TSTP Solution File: LCL778-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL778-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:57:51 EDT 2022
% Result : Unsatisfiable 0.98s 1.34s
% Output : Refutation 0.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : LCL778-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.15 % Command : bliksem %s
% 0.15/0.37 % Computer : n021.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % DateTime : Mon Jul 4 05:54:31 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.98/1.33 *** allocated 10000 integers for termspace/termends
% 0.98/1.33 *** allocated 10000 integers for clauses
% 0.98/1.33 *** allocated 10000 integers for justifications
% 0.98/1.33 *** allocated 15000 integers for termspace/termends
% 0.98/1.33 Bliksem 1.12
% 0.98/1.33
% 0.98/1.33
% 0.98/1.33 Automatic Strategy Selection
% 0.98/1.33
% 0.98/1.33 Clauses:
% 0.98/1.33 [
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.98/1.33 , X ), X ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.98/1.33 , X ), X ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.98/1.33 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.98/1.33 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.98/1.33 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.98/1.33 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.98/1.33 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 0.98/1.33 ), Y, X ) ), =( Z, T ) ],
% 0.98/1.33 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.33 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.98/1.33 [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 0.98/1.33 X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'( X, hAPP( hAPP(
% 0.98/1.33 hAPP( 'c_Lambda_Osubst', U ), Y ), T ), W ) ],
% 0.98/1.33 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ), hAPP(
% 0.98/1.33 hAPP( 'c_Lambda_Olift', T ), Y ), U ), ~( 'c_Type_Otyping'( X, T, U ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.33 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.98/1.33 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.98/1.33 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.98/1.33 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.98/1.33 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.98/1.33 , Y, X ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.33 X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.98/1.33 'c_Lambda_Olift', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.98/1.33 , T ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( hAPP(
% 0.98/1.33 'c_Lambda_Olift', Y ), T ) ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.33 X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.98/1.33 'c_Lambda_Olift', X ), T ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), T ) ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X ) ), Y ),
% 0.98/1.33 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.33 X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.98/1.33 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.98/1.33 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.33 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.98/1.33 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.98/1.33 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.98/1.33 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.98/1.33 'c_lessequals'( Z, Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.98/1.33 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.33 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.33 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.33 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.33 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.33 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 0.98/1.33 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.98/1.33 , X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.98/1.33 , X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.33 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.98/1.33 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.98/1.33 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.98/1.33 'c_lessequals'( Z, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.98/1.33 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.98/1.33 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.98/1.33 'c_lessequals'( Z, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.98/1.33 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.98/1.33 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.98/1.33 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.98/1.33 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 0.98/1.33 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.98/1.33 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.98/1.33 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.98/1.33 X ), Y ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.33 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.98/1.33 X ), Y ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.98/1.33 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 0.98/1.33 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.98/1.33 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.98/1.33 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 0.98/1.33 X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.98/1.33 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.98/1.33 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.33 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.98/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.98/1.33 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.98/1.33 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.98/1.33 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.98/1.33 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.98/1.33 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 0.98/1.33 Z, T, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.98/1.33 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.33 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.98/1.33 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.98/1.33 X ), T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.33 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.98/1.33 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.98/1.33 X ), T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.33 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OAbs'( X ) ), Y ),
% 0.98/1.33 'c_Lambda_OdB_OAbs'( hAPP( hAPP( 'c_Lambda_Olift', X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.98/1.33 'tc_nat' ) ) ) ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ),
% 0.98/1.33 'c_Lambda_OdB_OAbs'( 'c_Lambda_Oliftn'( X, Y, hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.98/1.33 'tc_nat' ) ) ) ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 0.98/1.33 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubstn'( X, Y, hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.98/1.33 'tc_nat' ) ) ) ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.33 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.98/1.33 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.98/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OAbs'( X ) ), Y
% 0.98/1.33 ), Z ), 'c_Lambda_OdB_OAbs'( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ),
% 0.98/1.33 hAPP( hAPP( 'c_Lambda_Olift', Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.33 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.98/1.33 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ) ) ],
% 0.98/1.33 [ 'c_Type_Otypings'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ),
% 0.98/1.33 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Y, 'tc_Lambda_OdB', 'tc_nat'
% 0.98/1.33 , 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 0.98/1.33 'c_Type_Otypings'( X, T, U ) ) ],
% 0.98/1.33 [ 'c_Type_Otypings'( X, 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.98/1.33 'c_Lambda_Osubst', Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.98/1.33 'tc_nat', 'tc_Lambda_OdB' ) ), Z, 'tc_Lambda_OdB', 'tc_nat',
% 0.98/1.33 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 0.98/1.33 'c_Type_Otypings'( 'c_Type_Oshift'( X, Z, W, 'tc_Type_Otype' ), T, U ) )
% 0.98/1.33 , ~( 'c_Type_Otyping'( X, Y, W ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3'( X ) )
% 0.98/1.33 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4'( X )
% 0.98/1.33 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.98/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1'( X ) )
% 0.98/1.33 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2'( X )
% 0.98/1.33 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ],
% 0.98/1.33 [ ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.33 'c_Lambda_OdB_OAbs'(
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__Xlem__1__3'( X ) ),
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__Xlem__1__4'( X ),
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.98/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__Xlem__1__1'( X ) ),
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__Xlem__1__2'( X ),
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( X, Y ) ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.98/1.33 ) ],
% 0.98/1.33 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.98/1.33 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.98/1.33 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 0.98/1.33 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U
% 0.98/1.33 ), 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ) ) ],
% 0.98/1.33 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 0.98/1.33 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.98/1.33 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.98/1.33 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.33 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.98/1.33 ), Z ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.98/1.33 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.98/1.33 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.33 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.98/1.33 ), Z ) ) ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 0.98/1.33 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 0.98/1.33 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 0.98/1.33 'c_List_Olist_ONil'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( T, Y
% 0.98/1.33 , X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, T
% 0.98/1.33 , X ), Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_ListOrder_Ostep1'( X, T, U, W ),
% 0.98/1.33 ~( 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y
% 0.98/1.33 , 'c_List_Olist_ONil'( W ), W ), W ), 'c_List_Oappend'( U,
% 0.98/1.33 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W ), W ), W ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.33 'c_Predicate_Oconversep'( X, Y, Y ), Y ), Z ), T ) ), ~( hBOOL( hAPP(
% 0.98/1.33 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), T ), Z ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.98/1.33 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.33 'c_Predicate_Oconversep'( X, Y, Y ), Y ), T ), Z ) ) ) ],
% 0.98/1.33 [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 0.98/1.33 'c_List_Olist_ONil'( Z ) ) ],
% 0.98/1.33 [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T ), Z ) ],
% 0.98/1.33 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.33 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T ), U ) ),
% 0.98/1.33 ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.33 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T ), U ) ),
% 0.98/1.33 ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.98/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 X ), Y ), Z ) ), T ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 X ), Y ), Z ) ), T ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'c_ListOrder_Ostep1'( X, Y, Z, T ) ), 'c_ListOrder_Ostep1'( X,
% 0.98/1.33 'c_List_Oappend'( Y, U, T ), 'c_List_Oappend'( Z, U, T ), T ) ],
% 0.98/1.33 [ 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( Y, Z, T ), 'c_List_Oappend'(
% 0.98/1.33 Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.98/1.33 , 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ), 'c_Lambda_OdB_OAbs'( Y )
% 0.98/1.33 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.33 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Y ) ) ) ],
% 0.98/1.33 [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X, 'c_List_Oappend'(
% 0.98/1.33 Y, T, Z ), Z ) ) ],
% 0.98/1.33 [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X, 'c_List_Oappend'(
% 0.98/1.33 T, Y, Z ), Z ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OAbs'( T ), U ),
% 0.98/1.33 hAPP( Z, T ) ) ],
% 0.98/1.33 [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U, 'c_List_Olist_OCons'(
% 0.98/1.33 Y, T, W ), 'c_List_Olist_OCons'( X, Z, W ), W ) ) ],
% 0.98/1.33 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), 'c_ListOrder_Ostep1'( X,
% 0.98/1.33 'c_List_Olist_OCons'( Y, T, U ), 'c_List_Olist_OCons'( Z, T, U ), U ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ],
% 0.98/1.33 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 0.98/1.33 ), =( X, T ) ],
% 0.98/1.33 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, Y, Z ) ) ),
% 0.98/1.33 =( X, T ) ],
% 0.98/1.33 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( X, T, Z ) ) ),
% 0.98/1.33 =( Y, T ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 T, X ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), Z )
% 0.98/1.33 ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), Z )
% 0.98/1.33 ) ],
% 0.98/1.33 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.33 'c_Transitive__Closure_Ortranclp'( X, Z ), Y ), T ) ) ), ~(
% 0.98/1.33 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.98/1.33 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( 'c_Wellfounded_Oaccp'( X, T, Z )
% 0.98/1.33 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Z ), Y )
% 0.98/1.33 , T ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.98/1.33 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), U )
% 0.98/1.33 , T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.98/1.33 ), Z ), U ) ) ) ],
% 0.98/1.33 [ 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ), ~( hBOOL( hAPP(
% 0.98/1.33 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', X ) ), ~( 'c_Wellfounded_Oaccp'(
% 0.98/1.33 'c_Predicate_Oconversep'( 'c_Lambda_Obeta', 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.98/1.33 X ) ) ), =( X, 'c_Lambda_OdB_OAbs'( 'v_sko__InductTermi__XIT__Xcases__3'(
% 0.98/1.33 X ) ) ), 'c_List_Olistsp'( 'c_InductTermi_OIT',
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB' ), ~( hBOOL(
% 0.98/1.33 hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ), X ) ],
% 0.98/1.33 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 0.98/1.33 [ =( X, 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), Y, X ), Y ) ],
% 0.98/1.33 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.98/1.33 , 'tc_Lambda_OdB' ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ), Z ) )
% 0.98/1.33 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 0.98/1.33 hAPP( 'c_Lambda_Obeta', Y ), T ) ) ) ],
% 0.98/1.33 [ =( 'c_List_Omap'( X, 'c_List_Oreplicate'( Y, Z, T ), T, U ),
% 0.98/1.33 'c_List_Oreplicate'( Y, hAPP( X, Z ), U ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 0.98/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 X, T, 'tc_nat' ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.98/1.33 [ =( 'c_List_Ofoldr'( X, 'c_List_Oappend'( Y, Z, T ), U, T, W ),
% 0.98/1.33 'c_List_Ofoldr'( X, Y, 'c_List_Ofoldr'( X, Z, U, T, W ), T, W ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), =( Y, Z ), ~( 'c_ListOrder_Ostep1'(
% 0.98/1.33 X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( U )
% 0.98/1.33 , U ), U ), 'c_List_Oappend'( W, 'c_List_Olist_OCons'( Z,
% 0.98/1.33 'c_List_Olist_ONil'( U ), U ), U ), U ) ) ],
% 0.98/1.33 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.98/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.98/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.98/1.33 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X ) ) ), =( Z
% 0.98/1.33 , 'c_List_Olist_ONil'( T ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 0.98/1.33 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.98/1.33 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.98/1.33 , 'tc_Lambda_OdB' ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ), Z ) )
% 0.98/1.33 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', T ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 0.98/1.33 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.98/1.33 'tc_Lambda_OdB' ), X ), T ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.98/1.33 , 'tc_Lambda_OdB' ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ), Z ) )
% 0.98/1.33 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 0.98/1.33 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.98/1.33 'tc_Lambda_OdB' ), Y ), T ) ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( 'c_List_Ofoldr'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), 'c_List_Ofoldl'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.98/1.33 ), ~( hBOOL( hAPP( hAPP( X, Z ), T ) ) ) ],
% 0.98/1.33 [ ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_ONil'( Y ), Z, Y ) ) ],
