% 1.00/1.39 ), ~( 'c_Type_Otyping'( X, T, Z ) ) ] )
% 1.00/1.39 , clause( 1406, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( Y, X ), ~(
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( 'c_List_Oappend'( Y, Z, X ), X ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1407, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( Y, X ), ~(
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( 'c_List_Oappend'( Z, Y, X ), X ) ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1408, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP(
% 1.00/1.39 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 1.00/1.39 , clause( 1409, [ =( 'c_List_Olist__update'( 'c_List_Olist__update'( X, Y,
% 1.00/1.39 Z, T ), U, W, T ), 'c_List_Olist__update'( 'c_List_Olist__update'( X, U,
% 1.00/1.39 W, T ), Y, Z, T ) ), =( Y, U ) ] )
% 1.00/1.39 , clause( 1410, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( 'c_List_Oremdups'( Y, X ), X ), ~(
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( Y, X ) ) ] )
% 1.00/1.39 , clause( 1411, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y )
% 1.00/1.39 ) ), =( X, Y ) ] )
% 1.00/1.39 , clause( 1412, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 1.00/1.39 'c_Lambda_OdB_OAbs'( Z ) ) ) ] )
% 1.00/1.39 , clause( 1413, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y )
% 1.00/1.39 ) ) ] )
% 1.00/1.39 , clause( 1414, [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 1.00/1.39 'c_List_Olist_OCons'( Y, T, Z ), Z ), 'c_List_Olist_OCons'( Y,
% 1.00/1.39 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ), T, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1415, [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( W,
% 1.00/1.39 V0, V1, T, U ) ) ), =( hAPP( X, hAPP( Y, V2 ) ), hAPP( W, hAPP( V0, V2 )
% 1.00/1.39 ) ) ] )
% 1.00/1.39 , clause( 1416, [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( U, W ) ) )
% 1.00/1.39 ), =( hAPP( 'c_Fun_Ocomp'( X, Y, V0, V1, V2 ), Z ), hAPP( 'c_Fun_Ocomp'(
% 1.00/1.39 T, U, V3, V1, V4 ), W ) ) ] )
% 1.00/1.39 , clause( 1417, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Orev'( X, Y ),
% 1.00/1.39 'tc_List_Olist'( Y ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y
% 1.00/1.39 ) ) ) ] )
% 1.00/1.39 , clause( 1418, [ =( 'c_List_Ofilter'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 1.00/1.39 T ), 'c_List_Ofilter'( X, Z, T ) ), hBOOL( hAPP( X, Y ) ) ] )
% 1.00/1.39 , clause( 1419, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.00/1.39 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ] )
% 1.00/1.39 , clause( 1420, [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.39 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~(
% 1.00/1.39 hBOOL( hAPP( X, T ) ) ) ] )
% 1.00/1.39 , clause( 1421, [ =( 'c_List_Orev'( 'c_List_Ofilter'( X, Y, Z ), Z ),
% 1.00/1.39 'c_List_Ofilter'( X, 'c_List_Orev'( Y, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1422, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.00/1.39 'c_List_Olistsum'( 'c_List_Oappend'( Y, Z, X ), X ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_List_Olistsum'( Y, X ) ),
% 1.00/1.39 'c_List_Olistsum'( Z, X ) ) ) ] )
% 1.00/1.39 , clause( 1423, [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 1.00/1.39 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 1.00/1.39 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( X, T
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1424, [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 1.00/1.39 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 1.00/1.39 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( Y, U
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1425, [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 1.00/1.39 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 1.00/1.39 ), Y ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 1.00/1.39 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.39 , clause( 1426, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OAbs'( X )
% 1.00/1.39 ), Y ), 'c_Lambda_OdB_OAbs'( hAPP( hAPP( 'c_Lambda_Olift', X ), hAPP(
% 1.00/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.00/1.39 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ) ) ] )
% 1.00/1.39 , clause( 1427, [ ~( hBOOL( hAPP( X, 'c_List_Olist_Olist__case'( Y, Z,
% 1.00/1.39 'c_List_Olist_OCons'( T, U, 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X
% 1.00/1.39 , hAPP( hAPP( Z, T ), U ) ) ) ] )
% 1.00/1.39 , clause( 1428, [ ~( hBOOL( hAPP( X, 'c_List_Olist_Olist__case'( Y, Z,