% 0.98/1.33 [ ~( 'c_ListOrder_Ostep1'( X, Y, 'c_List_Olist_ONil'( Z ), Z ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.33 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.98/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.98/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.98/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.98/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.98/1.33 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.98/1.33 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 0.98/1.33 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.98/1.33 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 0.98/1.33 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 0.98/1.33 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 0.98/1.33 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 0.98/1.33 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.98/1.33 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.98/1.33 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 0.98/1.33 , V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.98/1.33 T, X, U, W, Y, V0 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.98/1.33 T, X, U, Y, W, V0 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.98/1.33 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.98/1.33 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 0.98/1.33 , V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.98/1.33 X, T, U, Y, W, V0 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.98/1.33 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 0.98/1.33 , V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.98/1.33 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 0.98/1.33 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 0.98/1.33 , V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 0.98/1.33 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 0.98/1.33 W, V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.98/1.33 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 0.98/1.33 W, V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.98/1.33 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 0.98/1.33 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 0.98/1.33 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 0.98/1.33 W, V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.98/1.33 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 0.98/1.33 , V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.98/1.33 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 0.98/1.33 W, V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 0.98/1.33 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 0.98/1.33 , V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.98/1.33 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 0.98/1.33 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.98/1.33 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 0.98/1.33 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.98/1.33 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 0.98/1.33 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.98/1.33 T, X, U, W, Z, V0 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.98/1.33 T, X, U, W, Y, V0 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.98/1.33 T, X, U, Z, W, V0 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.98/1.33 T, X, U, Y, W, V0 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 0.98/1.33 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 0.98/1.33 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.98/1.33 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.98/1.33 X, T, U, Z, W, V0 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.98/1.33 X, T, U, Y, W, V0 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 0.98/1.33 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 0.98/1.33 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 0.98/1.33 , V0, U, V1 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 0.98/1.33 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 0.98/1.33 , V0, U, V1 ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 0.98/1.33 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 0.98/1.33 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 0.98/1.33 [ =( X, Y ), hBOOL( hAPP( hAPP( Z, Y ), X ) ), ~( 'c_ListOrder_Ostep1'(
% 0.98/1.33 Z, 'c_List_Olist_OCons'( Y, T, U ), 'c_List_Olist_OCons'( X, W, U ), U )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.98/1.33 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.98/1.33 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.98/1.33 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.33 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.98/1.33 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.33 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 0.98/1.33 Z, Y, X ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.98/1.33 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Type_Otyping'( X, T, Z ) ), ~(
% 0.98/1.33 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.98/1.33 'tc_Lambda_OdB' ), T ), Y ) ) ) ],
% 0.98/1.33 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 0.98/1.33 , 'c_List_Olist_ONil'( Y ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X ) ), Y ),
% 0.98/1.33 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_Olift', X )
% 0.98/1.33 , Y ) ), hAPP( hAPP( 'c_Lambda_Olift', Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.33 'c_Lambda_Obeta', X ), Z ) ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ],
% 0.98/1.33 [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ],
% 0.98/1.33 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubstn'(
% 0.98/1.33 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'( X, Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.33 [ =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Oappend'(
% 0.98/1.33 'c_List_Olist_ONil'( Z ), 'c_List_Olist_OCons'( X, Y, Z ), Z ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ), T ),
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.98/1.33 ), Y ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X )
% 0.98/1.33 ) ],
% 0.98/1.33 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, 'c_List_Olist_ONil'( Z
% 0.98/1.33 ), Z, X ) ) ],
% 0.98/1.33 [ =( X, Y ), 'c_ListOrder_Ostep1'( Z, X, Y, T ), ~( 'c_ListOrder_Ostep1'(
% 0.98/1.33 Z, 'c_List_Oappend'( X, 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( T )
% 0.98/1.33 , T ), T ), 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( W,
% 0.98/1.33 'c_List_Olist_ONil'( T ), T ), T ), T ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.98/1.33 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.98/1.33 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.98/1.33 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( 'c_List_Olist_ONil'( X
% 0.98/1.33 ), 'c_List_Olist_ONil'( X ), X ) ) ],
% 0.98/1.33 [ =( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.33 'c_Transitive__Closure_Ortranclp'( X, Y ), Y ),
% 0.98/1.33 'c_Transitive__Closure_Ortranclp'( X, Y ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'( X ) ),
% 0.98/1.33 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X )
% 0.98/1.33 , Y ) ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.98/1.33 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.98/1.33 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( Z ), Z ), Z ),
% 0.98/1.33 'c_List_Olist_OCons'( Y, 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_OrderedGroup_Omonoid__add'( Z,
% 0.98/1.33 X, T ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_OrderedGroup_Omonoid__add'( Y,
% 0.98/1.33 X, T ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 0.98/1.33 , 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.98/1.33 , 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.98/1.33 X ) ) ), =( X, 'c_Lambda_OdB_OAbs'( 'v_sko__InductTermi__XIT__Xcases__3'(
% 0.98/1.33 X ) ) ), =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.98/1.33 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.98/1.33 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.98/1.33 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.98/1.33 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.98/1.33 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.98/1.33 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.98/1.33 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.98/1.33 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.98/1.33 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 0.98/1.33 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.98/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.33 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.98/1.33 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.98/1.33 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.98/1.33 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.98/1.33 Y ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.98/1.33 Y ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.98/1.33 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.98/1.33 Y ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.98/1.33 Y ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.98/1.33 Y ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.98/1.33 Y ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.98/1.33 Y ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 0.98/1.33 X ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.98/1.33 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.98/1.33 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 0.98/1.33 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.98/1.33 ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.98/1.33 ), 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), 'c_HOL_Oord__class_Oless'( Y, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 Y, 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.98/1.33 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.98/1.33 'tc_nat' ) ],
% 0.98/1.33 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Y
% 0.98/1.33 , 'c_List_Olist_ONil'( X ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Z
% 0.98/1.33 , 'c_List_Olist_ONil'( X ) ) ],
% 0.98/1.33 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( X
% 0.98/1.33 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y
% 0.98/1.33 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.98/1.33 [ =( 'c_Predicate_Oconversep'( 'c_fequal'( X ), X, X ), 'c_fequal'( X )
% 0.98/1.33 ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.98/1.33 X ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.98/1.33 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.98/1.33 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, X ) ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.98/1.33 , X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.33 , Y, X ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.33 , Y, X ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.98/1.33 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.33 Y ), X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.98/1.33 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_Olift', X ), Y ) ), hAPP( hAPP(
% 0.98/1.33 'c_Lambda_Olift', Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.33 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.98/1.33 ), Z ) ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), =( Z, Y ), ~( 'c_ListOrder_Ostep1'(
% 0.98/1.33 X, 'c_List_Olist_OCons'( U, Y, T ), 'c_List_Olist_OCons'( W, Z, T ), T )
% 0.98/1.33 ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.98/1.33 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_OrderedGroup_Osemigroup__add'( X, U )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 0.98/1.33 'c_List_Olist_OCons'( Y, Z, X ), X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Olistsum'( Z, X ) ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( 'c_List_Omap'( X, 'c_List_Oappend'( Y, Z, T ), T, U ),
% 0.98/1.33 'c_List_Oappend'( 'c_List_Omap'( X, Y, T, U ), 'c_List_Omap'( X, Z, T, U
% 0.98/1.33 ), U ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.98/1.33 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.98/1.33 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.98/1.33 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.98/1.33 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.98/1.33 ), =( Z, Y ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.33 ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 0.98/1.33 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.98/1.33 'c_List_Oreplicate'( T, Y, Z ), Z ), 'c_List_Oappend'(
% 0.98/1.33 'c_List_Oreplicate'( T, Y, Z ), 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.33 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.33 T, X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.98/1.33 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 0.98/1.33 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.98/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.98/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'( Y,
% 0.98/1.33 X ), 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X, X ) ) ],
% 0.98/1.33 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ =( 'c_List_Oreplicate'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'tc_nat' ), X ), Y ), Z, T ), 'c_List_Oappend'( 'c_List_Oreplicate'( X, Z
% 0.98/1.33 , T ), 'c_List_Oreplicate'( Y, Z, T ), T ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.98/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.98/1.33 [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U, 'c_List_Oappend'( X
% 0.98/1.33 , 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W ), W ),
% 0.98/1.33 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( T, 'c_List_Olist_ONil'( W ), W
% 0.98/1.33 ), W ), W ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.98/1.33 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_Olift', X ), Z ),
% 0.98/1.33 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Z, 'tc_Lambda_OdB', 'tc_nat'
% 0.98/1.33 , 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ),
% 0.98/1.33 =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_List_Olistsp'( X, 'c_List_Oappend'( Y, Z, T ), T ), ~(
% 0.98/1.33 'c_List_Olistsp'( X, Z, T ) ), ~( 'c_List_Olistsp'( X, Y, T ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OAbs'( T ), U ),
% 0.98/1.33 hAPP( hAPP( Z, T ), 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, U ) ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ),
% 0.98/1.33 'c_OrderedGroup_Osemigroup__add'( 'c_HOL_Oplus__class_Oplus'( X ), X ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'( Y, Z, X ) ) ),
% 0.98/1.33 =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.98/1.33 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_OCons'( Y, Z, T ), U, T, W ),
% 0.98/1.33 hAPP( hAPP( X, Y ), 'c_List_Ofoldr'( X, Z, U, T, W ) ) ) ],
% 0.98/1.33 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.98/1.33 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.98/1.33 ],
% 0.98/1.33 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.98/1.33 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.98/1.33 ],
% 0.98/1.33 [ =( 'c_Predicate_Oconversep'( 'c_Predicate_Oconversep'( X, Y, Z ), Z, Y
% 0.98/1.33 ), X ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Oappend'( X, Y, Z ), X ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( =( X, 'c_List_Oappend'( X, Y, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Oappend'( X, Y, Z ), Y ) ), =( X, 'c_List_Olist_ONil'( Z
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( =( X, 'c_List_Oappend'( Y, X, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y
% 0.98/1.33 , Z, X ), X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.98/1.33 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 0.98/1.33 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.98/1.33 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 0.98/1.33 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.98/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.98/1.33 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.98/1.33 ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.98/1.33 , Z ), Y ), 'tc_nat' ) ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.98/1.33 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 0.98/1.33 ],
% 0.98/1.33 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.98/1.33 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.98/1.33 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 0.98/1.33 ) ), =( X, T ) ],
% 0.98/1.33 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 0.98/1.33 ) ), =( Y, U ) ],
% 0.98/1.33 [ 'c_Type_Otyping'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', T
% 0.98/1.33 ), Y ) ) ), ~( 'c_Type_Otyping'( X, T, Z ) ) ],
% 0.98/1.33 [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), hBOOL( hAPP( hAPP( X, U ), W ) ),
% 0.98/1.33 ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( U, Y, T ),
% 0.98/1.33 'c_List_Olist_OCons'( W, Z, T ), T ) ) ],
% 0.98/1.33 [ 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 0.98/1.33 'c_List_Olist_OCons'( Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.98/1.33 'c_List_Olist_OCons'( Y, T, Z ), Z ), 'c_List_Olist_OCons'( Y,
% 0.98/1.33 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ), T, Z ), Z ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.98/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.98/1.33 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) ) ), =( Y
% 0.98/1.33 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 0.98/1.33 'c_List_Oappend'( Y, Z, X ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 X ), 'c_List_Olistsum'( Y, X ) ), 'c_List_Olistsum'( Z, X ) ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.98/1.33 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.98/1.33 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( X, T