% 1.00/1.39 'c_List_Olist_OCons'( T, U, 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X
% 1.00/1.39 , hAPP( hAPP( Z, T ), U ) ) ) ] )
% 1.00/1.39 , clause( 1429, [ =( 'c_List_Olist__update'( 'c_List_Olist__update'( X, Y,
% 1.00/1.39 Z, T ), Y, U, T ), 'c_List_Olist__update'( X, Y, U, T ) ) ] )
% 1.00/1.39 , clause( 1430, [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z )
% 1.00/1.39 , 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1431, [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T )
% 1.00/1.39 , 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ] )
% 1.00/1.39 , clause( 1432, [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z )
% 1.00/1.39 , 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1433, [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T )
% 1.00/1.39 , 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ] )
% 1.00/1.39 , clause( 1434, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( 'c_List_Oremove1'( Y, Z, X ), X ), ~(
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( Z, X ) ) ] )
% 1.00/1.39 , clause( 1435, [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z,
% 1.00/1.39 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_Olift', T ), Y ), U ), ~(
% 1.00/1.39 'c_Type_Otyping'( X, T, U ) ) ] )
% 1.00/1.39 , clause( 1436, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.00/1.39 'v_sko__List__Xtake__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 1.00/1.39 , clause( 1437, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.00/1.39 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_ONil'( X ), X ) ] )
% 1.00/1.39 , clause( 1438, [ =( 'c_List_Ofiltermap'( X, 'c_List_Olist_ONil'( Y ), Y, Z
% 1.00/1.39 ), 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.39 , clause( 1439, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oremdups'( Y, X )
% 1.00/1.39 ) ), =( Y, 'c_List_Olist_ONil'( X ) ) ] )
% 1.00/1.39 , clause( 1440, [ =( 'c_List_Ofilter'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.00/1.39 'c_List_Olist_ONil'( Y ) ) ] )
% 1.00/1.39 , clause( 1441, [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z
% 1.00/1.39 , X ), 'c_List_Olist_ONil'( X ) ) ] )
% 1.00/1.39 , clause( 1442, [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z
% 1.00/1.39 , X ), 'c_List_Olist_ONil'( X ) ) ] )
% 1.00/1.39 , clause( 1443, [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z
% 1.00/1.39 , X ), 'c_List_Olist_ONil'( X ) ) ] )
% 1.00/1.39 , clause( 1444, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.00/1.39 'v_sko__List__Xconcat__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 1.00/1.39 , clause( 1445, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 1.00/1.39 'c_List_Olist_ONil'( Z ) ) ) ] )
% 1.00/1.39 , clause( 1446, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 1.00/1.39 'c_List_Olist_ONil'( Z ) ) ) ] )
% 1.00/1.39 , clause( 1447, [ =( 'c_List_Oremove1'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.00/1.39 'c_List_Olist_ONil'( Y ) ) ] )
% 1.00/1.39 , clause( 1448, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.00/1.39 'v_sko__List__Xdistinct__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 1.00/1.39 , clause( 1449, [ =( 'c_Map_Omap__upds'( X, Y, 'c_List_Olist_ONil'( Z ), T
% 1.00/1.39 , Z ), X ) ] )
% 1.00/1.39 , clause( 1450, [ =( 'c_Map_Omap__upds'( X, 'c_List_Olist_ONil'( Y ), Z, Y
% 1.00/1.39 , T ), X ) ] )
% 1.00/1.39 , clause( 1451, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.00/1.39 'v_sko__List__Xremove1__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 1.00/1.39 , clause( 1452, [ =( 'c_List_Olist_Olist__case'( X, Y, 'c_List_Olist_ONil'(
% 1.00/1.39 Z ), T, Z ), X ) ] )
% 1.00/1.39 , clause( 1453, [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_ONil'( Y ) ) )
% 1.00/1.39 , =( X, 'c_List_Olist_ONil'( Y ) ) ] )
% 1.00/1.39 , clause( 1454, [ =( 'c_List_Orotate'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.00/1.39 'c_List_Olist_ONil'( Y ) ) ] )
% 1.00/1.39 , clause( 1455, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.00/1.39 'v_sko__List__Xlist__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 1.00/1.39 , clause( 1456, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'(
% 1.00/1.39 'c_List_Olist_ONil'( X ), 'c_List_Olist_ONil'( X ), X ) ) ] )
% 1.00/1.39 , clause( 1457, [ 'c_List_Olistrelp'( X, 'c_List_Olist_ONil'( Y ),
% 1.00/1.39 'c_List_Olist_ONil'( Y ), Y ) ] )
% 1.00/1.39 , clause( 1458, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.00/1.39 'v_sko__List__Xmap__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 1.00/1.39 , clause( 1459, [ =( 'c_List_Orev'( 'c_List_Olist_ONil'( X ), X ),
% 1.00/1.39 'c_List_Olist_ONil'( X ) ) ] )
% 1.00/1.39 , clause( 1460, [ ~( =( 'c_List_Olist__update'( X, Y, Z, T ),
% 1.00/1.39 'c_List_Olist_ONil'( T ) ) ), =( X, 'c_List_Olist_ONil'( T ) ) ] )
% 1.00/1.39 , clause( 1461, [ =( 'c_Lambda_Osubstn'( X, Y, Z ), hAPP( hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Osubst', X ), 'c_Lambda_Oliftn'( Z, Y,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), Z ) ) ] )
% 1.00/1.39 , clause( 1462, [ =( 'c_List_Odrop'( X, 'c_List_Omap'( Y, Z, T, U ), U ),
% 1.00/1.39 'c_List_Omap'( Y, 'c_List_Odrop'( X, Z, T ), T, U ) ) ] )
% 1.00/1.39 , clause( 1463, [ ~( =( hAPP( X, 'c_List_Osko__List__Xmap__idI__1__1'( X, Y
% 1.00/1.39 , Z ) ), 'c_List_Osko__List__Xmap__idI__1__1'( X, Y, Z ) ) ), =(
% 1.00/1.39 'c_List_Omap'( X, Y, Z, Z ), Y ) ] )
% 1.00/1.39 , clause( 1464, [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'(
% 1.00/1.39 'c_List_Omap'( Z, X, Y, T ), T ) ) ] )
% 1.00/1.39 , clause( 1465, [ =( 'c_List_Omap'( X, 'c_List_Oappend'( Y, Z, T ), T, U )
% 1.00/1.39 , 'c_List_Oappend'( 'c_List_Omap'( X, Y, T, U ), 'c_List_Omap'( X, Z, T,
% 1.00/1.39 U ), U ) ) ] )
% 1.00/1.39 , clause( 1466, [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Omap'( X, U, Z
% 1.00/1.39 , T ) ) ), =( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ),
% 1.00/1.39 'c_Nat_Osize__class_Osize'( U, 'tc_List_Olist'( Z ) ) ) ] )
% 1.00/1.39 , clause( 1467, [ =( 'c_List_Omap'( X, 'c_List_Oreplicate'( Y, Z, T ), T, U
% 1.00/1.39 ), 'c_List_Oreplicate'( Y, hAPP( X, Z ), U ) ) ] )
% 1.00/1.39 , clause( 1468, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Omap'( X, Y, Z, T
% 1.00/1.39 ), 'tc_List_Olist'( T ) ), 'c_Nat_Osize__class_Osize'( Y,
% 1.00/1.39 'tc_List_Olist'( Z ) ) ) ] )
% 1.00/1.39 , clause( 1469, [ =( 'c_List_Orotate'( X, 'c_List_Omap'( Y, Z, T, U ), U )
% 1.00/1.39 , 'c_List_Omap'( Y, 'c_List_Orotate'( X, Z, T ), T, U ) ) ] )
% 1.00/1.39 , clause( 1470, [ =( 'c_List_Orev'( 'c_List_Omap'( X, Y, Z, T ), T ),
% 1.00/1.39 'c_List_Omap'( X, 'c_List_Orev'( Y, Z ), Z, T ) ) ] )
% 1.00/1.39 , clause( 1471, [ ~( =( hAPP( X, 'c_List_Osko__List__Xmap__ext__1__1'( X, Y
% 1.00/1.39 , Z, T, U ) ), hAPP( Y, 'c_List_Osko__List__Xmap__ext__1__1'( X, Y, Z, T
% 1.00/1.39 , U ) ) ) ), =( 'c_List_Omap'( X, Z, T, U ), 'c_List_Omap'( Y, Z, T, U )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1472, [ =( 'c_List_Otake'( X, 'c_List_Omap'( Y, Z, T, U ), U ),
% 1.00/1.39 'c_List_Omap'( Y, 'c_List_Otake'( X, Z, T ), T, U ) ) ] )
% 1.00/1.39 , clause( 1473, [ =( 'c_List_Omap'( X, 'c_List_Omap'( Y, Z, T, U ), U, W )
% 1.00/1.39 , 'c_List_Omap'( 'c_Fun_Ocomp'( X, Y, U, W, T ), Z, T, W ) ) ] )
% 1.00/1.39 , clause( 1474, [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T,
% 1.00/1.39 U ), 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1475, [ =( 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X,
% 1.00/1.39 Z, T, U ), U ), 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1476, [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T,
% 1.00/1.39 U ), 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1477, [ ~( =( hAPP( X, 'c_List_Osko__List__Xmap__cong__1__1'( X,
% 1.00/1.39 Y, Z, T, U ) ), hAPP( Y, 'c_List_Osko__List__Xmap__cong__1__1'( X, Y, Z,
% 1.00/1.39 T, U ) ) ) ), =( 'c_List_Omap'( X, Z, T, U ), 'c_List_Omap'( Y, Z, T, U )
% 1.00/1.39 ) ] )
% 1.00/1.39 , clause( 1478, [ ~( =( hAPP( X, 'c_List_Osko__List__Xmap__eq__conv__1__1'(
% 1.00/1.39 X, Y, Z, T, U ) ), hAPP( Y, 'c_List_Osko__List__Xmap__eq__conv__1__1'( X
% 1.00/1.39 , Y, Z, T, U ) ) ) ), =( 'c_List_Omap'( X, Z, T, U ), 'c_List_Omap'( Y, Z
% 1.00/1.39 , T, U ) ) ] )
% 1.00/1.39 , clause( 1479, [ =( 'c_List_Omap'( X, 'c_List_Olist__update'( Y, Z, T, U )
% 1.00/1.39 , U, W ), 'c_List_Olist__update'( 'c_List_Omap'( X, Y, U, W ), Z, hAPP( X
% 1.00/1.39 , T ), W ) ) ] )
% 1.00/1.39 , clause( 1480, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 1.00/1.39 X ) ), Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 1.00/1.39 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 1.00/1.39 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 1.00/1.39 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB'
% 1.00/1.39 , 'tc_Lambda_OdB' ) ) ) ) ] )
% 1.00/1.39 , clause( 1481, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 1.00/1.39 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), T ), hAPP( hAPP(