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.98/1.33 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.98/1.33 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( Y, U
% 0.98/1.33 ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_ONil'( X
% 0.98/1.33 ), X ), 'c_List_Olist_ONil'( X ) ) ],
% 0.98/1.33 [ 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'( 'c_COMBC'(
% 0.98/1.33 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_Lambda_OdB'
% 0.98/1.33 , 'tc_nat', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.98/1.33 'tc_Lambda_OdB' ), ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', X,
% 0.98/1.33 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.98/1.33 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.98/1.33 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.98/1.33 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.98/1.33 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.98/1.33 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.98/1.33 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.98/1.33 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), U )
% 0.98/1.33 , T ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.98/1.33 ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.33 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.33 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.98/1.33 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) )
% 0.98/1.33 ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.33 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.98/1.33 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) )
% 0.98/1.33 ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.98/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.33 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.98/1.33 [ =( 'c_Nat_Osize__class_Osize'( X, 'tc_String_Ochar' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 0.98/1.33 , 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, Y ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( 'c_Orderings_Oord__class_Omax'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.98/1.33 [ =( 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), X, 'tc_nat' ), X ) ],
% 0.98/1.33 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 0.98/1.33 ), =( Y, U ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 0.98/1.33 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X
% 0.98/1.33 ), 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), X, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'( Y,
% 0.98/1.33 X ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.98/1.33 ) ) ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 0.98/1.33 Z ) ) ) ],
% 0.98/1.33 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.98/1.33 Z ) ) ) ],
% 0.98/1.33 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP( hAPP(
% 0.98/1.33 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.98/1.33 Z, U ), W ) ) ) ],
% 0.98/1.33 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP( hAPP(
% 0.98/1.33 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.98/1.33 Z, U ), W ) ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.98/1.33 , Y ) ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.33 'c_Lambda_Olift', X ), Z ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ) )
% 0.98/1.33 ],
% 0.98/1.33 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, hAPP( hAPP( 'c_Lambda_OdB_OApp'
% 0.98/1.33 , T ), U ), W ), hAPP( hAPP( Y, T ), U ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.98/1.33 T ), U ), W ), hAPP( hAPP( hAPP( hAPP( Y, T ), U ),
% 0.98/1.33 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, W ) ), 'c_Lambda_OdB_OdB__rec'( X, Y
% 0.98/1.33 , Z, U, W ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.98/1.33 X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP(
% 0.98/1.33 hAPP( 'c_Lambda_Obeta', Y ), Z ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.98/1.33 X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP(
% 0.98/1.33 hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T
% 0.98/1.33 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y, T ) ),
% 0.98/1.33 'c_Lambda_Oliftn'( X, Z, T ) ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 0.98/1.33 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X, Z, T ) ),
% 0.98/1.33 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_Osubstn'( X, Y, Z ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.98/1.33 , X ), 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.98/1.33 ), Z ) ) ],
% 0.98/1.33 [ ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.98/1.33 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ), ~( 'c_Wellfounded_Oaccp'(
% 0.98/1.33 'c_Predicate_Oconversep'( 'c_Lambda_Obeta', 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB' ) ), 'c_Wellfounded_Oaccp'(
% 0.98/1.33 'c_Predicate_Oconversep'( 'c_Lambda_Obeta', 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z, 'tc_Lambda_OdB'
% 0.98/1.33 , 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.98/1.33 , 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~(
% 0.98/1.33 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.98/1.33 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.98/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Z, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ) ), ~( 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', Y, Z,
% 0.98/1.33 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.33 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.98/1.33 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.33 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', Z, T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X,
% 0.98/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z,
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1'( X
% 0.98/1.33 , Y, Z, T ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), =( T,
% 0.98/1.33 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2'( X ),
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1'( X ),
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.98/1.33 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.98/1.33 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.98/1.33 ), 'c_Lambda_OdB_OAbs'( X ) ) ],
% 0.98/1.33 [ =( 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, U, U ), hAPP( hAPP(
% 0.98/1.33 X, Y ), 'c_List_Ofoldl'( X, Z, T, U, U ) ) ), ~(
% 0.98/1.33 'c_OrderedGroup_Osemigroup__add'( X, U ) ) ],
% 0.98/1.33 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), Y ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.33 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.33 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( hAPP( hAPP( X, Y ), 'c_List_Ofoldl'( X, Z, T, U, U ) ),
% 0.98/1.33 'c_List_Ofoldl'( X, Y, T, U, U ) ), ~( 'c_OrderedGroup_Omonoid__add'( Z,
% 0.98/1.33 X, U ) ) ],
% 0.98/1.33 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_OCons'( Z, T, U ), W, U ),
% 0.98/1.33 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, W, U ) ) ],
% 0.98/1.33 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Oappend'( Z, T, U ), W, U ),
% 0.98/1.33 'c_List_Ofoldl'( X, 'c_List_Ofoldl'( X, Y, Z, W, U ), T, W, U ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), T )
% 0.98/1.33 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP(
% 0.98/1.33 'c_Lambda_Osubst', X ), Z ), T ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.98/1.33 'c_Lambda_Osubst', Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.98/1.33 'tc_nat', 'tc_Lambda_OdB' ) ), T, 'tc_Lambda_OdB', 'tc_nat',
% 0.98/1.33 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB'
% 0.98/1.33 , 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( X, 'c_ListApplication_Osko__ListApplication__Xlem__1__3'(
% 0.98/1.33 X ) ) ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.33 'c_Lambda_OdB_OVar'(
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__Xlem__1__1'( X ) ),
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__Xlem__1__2'( X ),
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( X, Y ) ) ],
% 0.98/1.33 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__typesE__1__1'(
% 0.98/1.33 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ), Z ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3'( X ) )
% 0.98/1.33 ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.33 'c_Lambda_OdB_OVar'(
% 0.98/1.33 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1'( X ) )
% 0.98/1.33 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2'( X )
% 0.98/1.33 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ],
% 0.98/1.33 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__types__1__1'(
% 0.98/1.33 Z, T, X, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ), T ) ), ~( 'c_Type_Otypings'( X, W, V0 ) ), ~(
% 0.98/1.33 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.98/1.33 , Z ) ) ],
% 0.98/1.33 [ 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', X,
% 0.98/1.33 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, X, Z ),
% 0.98/1.33 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.98/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), X,
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.98/1.33 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.98/1.33 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( hAPP(
% 0.98/1.33 'c_Lambda_Osubst', X ), Y ), Z ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.33 T ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), T ) ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( 'c_Lambda_Olift',
% 0.98/1.33 X ), Y ) ), Z ), Y ), X ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.98/1.33 X ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.98/1.33 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.98/1.33 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.98/1.33 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.98/1.33 ],
% 0.98/1.33 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.98/1.33 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.98/1.33 ],
% 0.98/1.33 [ ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.98/1.33 ) ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OVar'( T ), U ),
% 0.98/1.33 hAPP( X, T ) ) ],
% 0.98/1.33 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.98/1.33 [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y )
% 0.98/1.33 , Z ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OVar'( T ), U ),
% 0.98/1.33 hAPP( X, T ) ) ],
% 0.98/1.33 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 0.98/1.33 ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X ) ) ), ~(
% 0.98/1.33 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.98/1.33 'c_Lambda_OdB_OAbs'( X ) ), Y ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X
% 0.98/1.33 ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.98/1.33 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ),
% 0.98/1.33 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.33 'c_Lambda_Obeta', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.33 'c_Lambda_OdB_OVar'( Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ) )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.98/1.33 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.98/1.33 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.98/1.33 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.98/1.33 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.98/1.33 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.33 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.98/1.33 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.98/1.33 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.98/1.33 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.98/1.33 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.98/1.33 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.33 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.98/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.98/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.98/1.33 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.98/1.33 ,
% 0.98/1.33 [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.98/1.33 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.98/1.33 [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OVar'( X ),
% 0.98/1.33 'tc_Lambda_OdB' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OVar'( X ) ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.98/1.33 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.98/1.33 ) ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.98/1.33 'c_Lambda_OdB_OApp', X ), Y ), Z ) ],
% 0.98/1.33 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.98/1.33 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.98/1.33 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.98/1.33 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.98/1.33 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.98/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) )
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.33 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 0.98/1.33 , Y ) ],
% 0.98/1.33 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.98/1.33 ), Z ), 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.98/1.33 'tc_nat' ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.98/1.33 ), Z ), 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.33 Z, X, 'tc_nat' ) ],
% 0.98/1.33 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( hAPP( hAPP( hAPP(
% 0.98/1.33 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y ) ],
% 0.98/1.33 [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ), X ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.98/1.33 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ) ) ],
% 0.98/1.33 [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.33 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.33 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.98/1.33 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y )
% 0.98/1.33 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.98/1.33 , 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ),
% 0.98/1.33 ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y, 'tc_Lambda_OdB' ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.98/1.33 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.98/1.33 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.98/1.33 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB'
% 0.98/1.33 , 'tc_Lambda_OdB' ) ) ) ) ],
% 0.98/1.33 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.98/1.33 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), T ), hAPP( hAPP(
% 0.98/1.33 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Z ), T ) )
% 0.98/1.33 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', Y ), Z ), T ) ) ) ],
% 0.98/1.33 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.98/1.33 ) ],
% 0.98/1.33 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.98/1.33 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.98/1.33 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.98/1.33 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.98/1.33 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.98/1.33 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.98/1.33 ), X ), Y ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.98/1.33 , X ), 'c_Lambda_OdB_OVar'( Y ) ), Z ) ) ), ~( hBOOL( hAPP(
% 0.98/1.33 'c_InductTermi_OIT', X ) ) ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.98/1.33 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.98/1.33 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 0.98/1.33 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.33 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OVar'( X )
% 0.98/1.33 , Y ) ],
% 0.98/1.33 [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.98/1.33 Z ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X ) ) ) ],
% 0.98/1.33 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.98/1.33 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OVar'(
% 0.98/1.33 Z ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.98/1.33 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_r' ), 'v_s' ),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_ss', 'tc_Lambda_OdB',
% 0.98/1.33 'tc_Lambda_OdB' ) ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.98/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.98/1.33 , 'v_r' ), 'v_s' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_ss',
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_Lambda_OdB_OVar'( 'v_i' ) ) ) )
% 0.98/1.33 ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_s' ) ) ],
% 0.98/1.33 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.98/1.33 'v_s' ), 'c_Lambda_OdB_OVar'( 'v_i' ) ) ) ) ],
% 0.98/1.33 [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.98/1.33 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.98/1.33 , 'v_r' ), 'v_s' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_ss',
% 0.98/1.33 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_Lambda_OdB_OVar'( 'v_i' ) ) ) )
% 0.98/1.33 ) ],
% 0.98/1.33 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.98/1.33 'class_Orderings_Opreorder'( Y ) ) ],
% 0.98/1.33 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.98/1.33 'class_Orderings_Oorder'( Y ) ) ],
% 0.98/1.33 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.98/1.33 ],
% 0.98/1.33 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.98/1.33 ) ],
% 0.98/1.33 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 0.98/1.33 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 0.98/1.33 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 0.98/1.33 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 0.98/1.33 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 0.98/1.33 ] .