% 1.00/1.39 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Z ), T ) )
% 1.00/1.39 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', Y ), Z ), T ) ) ) ] )
% 1.00/1.39 , clause( 1482, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 1.00/1.39 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y ) ] )
% 1.00/1.39 , clause( 1483, [ 'c_Lambda_Obeta'( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X
% 1.00/1.39 ), Y ), Z ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', T ), Y ), Z ) ), ~(
% 1.00/1.39 'c_Lambda_Obeta'( X, T ) ) ] )
% 1.00/1.39 , clause( 1484, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 1.00/1.39 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z ), 'c_Lambda_OdB_OAbs'( hAPP( hAPP(
% 1.00/1.39 hAPP( 'c_Lambda_Osubst', X ), hAPP( hAPP( 'c_Lambda_Olift', Y ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( hAPP(
% 1.00/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.00/1.39 'tc_nat' ) ) ) ) ) ] )
% 1.00/1.39 , clause( 1485, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X
% 1.00/1.39 ) ) ) ] )
% 1.00/1.39 , clause( 1486, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_ua______' ) ) ] )
% 1.00/1.39 , clause( 1487, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X
% 1.00/1.39 ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 1.00/1.39 , clause( 1488, [ 'c_List_Olistsp'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 1.00/1.39 ~( 'c_List_Olistsp'( X, Z, T ) ), ~( 'c_List_Olistsp'( X, Y, T ) ) ] )
% 1.00/1.39 , clause( 1489, [ 'c_List_Olistsp'( X, Y, Z ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Osko__List__Xin__listsp__conv__set__1__1'( X, Y, Z ) ) ) ) ] )
% 1.00/1.39 , clause( 1490, [ 'c_List_Olistsp'(
% 1.00/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.00/1.39 'tc_bool' ) ), T, Z ), ~( 'c_List_Olistsp'( Y, T, Z ) ), ~(
% 1.00/1.39 'c_List_Olistsp'( X, T, Z ) ) ] )
% 1.00/1.39 , clause( 1491, [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X,
% 1.00/1.39 'c_List_Oappend'( T, Y, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1492, [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X,
% 1.00/1.39 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 1.00/1.39 , clause( 1493, [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP(
% 1.00/1.39 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 1.00/1.39 hAPP( hAPP( 'c_Lambda_Olift', X ), Z ) ), hAPP( hAPP( 'c_Lambda_Olift', Y
% 1.00/1.39 ), Z ) ) ) ] )
% 1.00/1.39 , clause( 1494, [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_Olift', X ), Y )
% 1.00/1.39 , hAPP( hAPP( 'c_Lambda_Olift', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1495, [ =( 'v_n____', 'v_i____' ) ] )
% 1.00/1.39 , clause( 1496, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.00/1.39 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.00/1.39 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.00/1.39 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.00/1.39 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1497, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.00/1.39 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.39 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1498, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.00/1.39 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.00/1.39 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.00/1.39 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 1.00/1.39 , clause( 1499, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.00/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.00/1.39 , clause( 1500, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.00/1.39 'c_List_Olistsum'( 'c_List_Olist_ONil'( X ), X ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.00/1.39 , clause( 1501, [ =( 'c_List_Olist_Olist__size'( X, 'c_List_Olist_ONil'( Y
% 1.00/1.39 ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1502, [ =( 'c_List_Olist_Olist__size'( X, 'c_List_Olist_ONil'( Y
% 1.00/1.39 ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1503, [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y )
% 1.00/1.39 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_List_Olist_ONil'(
% 1.00/1.39 Y ) ) ] )
% 1.00/1.39 , clause( 1504, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'( Y, Z
% 1.00/1.39 , X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1505, [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Olist_ONil'(
% 1.00/1.39 Z ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1506, [ =( 'c_List_Otake'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.00/1.39 , X, Y ), 'c_List_Olist_ONil'( Y ) ) ] )
% 1.00/1.39 , clause( 1507, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'(
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, X ) ) ] )
% 1.00/1.39 , clause( 1508, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ),
% 1.00/1.39 'tc_List_Olist'( X ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1509, [ ~( =( 'c_List_Otake'( X, Y, Z ), 'c_List_Olist_ONil'( Z )
% 1.00/1.39 ) ), =( Y, 'c_List_Olist_ONil'( Z ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1510, [ =( 'c_List_Olength__unique'( 'c_List_Olist_ONil'( X ), X
% 1.00/1.39 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.00/1.39 , clause( 1511, [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ), X, Y ), 'c_List_Olist_ONil'( Y ) ) ] )
% 1.00/1.39 , clause( 1512, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.39 'tc_nat' ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 1.00/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 1.00/1.39 , clause( 1513, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z,
% 1.00/1.39 'v_sko__List__Xlistsp__Xinducts__1'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1514, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.00/1.39 'v_sko__List__Xlistsp__Xinducts__2'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1515, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z,
% 1.00/1.39 'v_sko__List__Xlistsp__Xinduct__1'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1516, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.00/1.39 'v_sko__List__Xlistsp__Xinduct__2'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1517, [ 'c_List_Olistsp'( X, 'v_sko__List__Xlistsp__Xcases__2'( X
% 1.00/1.39 , Y ), 't_a' ), =( Y, 'c_List_Olist_ONil'( 't_a' ) ), ~( 'c_List_Olistsp'(
% 1.00/1.39 X, Y, 't_a' ) ) ] )
% 1.00/1.39 , clause( 1518, [ hBOOL( hAPP( X, 'v_sko__List__Xlistsp__Xcases__1'( X, Y )
% 1.00/1.39 ) ), =( Y, 'c_List_Olist_ONil'( 't_a' ) ), ~( 'c_List_Olistsp'( X, Y,
% 1.00/1.39 't_a' ) ) ] )
% 1.00/1.39 , clause( 1519, [ hBOOL( hAPP( X, Y ) ), 'c_List_Olistsp'( Z,
% 1.00/1.39 'v_sko__List__Xlistsp__Xinducts__2'( Z, X ), 't_a' ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1520, [ hBOOL( hAPP( X, Y ) ), 'c_List_Olistsp'( Z,
% 1.00/1.39 'v_sko__List__Xlistsp__Xinduct__2'( Z, X ), 't_a' ), ~( hBOOL( hAPP( X,
% 1.00/1.39 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( 'c_List_Olistsp'( Z, Y, 't_a' ) )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1521, [ 'c_Type_Otypings'( X, 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 1.00/1.39 'c_Lambda_Osubst', Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 1.00/1.39 'tc_nat', 'tc_Lambda_OdB' ) ), Z, 'tc_Lambda_OdB', 'tc_nat',
% 1.00/1.39 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 1.00/1.39 'c_Type_Otypings'( 'c_Type_Oshift'( X, Z, W, 'tc_Type_Otype' ), T, U ) )
% 1.00/1.39 , ~( 'c_Type_Otyping'( X, Y, W ) ) ] )
% 1.00/1.39 , clause( 1522, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Osubst', X ), 'c_Lambda_OdB_OVar'( Y ) ), Z ) ) ), ~( hBOOL(
% 1.00/1.39 hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 1.00/1.39 , clause( 1523, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ),
% 1.00/1.39 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_Olift', X ),
% 1.00/1.39 Z ), 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Z, 'tc_Lambda_OdB',
% 1.00/1.39 'tc_nat', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.39 , clause( 1524, [ 'c_Type_Otypings'( 'c_Type_Oshift'( X, Y, Z,
% 1.00/1.39 'tc_Type_Otype' ), 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Y,
% 1.00/1.39 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB',
% 1.00/1.39 'tc_Lambda_OdB' ), U ), ~( 'c_Type_Otypings'( X, T, U ) ) ] )
% 1.00/1.39 , clause( 1525, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_List_Ofoldl'(
% 1.00/1.39 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), T )
% 1.00/1.39 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Osubst', X ), Z ), T ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 1.00/1.39 'c_Lambda_Osubst', Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 1.00/1.39 'tc_nat', 'tc_Lambda_OdB' ) ), T, 'tc_Lambda_OdB', 'tc_nat',
% 1.00/1.39 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB'
% 1.00/1.39 , 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.39 , clause( 1526, [ 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'(
% 1.00/1.39 'c_COMBC'( 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.00/1.39 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB',