% 0.98/1.33
% 0.98/1.33
% 0.98/1.33 percentage equality = 0.310823, percentage horn = 0.906639
% 0.98/1.33 This is a problem with some equality
% 0.98/1.33
% 0.98/1.33
% 0.98/1.33
% 0.98/1.33 Options Used:
% 0.98/1.33
% 0.98/1.33 useres = 1
% 0.98/1.33 useparamod = 1
% 0.98/1.33 useeqrefl = 1
% 0.98/1.33 useeqfact = 1
% 0.98/1.33 usefactor = 1
% 0.98/1.33 usesimpsplitting = 0
% 0.98/1.33 usesimpdemod = 5
% 0.98/1.33 usesimpres = 3
% 0.98/1.33
% 0.98/1.33 resimpinuse = 1000
% 0.98/1.33 resimpclauses = 20000
% 0.98/1.33 substype = eqrewr
% 0.98/1.33 backwardsubs = 1
% 0.98/1.33 selectoldest = 5
% 0.98/1.33
% 0.98/1.33 litorderings [0] = split
% 0.98/1.33 litorderings [1] = extend the termordering, first sorting on arguments
% 0.98/1.33
% 0.98/1.33 termordering = kbo
% 0.98/1.33
% 0.98/1.33 litapriori = 0
% 0.98/1.33 termapriori = 1
% 0.98/1.33 litaposteriori = 0
% 0.98/1.33 termaposteriori = 0
% 0.98/1.33 demodaposteriori = 0
% 0.98/1.33 ordereqreflfact = 0
% 0.98/1.33
% 0.98/1.33 litselect = negord
% 0.98/1.33
% 0.98/1.33 maxweight = 15
% 0.98/1.33 maxdepth = 30000
% 0.98/1.33 maxlength = 115
% 0.98/1.33 maxnrvars = 195
% 0.98/1.33 excuselevel = 1
% 0.98/1.33 increasemaxweight = 1
% 0.98/1.33
% 0.98/1.33 maxselected = 10000000
% 0.98/1.33 maxnrclauses = 10000000
% 0.98/1.33
% 0.98/1.33 showgenerated = 0
% 0.98/1.33 showkept = 0
% 0.98/1.33 showselected = 0
% 0.98/1.33 showdeleted = 0
% 0.98/1.33 showresimp = 1
% 0.98/1.33 showstatus = 2000
% 0.98/1.33
% 0.98/1.33 prologoutput = 1
% 0.98/1.33 nrgoals = 5000000
% 0.98/1.33 totalproof = 1
% 0.98/1.33
% 0.98/1.33 Symbols occurring in the translation:
% 0.98/1.33
% 0.98/1.33 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.98/1.33 . [1, 2] (w:1, o:165, a:1, s:1, b:0),
% 0.98/1.33 ! [4, 1] (w:0, o:105, a:1, s:1, b:0),
% 0.98/1.33 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.98/1.33 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.98/1.33 'class_Ring__and__Field_Oordered__semidom' [40, 1] (w:1, o:112, a:1
% 0.98/1.33 , s:1, b:0),
% 0.98/1.33 'c_HOL_Ozero__class_Ozero' [41, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.98/1.33 'c_Nat_Osemiring__1__class_Oof__nat' [43, 2] (w:1, o:190, a:1, s:1
% 0.98/1.33 , b:0),
% 0.98/1.33 'c_lessequals' [44, 3] (w:1, o:197, a:1, s:1, b:0),
% 0.98/1.33 'c_Power_Opower__class_Opower' [47, 3] (w:1, o:200, a:1, s:1, b:0),
% 0.98/1.33 'c_HOL_Oone__class_Oone' [49, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.98/1.33 'c_HOL_Oord__class_Oless' [50, 3] (w:1, o:201, a:1, s:1, b:0),
% 0.98/1.33 'class_Power_Opower' [51, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.98/1.33 'tc_nat' [52, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.98/1.33 'class_Ring__and__Field_Ocomm__semiring__1' [53, 1] (w:1, o:134, a:1
% 0.98/1.33 , s:1, b:0),
% 0.98/1.33 'c_Type_Otyping' [58, 3] (w:1, o:202, a:1, s:1, b:0),
% 0.98/1.33 'tc_Type_Otype' [60, 0] (w:1, o:54, a:1, s:1, b:0),
% 0.98/1.33 'c_Type_Oshift' [61, 4] (w:1, o:213, a:1, s:1, b:0),
% 0.98/1.33 'c_Lambda_Osubst' [64, 0] (w:1, o:55, a:1, s:1, b:0),
% 0.98/1.33 hAPP [65, 2] (w:1, o:191, a:1, s:1, b:0),
% 0.98/1.33 'c_Lambda_Olift' [67, 0] (w:1, o:57, a:1, s:1, b:0),
% 0.98/1.33 'c_HOL_Oplus__class_Oplus' [71, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.98/1.34 'c_Lambda_OdB_OVar' [72, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [74, 1]
% 0.98/1.34 (w:1, o:116, a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Opordered__comm__monoid__add' [77, 1] (w:1, o:117
% 0.98/1.34 , a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Olordered__ab__group__add' [78, 1] (w:1, o:118
% 0.98/1.34 , a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [80, 1]
% 0.98/1.34 (w:1, o:119, a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Ocomm__monoid__add' [81, 1] (w:1, o:120, a:1, s:1
% 0.98/1.34 , b:0),
% 0.98/1.34 'class_Orderings_Olinorder' [82, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.98/1.34 'class_Orderings_Oorder' [83, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__group__add' [84, 1] (w:1, o:123
% 0.98/1.34 , a:1, s:1, b:0),
% 0.98/1.34 'class_Orderings_Opreorder' [85, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add' [87, 1] (w:1, o:
% 0.98/1.34 125, a:1, s:1, b:0),
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring' [93, 6] (w:1, o:224, a:1, s:1, b:0)
% 0.98/1.34 ,
% 0.98/1.34 'c_Orderings_Oord__class_Omax' [94, 3] (w:1, o:198, a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Omonoid__mult' [95, 1] (w:1, o:126, a:1, s:1, b:0
% 0.98/1.34 ),
% 0.98/1.34 'class_Ring__and__Field_Osemiring__1' [96, 1] (w:1, o:139, a:1, s:1
% 0.98/1.34 , b:0),
% 0.98/1.34 'class_Ring__and__Field_Ozero__neq__one' [97, 1] (w:1, o:140, a:1, s:
% 0.98/1.34 1, b:0),
% 0.98/1.34 'class_Ring__and__Field_Osemiring__0' [98, 1] (w:1, o:138, a:1, s:1
% 0.98/1.34 , b:0),
% 0.98/1.34 'c_Lambda_OdB_OAbs' [99, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.98/1.34 'c_Lambda_Oliftn' [100, 3] (w:1, o:203, a:1, s:1, b:0),
% 0.98/1.34 'c_Lambda_Osubstn' [101, 3] (w:1, o:204, a:1, s:1, b:0),
% 0.98/1.34 'tc_Lambda_OdB' [102, 0] (w:1, o:72, a:1, s:1, b:0),
% 0.98/1.34 'c_COMBC' [103, 5] (w:1, o:219, a:1, s:1, b:0),
% 0.98/1.34 'c_List_Omap' [105, 4] (w:1, o:214, a:1, s:1, b:0),
% 0.98/1.34 'c_Type_Otypings' [107, 3] (w:1, o:205, a:1, s:1, b:0),
% 0.98/1.34 'tc_fun' [108, 2] (w:1, o:192, a:1, s:1, b:0),
% 0.98/1.34 hBOOL [110, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.98/1.34 'c_Lambda_OdB_OApp' [111, 0] (w:1, o:74, a:1, s:1, b:0),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3' [112, 1
% 0.98/1.34 ] (w:1, o:144, a:1, s:1, b:0),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4' [113, 1
% 0.98/1.34 ] (w:1, o:145, a:1, s:1, b:0),
% 0.98/1.34 'c_List_Ofoldl' [114, 5] (w:1, o:220, a:1, s:1, b:0),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1' [115, 1
% 0.98/1.34 ] (w:1, o:146, a:1, s:1, b:0),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2' [116, 1
% 0.98/1.34 ] (w:1, o:143, a:1, s:1, b:0),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__Xlem__1__3' [117, 1] (w:1
% 0.98/1.34 , o:148, a:1, s:1, b:0),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__Xlem__1__4' [118, 1] (w:1
% 0.98/1.34 , o:149, a:1, s:1, b:0),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__Xlem__1__1' [119, 1] (w:1
% 0.98/1.34 , o:150, a:1, s:1, b:0),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__Xlem__1__2' [120, 1] (w:1
% 0.98/1.34 , o:147, a:1, s:1, b:0),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__4' [121, 1] (w:1, o:153, a:1, s:1
% 0.98/1.34 , b:0),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__5' [122, 1] (w:1, o:154, a:1, s:1
% 0.98/1.34 , b:0),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__6' [123, 1] (w:1, o:155, a:1, s:1
% 0.98/1.34 , b:0),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__3' [124, 1] (w:1, o:152, a:1, s:1
% 0.98/1.34 , b:0),
% 0.98/1.34 'c_InductTermi_OIT' [125, 0] (w:1, o:75, a:1, s:1, b:0),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__1' [126, 1] (w:1, o:156, a:1, s:1
% 0.98/1.34 , b:0),
% 0.98/1.34 'c_List_Olistsp' [127, 3] (w:1, o:206, a:1, s:1, b:0),
% 0.98/1.34 'c_List_Olist_OCons' [131, 3] (w:1, o:207, a:1, s:1, b:0),
% 0.98/1.34 'c_Lambda_Obeta' [134, 0] (w:1, o:79, a:1, s:1, b:0),
% 0.98/1.34 'c_Transitive__Closure_Ortranclp' [135, 2] (w:1, o:193, a:1, s:1, b:0
% 0.98/1.34 ),
% 0.98/1.34 'c_List_Oappend' [139, 3] (w:1, o:208, a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Omonoid__add' [141, 1] (w:1, o:127, a:1, s:1, b:0
% 0.98/1.34 ),
% 0.98/1.34 'c_List_Olist_ONil' [142, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.98/1.34 'c_List_Olistsum' [143, 2] (w:1, o:194, a:1, s:1, b:0),
% 0.98/1.34 'c_ListOrder_Ostep1' [145, 4] (w:1, o:215, a:1, s:1, b:0),
% 0.98/1.34 'c_Predicate_Oconversep' [146, 3] (w:1, o:209, a:1, s:1, b:0),
% 0.98/1.34 'c_List_Ofoldr' [147, 5] (w:1, o:221, a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Oab__group__add' [151, 1] (w:1, o:128, a:1, s:1
% 0.98/1.34 , b:0),
% 0.98/1.34 'class_OrderedGroup_Oab__semigroup__add' [154, 1] (w:1, o:129, a:1
% 0.98/1.34 , s:1, b:0),
% 0.98/1.34 'c_Lambda_OdB_OdB__case' [162, 5] (w:1, o:222, a:1, s:1, b:0),
% 0.98/1.34 'c_List_Oreplicate' [163, 3] (w:1, o:210, a:1, s:1, b:0),
% 0.98/1.34 'c_Wellfounded_Oaccp' [164, 3] (w:1, o:211, a:1, s:1, b:0),
% 0.98/1.34 'class_Nat_Osemiring__char__0' [166, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.98/1.34
% 0.98/1.34 'class_Ring__and__Field_Oidom' [169, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.98/1.34
% 0.98/1.34 'class_Int_Onumber__ring' [170, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Ocancel__ab__semigroup__add' [171, 1] (w:1, o:130
% 0.98/1.34 , a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Ocancel__semigroup__add' [172, 1] (w:1, o:131, a:
% 0.98/1.34 1, s:1, b:0),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__2' [180, 1] (w:1, o:151, a:1, s:1
% 0.98/1.34 , b:0),
% 0.98/1.34 'c_OrderedGroup_Omonoid__add' [183, 3] (w:1, o:199, a:1, s:1, b:0),
% 0.98/1.34 'class_Ring__and__Field_Ono__zero__divisors' [184, 1] (w:1, o:111, a:
% 0.98/1.34 1, s:1, b:0),
% 0.98/1.34 'class_Ring__and__Field_Omult__zero' [185, 1] (w:1, o:110, a:1, s:1
% 0.98/1.34 , b:0),
% 0.98/1.34 'class_Ring__and__Field_Oring__1__no__zero__divisors' [186, 1] (w:1
% 0.98/1.34 , o:137, a:1, s:1, b:0),
% 0.98/1.34 'class_Ring__and__Field_Oordered__idom' [187, 1] (w:1, o:160, a:1, s:
% 0.98/1.34 1, b:0),
% 0.98/1.34 'c_fequal' [189, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.98/1.34 'c_OrderedGroup_Osemigroup__add' [190, 2] (w:1, o:196, a:1, s:1, b:0)
% 0.98/1.34 ,
% 0.98/1.34 'c_Lambda_OdB_OdB__rec' [191, 5] (w:1, o:223, a:1, s:1, b:0),
% 0.98/1.34 'class_OrderedGroup_Osemigroup__add' [192, 1] (w:1, o:132, a:1, s:1
% 0.98/1.34 , b:0),
% 0.98/1.34 't_a' [193, 0] (w:1, o:92, a:1, s:1, b:0),
% 0.98/1.34 'tc_String_Ochar' [195, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.98/1.34 'c_Nat_Osize__class_Osize' [196, 2] (w:1, o:195, a:1, s:1, b:0),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1' [
% 0.98/1.34 202, 4] (w:1, o:216, a:1, s:1, b:0),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2' [203, 1
% 0.98/1.34 ] (w:1, o:163, a:1, s:1, b:0),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1' [204, 1
% 0.98/1.34 ] (w:1, o:162, a:1, s:1, b:0),
% 0.98/1.34 'c_Type_Osko__Type__Xvar__app__typesE__1__1' [205, 4] (w:1, o:217, a:
% 0.98/1.34 1, s:1, b:0),
% 0.98/1.34 'c_Type_Osko__Type__Xvar__app__types__1__1' [206, 4] (w:1, o:218, a:1
% 0.98/1.34 , s:1, b:0),
% 0.98/1.34 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1' [208, 3] (w:
% 0.98/1.34 1, o:212, a:1, s:1, b:0),
% 0.98/1.34 'c_Lambda_OdB_OdB__size' [212, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.98/1.34 'v_r' [216, 0] (w:1, o:96, a:1, s:1, b:0),
% 0.98/1.34 'v_s' [217, 0] (w:1, o:97, a:1, s:1, b:0),
% 0.98/1.34 'v_ss' [218, 0] (w:1, o:98, a:1, s:1, b:0),
% 0.98/1.34 'v_i' [219, 0] (w:1, o:99, a:1, s:1, b:0),
% 0.98/1.34 'tc_bool' [222, 0] (w:1, o:102, a:1, s:1, b:0).
% 0.98/1.34
% 0.98/1.34
% 0.98/1.34 Starting Search:
% 0.98/1.34
% 0.98/1.34
% 0.98/1.34 Bliksems!, er is een bewijs:
% 0.98/1.34 % SZS status Unsatisfiable
% 0.98/1.34 % SZS output start Refutation
% 0.98/1.34
% 0.98/1.34 clause( 383, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.98/1.34 .
% 0.98/1.34 clause( 411, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.34 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.34 'c_Lambda_Osubstn'( 'v_r', 'v_s', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.34 ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_Lambda_OdB_OVar'(
% 0.98/1.34 'v_i' ) ) ) ) ] )
% 0.98/1.34 .
% 0.98/1.34 clause( 414, [] )
% 0.98/1.34 .
% 0.98/1.34
% 0.98/1.34
% 0.98/1.34 % SZS output end Refutation
% 0.98/1.34 found a proof!
% 0.98/1.34
% 0.98/1.34 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.98/1.34
% 0.98/1.34 initialclauses(
% 0.98/1.34 [ clause( 416, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 0.98/1.34 , clause( 417, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 0.98/1.34 , clause( 418, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.34 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 419, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.98/1.34 , clause( 420, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.98/1.34 =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 0.98/1.34 , T ) ] )
% 0.98/1.34 , clause( 421, [ ~( 'class_Power_Opower'( X ) ), =(
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.34 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.98/1.34 , clause( 422, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.34 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.98/1.34 , clause( 423, [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'(
% 0.98/1.34 'c_Type_Oshift'( X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'(
% 0.98/1.34 X, hAPP( hAPP( hAPP( 'c_Lambda_Osubst', U ), Y ), T ), W ) ] )
% 0.98/1.34 , clause( 424, [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z,
% 0.98/1.34 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_Olift', T ), Y ), U ), ~(
% 0.98/1.34 'c_Type_Otyping'( X, T, U ) ) ] )
% 0.98/1.34 , clause( 425, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 426, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.98/1.34 =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.34 'c_Power_Opower__class_Opower'( T, Z, X ) ) ), =( Y, T ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.98/1.34 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 0.98/1.34 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.98/1.34 , clause( 427, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.98/1.34 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.98/1.34 , Y, X ) ) ] )
% 0.98/1.34 , clause( 428, [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP(
% 0.98/1.34 'c_Lambda_Osubst', X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP(
% 0.98/1.34 'c_Lambda_Osubst', hAPP( hAPP( 'c_Lambda_Olift', X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 0.98/1.34 'tc_nat' ) ) ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), T ) ), Z ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 429, [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP(