% 1.00/1.39 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), ~( 'c_List_Olistsp'(
% 1.00/1.39 'c_InductTermi_OIT', X, 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.39 , clause( 1527, [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T
% 1.00/1.39 ) ) ), =( Y, 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.39 , clause( 1528, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Olift', X ), Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X )
% 1.00/1.39 ) ) ] )
% 1.00/1.39 , clause( 1529, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X
% 1.00/1.39 ) ) ), =( Z, 'c_List_Olist_ONil'( T ) ) ] )
% 1.00/1.39 , clause( 1530, [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ] )
% 1.00/1.39 , clause( 1531, [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X,
% 1.00/1.39 W ), Y ) ) ] )
% 1.00/1.39 , clause( 1532, [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 1.00/1.39 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.39 , clause( 1533, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ] )
% 1.00/1.39 , clause( 1534, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 1.00/1.39 'c_Lambda_Olift', X ), Y ) ), Z ), Y ), X ) ] )
% 1.00/1.39 , clause( 1535, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y,
% 1.00/1.39 'c_List_Olist_ONil'( Z ), Z, X ) ) ] )
% 1.00/1.39 , clause( 1536, [ ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'(
% 1.00/1.39 'c_COMBC'( 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.00/1.39 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), 'c_List_Omap'( 'c_COMBC'(
% 1.00/1.39 'c_COMBC'( 'c_Lambda_Osubst', 'v_u____', 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 1.00/1.39 , 'tc_fun'( 'tc_nat', 'tc_Lambda_OdB' ) ), 'v_i____', 'tc_Lambda_OdB',
% 1.00/1.39 'tc_nat', 'tc_Lambda_OdB' ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 1.00/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 1.00/1.39 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.39 , clause( 1537, [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) )
% 1.00/1.39 , ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 1.00/1.39 , clause( 1538, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.00/1.39 'class_Orderings_Opreorder'( Y ) ) ] )
% 1.00/1.39 , clause( 1539, [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.00/1.39 'class_Lattices_Olattice'( Y ) ) ] )
% 1.00/1.39 , clause( 1540, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.00/1.39 'class_Orderings_Oorder'( Y ) ) ] )
% 1.00/1.39 , clause( 1541, [
% 1.00/1.39 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1542, [
% 1.00/1.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1543, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 1.00/1.39 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1544, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 1.00/1.39 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1545, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.00/1.39 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1546, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1547, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 1.00/1.39 ] )
% 1.00/1.39 , clause( 1548, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1549, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ]
% 1.00/1.39 )
% 1.00/1.39 , clause( 1550, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1551, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1552, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1553, [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1554, [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1555, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1556, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1557, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1558, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1559, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1560, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1561, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1562, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1563, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1564, [ 'class_Lattices_Olattice'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1565, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1566, [ 'class_Power_Opower'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1567, [ 'class_Int_Onumber'( 'tc_nat' ) ] )
% 1.00/1.39 , clause( 1568, [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ] )