% 0.98/1.34 'c_Lambda_Osubst', X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP(
% 0.98/1.34 'c_Lambda_Osubst', hAPP( hAPP( 'c_Lambda_Olift', X ), T ) ), hAPP( hAPP(
% 0.98/1.34 'c_Lambda_Olift', Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 430, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X )
% 0.98/1.34 ), Y ), 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 0.98/1.34 , clause( 431, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.98/1.34 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ] )
% 0.98/1.34 , clause( 432, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.34 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 433, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.34 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.98/1.34 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 434, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.98/1.34 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 0.98/1.34 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.98/1.34 , clause( 435, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.34 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.34 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.98/1.34 , clause( 436, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.34 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.98/1.34 , clause( 437, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.98/1.34 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.98/1.34 , clause( 438, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.98/1.34 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.98/1.34 , clause( 439, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.98/1.34 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 0.98/1.34 Y, Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 440, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.98/1.34 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 0.98/1.34 Y, T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 441, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 0.98/1.34 , clause( 442, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.98/1.34 , clause( 443, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.98/1.34 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.98/1.34 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.98/1.34 , clause( 444, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.98/1.34 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.98/1.34 , clause( 445, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 0.98/1.34 , clause( 446, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.98/1.34 , clause( 447, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 0.98/1.34 , clause( 448, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.98/1.34 , clause( 449, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 0.98/1.34 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 0.98/1.34 , clause( 450, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 0.98/1.34 Y, Z ) ] )
% 0.98/1.34 , clause( 451, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.98/1.34 , X ) ) ] )
% 0.98/1.34 , clause( 452, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.98/1.34 , X ) ) ] )
% 0.98/1.34 , clause( 453, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.98/1.34 , clause( 454, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 0.98/1.34 Z, Y ) ] )
% 0.98/1.34 , clause( 455, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 0.98/1.34 , X ) ) ] )
% 0.98/1.34 , clause( 456, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.98/1.34 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 0.98/1.34 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ] )
% 0.98/1.34 , clause( 457, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 458, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 0.98/1.34 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 459, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 Y, X ) ] )
% 0.98/1.34 , clause( 460, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y,
% 0.98/1.34 X ) ] )
% 0.98/1.34 , clause( 461, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 462, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.98/1.34 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 0.98/1.34 , clause( 463, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.98/1.34 , clause( 464, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z,
% 0.98/1.34 X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 0.98/1.34 , clause( 465, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U )
% 0.98/1.34 ), ~( 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 466, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 0.98/1.34 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 0.98/1.34 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.98/1.34 'c_lessequals'( Z, T, X ) ) ] )
% 0.98/1.34 , clause( 467, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 0.98/1.34 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 0.98/1.34 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.98/1.34 'c_lessequals'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 468, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.98/1.34 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 0.98/1.34 , clause( 469, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.98/1.34 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.98/1.34 'c_lessequals'( Z, T, X ) ) ] )
% 0.98/1.34 , clause( 470, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.98/1.34 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 0.98/1.34 , clause( 471, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.98/1.34 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.98/1.34 'c_lessequals'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 472, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.98/1.34 , clause( 473, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z,
% 0.98/1.34 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.98/1.34 , clause( 474, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 0.98/1.34 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 0.98/1.34 , clause( 475, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 0.98/1.34 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.98/1.34 , clause( 476, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 0.98/1.34 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.98/1.34 , clause( 477, [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.98/1.34 ) ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 478, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.98/1.34 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 X ), X ) ) ] )
% 0.98/1.34 , clause( 479, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 0.98/1.34 'c_lessequals'( Y, Z, X ) ) ] )
% 0.98/1.34 , clause( 480, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'(
% 0.98/1.34 X ), X ) ] )
% 0.98/1.34 , clause( 481, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ] )
% 0.98/1.34 , clause( 482, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z,
% 0.98/1.34 X ) ) ] )
% 0.98/1.34 , clause( 483, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z,
% 0.98/1.34 X ) ) ] )
% 0.98/1.34 , clause( 484, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.98/1.34 X ) ) ] )
% 0.98/1.34 , clause( 485, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.98/1.34 X ) ) ] )
% 0.98/1.34 , clause( 486, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.98/1.34 X ) ) ] )
% 0.98/1.34 , clause( 487, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.98/1.34 X ) ) ] )
% 0.98/1.34 , clause( 488, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z,
% 0.98/1.34 X ) ) ] )
% 0.98/1.34 , clause( 489, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z,
% 0.98/1.34 X ) ) ] )
% 0.98/1.34 , clause( 490, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.98/1.34 X ), Y ) ] )
% 0.98/1.34 , clause( 491, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.98/1.34 X ), Y ) ] )
% 0.98/1.34 , clause( 492, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 Z, X ), 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ] )
% 0.98/1.34 , clause( 493, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ] )
% 0.98/1.34 , clause( 494, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ] )
% 0.98/1.34 , clause( 495, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.98/1.34 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 496, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.98/1.34 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 497, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.98/1.34 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 498, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 0.98/1.34 , clause( 499, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 0.98/1.34 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 0.98/1.34 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.98/1.34 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 500, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 0.98/1.34 X ) ) ] )
% 0.98/1.34 , clause( 501, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 502, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 0.98/1.34 X ) ) ] )
% 0.98/1.34 , clause( 503, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.98/1.34 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.98/1.34 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.98/1.34 , clause( 504, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 0.98/1.34 , clause( 505, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 0.98/1.34 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.98/1.34 , clause( 506, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 0.98/1.34 , clause( 507, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 508, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.98/1.34 Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 0.98/1.34 , clause( 509, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 0.98/1.34 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 0.98/1.34 , clause( 510, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 0.98/1.34 , clause( 511, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 0.98/1.34 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 0.98/1.34 , clause( 512, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.98/1.34 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.98/1.34 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.98/1.34 , clause( 513, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.98/1.34 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 0.98/1.34 , clause( 514, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ] )
% 0.98/1.34 , clause( 515, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.98/1.34 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.98/1.34 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z
% 0.98/1.34 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.98/1.34 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.98/1.34 , clause( 516, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.98/1.34 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.98/1.34 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.98/1.34 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.98/1.34 , clause( 517, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.98/1.34 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.98/1.34 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.98/1.34 , clause( 518, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.98/1.34 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.98/1.34 , clause( 519, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.98/1.34 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.98/1.34 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.98/1.34 , clause( 520, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.98/1.34 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.98/1.34 , clause( 521, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.98/1.34 'c_HOL_Oone__class_Oone'( X ) ), X ) ] )
% 0.98/1.34 , clause( 522, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 0.98/1.34 Z, T, X ), X ) ) ] )
% 0.98/1.34 , clause( 523, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.98/1.34 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.34 X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.98/1.34 , clause( 524, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.98/1.34 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.98/1.34 X ), T, X ) ) ] )
% 0.98/1.34 , clause( 525, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 526, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.98/1.34 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.98/1.34 X ), T, X ) ) ] )
% 0.98/1.34 , clause( 527, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 0.98/1.34 , clause( 528, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OAbs'( X )
% 0.98/1.34 ), Y ), 'c_Lambda_OdB_OAbs'( hAPP( hAPP( 'c_Lambda_Olift', X ), hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 0.98/1.34 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ) ) ] )
% 0.98/1.34 , clause( 529, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ),
% 0.98/1.34 'c_Lambda_OdB_OAbs'( 'c_Lambda_Oliftn'( X, Y, hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.98/1.34 'tc_nat' ) ) ) ) ) ] )
% 0.98/1.34 , clause( 530, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 0.98/1.34 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubstn'( X, Y, hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.98/1.34 'tc_nat' ) ) ) ) ) ] )
% 0.98/1.34 , clause( 531, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.34 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.98/1.34 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.98/1.34 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 532, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.34 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z ), 'c_Lambda_OdB_OAbs'( hAPP( hAPP(