% 1.00/1.42 , clause( 1569, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 1.00/1.42 , clause( 1570, [ 'class_Lattices_Olattice'( 'tc_bool' ) ] )
% 1.00/1.42 , clause( 1571, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 1.00/1.42 , clause( 1572, [
% 1.00/1.42 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_Int_Oint'
% 1.00/1.42 ) ] )
% 1.00/1.42 , clause( 1573, [
% 1.00/1.42 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.00/1.42 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1574, [ 'class_OrderedGroup_Olordered__ab__group__add__meet'(
% 1.00/1.42 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1575, [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.00/1.42 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1576, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 1.00/1.42 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1577, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 1.00/1.42 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1578, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.00/1.42 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1579, [ 'class_OrderedGroup_Opordered__ab__group__add'(
% 1.00/1.42 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1580, [ 'class_OrderedGroup_Olordered__ab__group__add'(
% 1.00/1.42 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1581, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 1.00/1.42 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1582, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 1.00/1.42 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1583, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint'
% 1.00/1.42 ) ] )
% 1.00/1.42 , clause( 1584, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 1.00/1.42 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1585, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' )
% 1.00/1.42 ] )
% 1.00/1.42 , clause( 1586, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' )
% 1.00/1.42 ] )
% 1.00/1.42 , clause( 1587, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' )
% 1.00/1.42 ] )
% 1.00/1.42 , clause( 1588, [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' )
% 1.00/1.42 ] )
% 1.00/1.42 , clause( 1589, [ 'class_OrderedGroup_Osemigroup__add'( 'tc_Int_Oint' ) ]
% 1.00/1.42 )
% 1.00/1.42 , clause( 1590, [ 'class_Lattices_Olower__semilattice'( 'tc_Int_Oint' ) ]
% 1.00/1.42 )
% 1.00/1.42 , clause( 1591, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ]
% 1.00/1.42 )
% 1.00/1.42 , clause( 1592, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ]
% 1.00/1.42 )
% 1.00/1.42 , clause( 1593, [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ]
% 1.00/1.42 )
% 1.00/1.42 , clause( 1594, [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ]
% 1.00/1.42 )
% 1.00/1.42 , clause( 1595, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1596, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1597, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1598, [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1599, [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1600, [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1601, [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1602, [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1603, [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1604, [ 'class_Lattices_Olattice'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1605, [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1606, [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1607, [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1608, [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1609, [ 'class_Power_Opower'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1610, [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ] )
% 1.00/1.42 , clause( 1611, [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X,
% 1.00/1.42 W ), Y ) ) ] )
% 1.00/1.42 , clause( 1612, [ =( 'c_COMBB'( X, Y, Z, T, U, W ), hAPP( X, hAPP( Y, Z ) )
% 1.00/1.42 ) ] )
% 1.00/1.42 , clause( 1613, [ 'c_fequal'( X, X, Y ) ] )
% 1.00/1.42 , clause( 1614, [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ] )
% 1.00/1.42 ] ).
% 1.00/1.42
% 1.00/1.42
% 1.00/1.42
% 1.00/1.42 subsumption(
% 1.00/1.42 clause( 689, [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ] )
% 1.00/1.42 , clause( 1530, [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ] )
% 1.00/1.42 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.00/1.42 )] ) ).