% 0.98/1.34 hAPP( 'c_Lambda_Osubst', X ), hAPP( hAPP( 'c_Lambda_Olift', Y ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.98/1.34 'tc_nat' ) ) ) ) ) ] )
% 0.98/1.34 , clause( 533, [ 'c_Type_Otypings'( 'c_Type_Oshift'( X, Y, Z,
% 0.98/1.34 'tc_Type_Otype' ), 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Y,
% 0.98/1.34 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB',
% 0.98/1.34 'tc_Lambda_OdB' ), U ), ~( 'c_Type_Otypings'( X, T, U ) ) ] )
% 0.98/1.34 , clause( 534, [ 'c_Type_Otypings'( X, 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.98/1.34 'c_Lambda_Osubst', Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.98/1.34 'tc_nat', 'tc_Lambda_OdB' ) ), Z, 'tc_Lambda_OdB', 'tc_nat',
% 0.98/1.34 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 0.98/1.34 'c_Type_Otypings'( 'c_Type_Oshift'( X, Z, W, 'tc_Type_Otype' ), T, U ) )
% 0.98/1.34 , ~( 'c_Type_Otyping'( X, Y, W ) ) ] )
% 0.98/1.34 , clause( 535, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'(
% 0.98/1.34 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3'( X ) )
% 0.98/1.34 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4'( X )
% 0.98/1.34 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.98/1.34 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1'( X ) )
% 0.98/1.34 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2'( X )
% 0.98/1.34 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.98/1.34 , clause( 536, [ ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.34 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__Xlem__1__3'( X ) ),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__Xlem__1__4'( X ),
% 0.98/1.34 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.98/1.34 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__Xlem__1__1'( X ) ),
% 0.98/1.34 'c_ListApplication_Osko__ListApplication__Xlem__1__2'( X ),
% 0.98/1.34 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( X, Y ) ) ] )
% 0.98/1.34 , clause( 537, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.34 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) )
% 0.98/1.34 ), =( X, Z ) ] )
% 0.98/1.34 , clause( 538, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.34 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) )
% 0.98/1.34 ), =( Y, Z ) ] )
% 0.98/1.34 , clause( 539, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.34 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.98/1.34 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.98/1.34 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.98/1.34 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.34 , clause( 540, [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U
% 0.98/1.34 ), 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U )
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 541, [ =( 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z
% 0.98/1.34 , T, U ), U ), 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U )
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 542, [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U
% 0.98/1.34 ), 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U )
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 543, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.98/1.34 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP(
% 0.98/1.34 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.98/1.34 'tc_Lambda_OdB' ), X ), Z ) ) ) ] )
% 0.98/1.34 , clause( 544, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.98/1.34 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP(
% 0.98/1.34 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.98/1.34 'tc_Lambda_OdB' ), Y ), Z ) ) ) ] )
% 0.98/1.34 , clause( 545, [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z
% 0.98/1.34 ), 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.98/1.34 , clause( 546, [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z
% 0.98/1.34 ), 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.98/1.34 , clause( 547, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.98/1.34 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.98/1.34 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.98/1.34 , clause( 548, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.98/1.34 'c_List_Olistsum'( 'c_List_Olist_ONil'( X ), X ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.98/1.34 , clause( 549, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ] )
% 0.98/1.34 , clause( 550, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ] )
% 0.98/1.34 , clause( 551, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 0.98/1.34 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 552, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 0.98/1.34 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.98/1.34 , clause( 553, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 0.98/1.34 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 554, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 0.98/1.34 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.98/1.34 , clause( 555, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_ListOrder_Ostep1'( X
% 0.98/1.34 , T, U, W ), ~( 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( T,
% 0.98/1.34 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( W ), W ), W ),
% 0.98/1.34 'c_List_Oappend'( U, 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W
% 0.98/1.34 ), W ), W ) ) ] )
% 0.98/1.34 , clause( 556, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Predicate_Oconversep'( X, Y, Y ), Y ), Z ), T ) ), ~( hBOOL( hAPP(
% 0.98/1.34 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), T ), Z ) ) ) ] )
% 0.98/1.34 , clause( 557, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.98/1.34 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Predicate_Oconversep'( X, Y, Y ), Y ), T ), Z ) ) ) ] )
% 0.98/1.34 , clause( 558, [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 0.98/1.34 'c_List_Olist_ONil'( Z ) ) ] )
% 0.98/1.34 , clause( 559, [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T )
% 0.98/1.34 , Z ) ] )
% 0.98/1.34 , clause( 560, [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W
% 0.98/1.34 ), Y ) ) ] )
% 0.98/1.34 , clause( 561, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ] )
% 0.98/1.34 , clause( 562, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.34 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ] )
% 0.98/1.34 , clause( 563, [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T
% 0.98/1.34 ), U ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ] )
% 0.98/1.34 , clause( 564, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.34 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ] )
% 0.98/1.34 , clause( 565, [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T
% 0.98/1.34 ), U ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ] )
% 0.98/1.34 , clause( 566, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 567, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.98/1.34 , clause( 568, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.98/1.34 , clause( 569, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 X ), Y ), T ) ), Z ) ) ] )
% 0.98/1.34 , clause( 570, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 X ), Y ), Z ) ), T ) ) ] )
% 0.98/1.34 , clause( 571, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.98/1.34 , clause( 572, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.98/1.34 , clause( 573, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.98/1.34 , clause( 574, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ] )
% 0.98/1.34 , clause( 575, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.98/1.34 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ] )
% 0.98/1.34 , clause( 576, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.98/1.34 , clause( 577, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 X ), Y ), Z ) ), T ) ) ] )
% 0.98/1.34 , clause( 578, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.98/1.34 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.98/1.34 , clause( 579, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 0.98/1.34 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 580, [ ~( 'c_ListOrder_Ostep1'( X, Y, Z, T ) ),
% 0.98/1.34 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( Y, U, T ), 'c_List_Oappend'( Z
% 0.98/1.34 , U, T ), T ) ] )
% 0.98/1.34 , clause( 581, [ 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( Y, Z, T ),
% 0.98/1.34 'c_List_Oappend'( Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T ) )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 582, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ),
% 0.98/1.34 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.34 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.98/1.34 ), Y ) ) ) ] )
% 0.98/1.34 , clause( 583, [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X,
% 0.98/1.34 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.98/1.34 , clause( 584, [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X,
% 0.98/1.34 'c_List_Oappend'( T, Y, Z ), Z ) ) ] )
% 0.98/1.34 , clause( 585, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 T ), U ), hAPP( Z, T ) ) ] )
% 0.98/1.34 , clause( 586, [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U,
% 0.98/1.34 'c_List_Olist_OCons'( Y, T, W ), 'c_List_Olist_OCons'( X, Z, W ), W ) ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 587, [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ),
% 0.98/1.34 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( Y, T, U ),
% 0.98/1.34 'c_List_Olist_OCons'( Z, T, U ), U ) ] )
% 0.98/1.34 , clause( 588, [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ] )
% 0.98/1.34 , clause( 589, [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'(
% 0.98/1.34 T, U, Z ) ) ), =( X, T ) ] )
% 0.98/1.34 , clause( 590, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, Y
% 0.98/1.34 , Z ) ) ), =( X, T ) ] )
% 0.98/1.34 , clause( 591, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( X, T
% 0.98/1.34 , Z ) ) ), =( Y, T ) ] )
% 0.98/1.34 , clause( 592, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T,
% 0.98/1.34 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 593, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.98/1.34 ), Z ), Z ) ) ] )
% 0.98/1.34 , clause( 594, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.98/1.34 ), Z ), Z ) ) ] )
% 0.98/1.34 , clause( 595, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.34 'c_Transitive__Closure_Ortranclp'( X, Z ), Y ), T ) ) ), ~(
% 0.98/1.34 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 0.98/1.34 , clause( 596, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( 'c_Wellfounded_Oaccp'(
% 0.98/1.34 X, T, Z ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X,
% 0.98/1.34 Z ), Y ), T ) ) ) ] )
% 0.98/1.34 , clause( 597, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.98/1.34 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 X, Y ), U ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.34 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ] )
% 0.98/1.34 , clause( 598, [ 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'(
% 0.98/1.34 'c_Lambda_Obeta', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB'
% 0.98/1.34 ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.34 , clause( 599, [ hBOOL( hAPP( 'c_InductTermi_OIT', X ) ), ~(
% 0.98/1.34 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.98/1.34 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.34 , clause( 600, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.98/1.34 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.98/1.34 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.34 , clause( 601, [ =( 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ), X )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 602, [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 603, [ =( X, 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ) )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 604, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), Y, X ), Y )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 605, [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 606, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.98/1.34 , X ), Y ), Z ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), T ), Z ) ) )
% 0.98/1.34 , ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', Y ), T ) ) ) ] )
% 0.98/1.34 , clause( 607, [ =( 'c_List_Omap'( X, 'c_List_Oreplicate'( Y, Z, T ), T, U
% 0.98/1.34 ), 'c_List_Oreplicate'( Y, hAPP( X, Z ), U ) ) ] )
% 0.98/1.34 , clause( 608, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 609, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 610, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 611, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 612, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 613, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.98/1.34 , clause( 614, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.98/1.34 , clause( 615, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.98/1.34 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 616, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.34 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) )
% 0.98/1.34 ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, T, 'tc_nat' ) ] )
% 0.98/1.34 , clause( 617, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.98/1.34 , clause( 618, [ =( 'c_List_Ofoldr'( X, 'c_List_Oappend'( Y, Z, T ), U, T,
% 0.98/1.34 W ), 'c_List_Ofoldr'( X, Y, 'c_List_Ofoldr'( X, Z, U, T, W ), T, W ) ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 619, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), =( Y, Z ), ~(
% 0.98/1.34 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y,
% 0.98/1.34 'c_List_Olist_ONil'( U ), U ), U ), 'c_List_Oappend'( W,
% 0.98/1.34 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( U ), U ), U ), U ) ) ] )
% 0.98/1.34 , clause( 620, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.98/1.34 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.98/1.34 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 0.98/1.34 , clause( 621, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X
% 0.98/1.34 ) ) ), =( Z, 'c_List_Olist_ONil'( T ) ) ] )
% 0.98/1.34 , clause( 622, [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y
% 0.98/1.34 , Z ), U ) ), hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 'tc_nat' ), T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y,
% 0.98/1.34 V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 623, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.98/1.34 , X ), Y ), Z ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', T ), Y ), Z ) ) )
% 0.98/1.34 , ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), T ) ) ) ] )
% 0.98/1.34 , clause( 624, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.98/1.34 , X ), Y ), Z ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), T ), Z ) ) )
% 0.98/1.34 , ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y ), T ) ) ) ] )
% 0.98/1.34 , clause( 625, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.98/1.34 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ),
% 0.98/1.34 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ] )
% 0.98/1.34 , clause( 626, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.98/1.34 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( X, Z ), T ) ) ) ] )
% 0.98/1.34 , clause( 627, [ ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_ONil'( Y ), Z, Y
% 0.98/1.34 ) ) ] )
% 0.98/1.34 , clause( 628, [ ~( 'c_ListOrder_Ostep1'( X, Y, 'c_List_Olist_ONil'( Z ), Z
% 0.98/1.34 ) ) ] )
% 0.98/1.34 , clause( 629, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.34 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.98/1.34 , clause( 630, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.34 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.98/1.34 , clause( 631, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.34 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) )
% 0.98/1.34 ), =( Y, Z ) ] )
% 0.98/1.34 , clause( 632, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.98/1.34 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.98/1.34 , clause( 633, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) )
% 0.98/1.34 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.98/1.34 , clause( 634, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.98/1.34 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.98/1.34 , clause( 635, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.98/1.34 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ] )
% 0.98/1.34 , clause( 636, [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T
% 0.98/1.34 ), 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ] )
% 0.98/1.34 , clause( 637, [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T
% 0.98/1.34 ), 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ] )
% 0.98/1.34 , clause( 638, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'(
% 0.98/1.34 Z ) ) ) ] )
% 0.98/1.34 , clause( 639, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'(
% 0.98/1.34 Z ) ) ) ] )
% 0.98/1.34 , clause( 640, [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP(
% 0.98/1.34 hAPP( Y, hAPP( hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 641, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP(
% 0.98/1.34 hAPP( Z, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 642, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ] )
% 0.98/1.34 , clause( 643, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 0.98/1.34 hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( U, X, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 644, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, Y, V0 ) ) ] )
% 0.98/1.34 , clause( 645, [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( T, X, U, Y, W, V0 ) ) ] )
% 0.98/1.34 , clause( 646, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ] )
% 0.98/1.34 , clause( 647, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 0.98/1.34 hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, U, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 648, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, T, U, Y, W, V0 ) ) ] )
% 0.98/1.34 , clause( 649, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 0.98/1.34 hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, U, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 650, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ] )
% 0.98/1.34 , clause( 651, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 0.98/1.34 hAPP( X, hAPP( hAPP( X, Y ), T ) ), Z ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, U, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 652, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 0.98/1.34 hAPP( X, Z ), hAPP( hAPP( X, Y ), T ) ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, U, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 653, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 0.98/1.34 hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, U, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 654, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X
% 0.98/1.34 , T ), U ) ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z
% 0.98/1.34 ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 )
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 655, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 0.98/1.34 hAPP( X, Z ), hAPP( hAPP( X, Y ), T ) ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( U, X, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 656, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 0.98/1.34 hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( U, X, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 657, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 0.98/1.34 hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( U, X, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 658, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 0.98/1.34 hAPP( X, hAPP( hAPP( X, Y ), T ) ), Z ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( U, X, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 659, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X
% 0.98/1.34 , T ), U ) ), hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z )
% 0.98/1.34 ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 )
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 660, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X
% 0.98/1.34 , T ), U ) ), hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T )
% 0.98/1.34 , U ) ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 )
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 661, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X
% 0.98/1.34 , T ), U ) ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z
% 0.98/1.34 ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 )
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 662, [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, Z, V0 ) ) ] )
% 0.98/1.34 , clause( 663, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, Y, V0 ) ) ] )
% 0.98/1.34 , clause( 664, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( T, X, U, Z, W, V0 ) ) ] )
% 0.98/1.34 , clause( 665, [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( T, X, U, Y, W, V0 ) ) ] )
% 0.98/1.34 , clause( 666, [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP(
% 0.98/1.34 hAPP( Y, hAPP( hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 667, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ] )
% 0.98/1.34 , clause( 668, [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, T, U, Z, W, V0 ) ) ] )
% 0.98/1.34 , clause( 669, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, T, U, Y, W, V0 ) ) ] )
% 0.98/1.34 , clause( 670, [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X,
% 0.98/1.34 T ), T ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T,
% 0.98/1.34 V0 ) ) ] )
% 0.98/1.34 , clause( 671, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP(
% 0.98/1.34 hAPP( Z, hAPP( hAPP( X, T ), U ) ), Y ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, Z, W, V0, U, V1 ) ) ] )
% 0.98/1.34 , clause( 672, [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP(
% 0.98/1.34 hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, U, V1 ) ) ] )
% 0.98/1.34 , clause( 673, [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y
% 0.98/1.34 , U ), T ) ), hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 0.98/1.34 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ] )
% 0.98/1.34 , clause( 674, [ =( X, Y ), hBOOL( hAPP( hAPP( Z, Y ), X ) ), ~(
% 0.98/1.34 'c_ListOrder_Ostep1'( Z, 'c_List_Olist_OCons'( Y, T, U ),
% 0.98/1.34 'c_List_Olist_OCons'( X, W, U ), U ) ) ] )
% 0.98/1.34 , clause( 675, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) )
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 676, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.98/1.34 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), ~( hBOOL( hAPP(
% 0.98/1.34 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.98/1.34 'tc_Lambda_OdB' ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.34 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.98/1.34 ), Z ) ) ) ] )
% 0.98/1.34 , clause( 677, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.98/1.34 , clause( 678, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 0.98/1.34 Z, Y, X ) ) ] )
% 0.98/1.34 , clause( 679, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.98/1.34 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.98/1.34 ) ) ] )
% 0.98/1.34 , clause( 680, [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Type_Otyping'( X, T, Z
% 0.98/1.34 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), T ), Y ) ) ) ] )
% 0.98/1.34 , clause( 681, [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ), X, Y ), 'c_List_Olist_ONil'( Y ) ) ] )
% 0.98/1.34 , clause( 682, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X )
% 0.98/1.34 ), Y ), 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.98/1.34 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 683, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.98/1.34 'c_Lambda_Olift', X ), Y ) ), hAPP( hAPP( 'c_Lambda_Olift', Z ), Y ) ) )
% 0.98/1.34 , ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ] )
% 0.98/1.34 , clause( 684, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ] )
% 0.98/1.34 , clause( 685, [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ] )
% 0.98/1.34 , clause( 686, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.34 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.98/1.34 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.98/1.34 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.98/1.34 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.34 , clause( 687, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 0.98/1.34 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'(
% 0.98/1.34 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.98/1.34 , clause( 688, [ =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Oappend'(
% 0.98/1.34 'c_List_Olist_ONil'( Z ), 'c_List_Olist_OCons'( X, Y, Z ), Z ) ) ] )
% 0.98/1.34 , clause( 689, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ), T ),
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.98/1.34 ), Y ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X )
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 690, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y,
% 0.98/1.34 'c_List_Olist_ONil'( Z ), Z, X ) ) ] )
% 0.98/1.34 , clause( 691, [ =( X, Y ), 'c_ListOrder_Ostep1'( Z, X, Y, T ), ~(
% 0.98/1.34 'c_ListOrder_Ostep1'( Z, 'c_List_Oappend'( X, 'c_List_Olist_OCons'( U,
% 0.98/1.34 'c_List_Olist_ONil'( T ), T ), T ), 'c_List_Oappend'( Y,
% 0.98/1.34 'c_List_Olist_OCons'( W, 'c_List_Olist_ONil'( T ), T ), T ), T ) ) ] )
% 0.98/1.34 , clause( 692, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.98/1.34 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 0.98/1.34 , clause( 693, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.98/1.34 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 0.98/1.34 , clause( 694, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'(
% 0.98/1.34 'c_List_Olist_ONil'( X ), 'c_List_Olist_ONil'( X ), X ) ) ] )
% 0.98/1.34 , clause( 695, [ =( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Transitive__Closure_Ortranclp'( X, Y ), Y ),
% 0.98/1.34 'c_Transitive__Closure_Ortranclp'( X, Y ) ) ] )
% 0.98/1.34 , clause( 696, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 X ) ), 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.34 'c_Lambda_Obeta', X ), Y ) ) ) ] )
% 0.98/1.34 , clause( 697, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.98/1.34 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ] )
% 0.98/1.34 , clause( 698, [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.98/1.34 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( Z ), Z ), Z ),
% 0.98/1.34 'c_List_Olist_OCons'( Y, 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ] )
% 0.98/1.34 , clause( 699, [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~(
% 0.98/1.34 'c_OrderedGroup_Omonoid__add'( Z, X, T ) ) ] )
% 0.98/1.34 , clause( 700, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 0.98/1.34 'c_OrderedGroup_Omonoid__add'( Y, X, T ) ) ] )