% 1.00/1.42
% 1.00/1.42
% 1.00/1.42 subsumption(
% 1.00/1.42 clause( 691, [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 1.00/1.42 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.42 , clause( 1532, [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 1.00/1.42 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.42 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.00/1.42 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.00/1.42
% 1.00/1.42
% 1.00/1.42 paramod(
% 1.00/1.42 clause( 5858, [ ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'(
% 1.00/1.42 'c_COMBC'( 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.00/1.42 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), 'c_List_Olist_ONil'(
% 1.00/1.42 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' )
% 1.00/1.42 ) ] )
% 1.00/1.42 , clause( 691, [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 1.00/1.42 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.42 , 0, clause( 1536, [ ~( 'c_List_Olistsp'( 'c_InductTermi_OIT',
% 1.00/1.42 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.42 'tc_nat' ), 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), 'c_List_Omap'(
% 1.00/1.42 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst', 'v_u____', 'tc_Lambda_OdB',
% 1.00/1.42 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat', 'tc_Lambda_OdB' ) ), 'v_i____',
% 1.00/1.42 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), 'c_List_Olist_ONil'(
% 1.00/1.42 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 1.00/1.42 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.42 , 0, 11, substitution( 0, [ :=( X, 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst'
% 1.00/1.42 , 'v_u____', 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat',
% 1.00/1.42 'tc_Lambda_OdB' ) ), 'v_i____', 'tc_Lambda_OdB', 'tc_nat',
% 1.00/1.42 'tc_Lambda_OdB' ) ), :=( Y, 'tc_Lambda_OdB' ), :=( Z, 'tc_Lambda_OdB' )] )
% 1.00/1.42 , substitution( 1, [] )).
% 1.00/1.42
% 1.00/1.42
% 1.00/1.42 paramod(
% 1.00/1.42 clause( 5860, [ ~( 'c_List_Olistsp'( 'c_InductTermi_OIT',
% 1.00/1.42 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.42 , clause( 691, [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 1.00/1.42 'c_List_Olist_ONil'( Z ) ) ] )
% 1.00/1.42 , 0, clause( 5858, [ ~( 'c_List_Olistsp'( 'c_InductTermi_OIT',
% 1.00/1.42 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.42 'tc_nat' ), 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ),
% 1.00/1.42 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 1.00/1.42 ), 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.42 , 0, 3, substitution( 0, [ :=( X, 'c_COMBC'( 'c_Lambda_Olift',
% 1.00/1.42 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_Lambda_OdB', 'tc_nat',
% 1.00/1.42 'tc_Lambda_OdB' ) ), :=( Y, 'tc_Lambda_OdB' ), :=( Z, 'tc_Lambda_OdB' )] )
% 1.00/1.42 , substitution( 1, [] )).
% 1.00/1.42
% 1.00/1.42
% 1.00/1.42 resolution(
% 1.00/1.42 clause( 5861, [] )
% 1.00/1.42 , clause( 5860, [ ~( 'c_List_Olistsp'( 'c_InductTermi_OIT',
% 1.00/1.42 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ) ] )
% 1.00/1.42 , 0, clause( 689, [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ] )
% 1.00/1.42 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_InductTermi_OIT' )
% 1.00/1.42 , :=( Y, 'tc_Lambda_OdB' )] )).
% 1.00/1.42
% 1.00/1.42
% 1.00/1.42 subsumption(
% 1.00/1.42 clause( 694, [] )
% 1.00/1.42 , clause( 5861, [] )
% 1.00/1.42 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.00/1.42
% 1.00/1.42
% 1.00/1.42 end.
% 1.00/1.42
% 1.00/1.42 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.00/1.42
% 1.00/1.42 Memory use:
% 1.00/1.42
% 1.00/1.42 space for terms: 44695
% 1.00/1.42 space for clauses: 70158
% 1.00/1.42
% 1.00/1.42
% 1.00/1.42 clauses generated: 841
% 1.00/1.42 clauses kept: 695
% 1.00/1.42 clauses selected: 0
% 1.00/1.42 clauses deleted: 0
% 1.00/1.42 clauses inuse deleted: 0
% 1.00/1.42
% 1.00/1.42 subsentry: 27966
% 1.00/1.42 literals s-matched: 11383
% 1.00/1.42 literals matched: 11124
% 1.00/1.42 full subsumption: 1334
% 1.00/1.42
% 1.00/1.42 checksum: -422546847
% 1.00/1.42
% 1.00/1.42
% 1.00/1.42 Bliksem ended
%------------------------------------------------------------------------------