% 0.98/1.34 , clause( 701, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.98/1.34 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 702, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.98/1.34 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 703, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 0.98/1.34 , clause( 704, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.98/1.34 , clause( 705, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.98/1.34 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.98/1.34 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.34 , clause( 706, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.98/1.34 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.98/1.34 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.98/1.34 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.98/1.34 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.34 , clause( 707, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.98/1.34 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.98/1.34 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.98/1.34 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.98/1.34 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.34 , clause( 708, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.98/1.34 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.98/1.34 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.98/1.34 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.98/1.34 ) ) ] )
% 0.98/1.34 , clause( 709, [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.98/1.34 X ) ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.98/1.34 ) ) ] )
% 0.98/1.34 , clause( 710, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.34 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.98/1.34 ) ) ] )
% 0.98/1.34 , clause( 711, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.98/1.34 'class_Int_Onumber__ring'( X ) ), ~( =( Y, hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), =( Z,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.98/1.34 , clause( 712, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.98/1.34 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.98/1.34 , clause( 713, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 X ) ), Y ), Y ) ] )
% 0.98/1.34 , clause( 714, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.98/1.34 , Y ), Y ) ] )
% 0.98/1.34 , clause( 715, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.98/1.34 'class_Int_Onumber__ring'( X ) ), =( Y, hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 716, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 0.98/1.34 ) ), Y ) ] )
% 0.98/1.34 , clause( 717, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.98/1.34 Y ) ] )
% 0.98/1.34 , clause( 718, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.98/1.34 Y ) ] )
% 0.98/1.34 , clause( 719, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 0.98/1.34 , clause( 720, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.98/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 X ) ), Y ), Y ) ] )
% 0.98/1.34 , clause( 721, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 722, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.98/1.34 ), X, Y ), X ) ] )
% 0.98/1.34 , clause( 723, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 724, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.34 X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 725, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.34 X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 726, [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.98/1.34 ), X ), Y ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 727, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.34 X ), Y ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 728, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 729, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 730, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 731, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.34 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.98/1.34 , clause( 732, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.34 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.98/1.34 , clause( 733, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.98/1.34 , clause( 734, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Y, T, X
% 0.98/1.34 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( T, Z
% 0.98/1.34 , X ), X ) ) ] )
% 0.98/1.34 , clause( 735, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.98/1.34 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.98/1.34 'tc_nat' ) ] )
% 0.98/1.34 , clause( 736, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X
% 0.98/1.34 ) ) ), =( Y, 'c_List_Olist_ONil'( X ) ) ] )
% 0.98/1.34 , clause( 737, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X
% 0.98/1.34 ) ) ), =( Z, 'c_List_Olist_ONil'( X ) ) ] )
% 0.98/1.34 , clause( 738, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.98/1.34 ), =( X, Y ) ] )
% 0.98/1.34 , clause( 739, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z
% 0.98/1.34 ) ) ), =( X, 'c_List_Olist_ONil'( Z ) ) ] )
% 0.98/1.34 , clause( 740, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z
% 0.98/1.34 ) ) ), =( Y, 'c_List_Olist_ONil'( Z ) ) ] )
% 0.98/1.34 , clause( 741, [ =( 'c_Predicate_Oconversep'( 'c_fequal'( X ), X, X ),
% 0.98/1.34 'c_fequal'( X ) ) ] )
% 0.98/1.34 , clause( 742, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), hBOOL( hAPP(
% 0.98/1.34 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ),
% 0.98/1.34 'c_List_Olistsp'( 'c_InductTermi_OIT',
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB' ), ~( hBOOL(
% 0.98/1.34 hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.34 , clause( 743, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'(
% 0.98/1.34 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, X ) ) ] )
% 0.98/1.34 , clause( 744, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 745, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 746, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.98/1.34 , clause( 747, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.98/1.34 , clause( 748, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.98/1.34 , clause( 749, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.98/1.34 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.34 Y ), X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ] )
% 0.98/1.34 , clause( 750, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.34 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 0.98/1.34 ) ), hAPP( hAPP( 'c_Lambda_Olift', Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.34 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.98/1.34 ), Z ) ) ) ] )
% 0.98/1.34 , clause( 751, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.98/1.34 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.98/1.34 , clause( 752, [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), =( Z, Y ), ~(
% 0.98/1.34 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( U, Y, T ),
% 0.98/1.34 'c_List_Olist_OCons'( W, Z, T ), T ) ) ] )
% 0.98/1.34 , clause( 753, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 0.98/1.34 hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ) ), ~(
% 0.98/1.34 'c_OrderedGroup_Osemigroup__add'( X, U ) ) ] )
% 0.98/1.34 , clause( 754, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.98/1.34 'c_List_Olistsum'( 'c_List_Olist_OCons'( Y, Z, X ), X ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Olistsum'( Z, X ) ) ) ] )
% 0.98/1.34 , clause( 755, [ =( 'c_List_Omap'( X, 'c_List_Oappend'( Y, Z, T ), T, U ),
% 0.98/1.34 'c_List_Oappend'( 'c_List_Omap'( X, Y, T, U ), 'c_List_Omap'( X, Z, T, U
% 0.98/1.34 ), U ) ) ] )
% 0.98/1.34 , clause( 756, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.98/1.34 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.34 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.98/1.34 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.98/1.34 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.98/1.34 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.34 , clause( 757, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.98/1.34 ), =( Z, Y ) ] )
% 0.98/1.34 , clause( 758, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 759, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 0.98/1.34 , clause( 760, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), =( Z, Y ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ] )
% 0.98/1.34 , clause( 761, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 0.98/1.34 , clause( 762, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.98/1.34 ), =( Z, Y ) ] )
% 0.98/1.34 , clause( 763, [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.98/1.34 'c_List_Oreplicate'( T, Y, Z ), Z ), 'c_List_Oappend'(
% 0.98/1.34 'c_List_Oreplicate'( T, Y, Z ), 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 764, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 0.98/1.34 , clause( 765, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 766, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.98/1.34 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ] )
% 0.98/1.34 , clause( 767, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.34 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.98/1.34 T, X ) ) ] )
% 0.98/1.34 , clause( 768, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 769, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y, Z
% 0.98/1.34 , X ) ) ) ] )
% 0.98/1.34 , clause( 770, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.98/1.34 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 771, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.98/1.34 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.98/1.34 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 0.98/1.34 , clause( 772, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.98/1.34 'c_List_Olistsum'( Y, X ), 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X
% 0.98/1.34 ), Y, 'c_HOL_Ozero__class_Ozero'( X ), X, X ) ) ] )
% 0.98/1.34 , clause( 773, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.34 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.98/1.34 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.98/1.34 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.98/1.34 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.34 , clause( 774, [ =( 'c_List_Oreplicate'( hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, T ),
% 0.98/1.34 'c_List_Oappend'( 'c_List_Oreplicate'( X, Z, T ), 'c_List_Oreplicate'( Y
% 0.98/1.34 , Z, T ), T ) ) ] )
% 0.98/1.34 , clause( 775, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.98/1.34 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.98/1.34 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 776, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.98/1.34 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.34 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 0.98/1.34 , clause( 777, [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U,
% 0.98/1.34 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W
% 0.98/1.34 ), W ), 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( T,
% 0.98/1.34 'c_List_Olist_ONil'( W ), W ), W ), W ) ) ] )
% 0.98/1.34 , clause( 778, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_List_Ofoldl'(
% 0.98/1.34 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ),
% 0.98/1.34 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_Olift', X ),
% 0.98/1.34 Z ), 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Z, 'tc_Lambda_OdB',
% 0.98/1.34 'tc_nat', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.98/1.34 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.34 , clause( 779, [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Olist_ONil'(
% 0.98/1.34 Z ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 780, [ 'c_List_Olistsp'( X, 'c_List_Oappend'( Y, Z, T ), T ), ~(
% 0.98/1.34 'c_List_Olistsp'( X, Z, T ) ), ~( 'c_List_Olistsp'( X, Y, T ) ) ] )
% 0.98/1.34 , clause( 781, [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 T ), U ), hAPP( hAPP( Z, T ), 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, U ) )
% 0.98/1.34 ) ] )
% 0.98/1.34 , clause( 782, [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ),
% 0.98/1.34 'c_OrderedGroup_Osemigroup__add'( 'c_HOL_Oplus__class_Oplus'( X ), X ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 783, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'( Y, Z
% 0.98/1.34 , X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 784, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.98/1.34 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.98/1.34 , clause( 785, [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_OCons'( Y, Z, T ), U
% 0.98/1.34 , T, W ), hAPP( hAPP( X, Y ), 'c_List_Ofoldr'( X, Z, U, T, W ) ) ) ] )
% 0.98/1.34 , clause( 786, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.98/1.34 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 787, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.98/1.34 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.98/1.34 ] )
% 0.98/1.34 , clause( 788, [ =( 'c_Predicate_Oconversep'( 'c_Predicate_Oconversep'( X,
% 0.98/1.34 Y, Z ), Z, Y ), X ) ] )
% 0.98/1.34 , clause( 789, [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 790, [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 791, [ ~( =( 'c_List_Oappend'( X, Y, Z ), X ) ), =( Y,
% 0.98/1.34 'c_List_Olist_ONil'( Z ) ) ] )
% 0.98/1.34 , clause( 792, [ ~( =( X, 'c_List_Oappend'( X, Y, Z ) ) ), =( Y,
% 0.98/1.34 'c_List_Olist_ONil'( Z ) ) ] )
% 0.98/1.34 , clause( 793, [ ~( =( 'c_List_Oappend'( X, Y, Z ), Y ) ), =( X,
% 0.98/1.34 'c_List_Olist_ONil'( Z ) ) ] )
% 0.98/1.34 , clause( 794, [ ~( =( X, 'c_List_Oappend'( Y, X, Z ) ) ), =( Y,
% 0.98/1.34 'c_List_Olist_ONil'( Z ) ) ] )
% 0.98/1.34 , clause( 795, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ),
% 0.98/1.34 'c_List_Olist_OCons'( Y, Z, X ), X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ]
% 0.98/1.34 )
% 0.98/1.34 , clause( 796, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.34 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 797, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.34 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.98/1.34 , clause( 798, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 0.98/1.34 , clause( 799, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.34 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.98/1.34 , clause( 800, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.98/1.34 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.98/1.34 , clause( 801, [ ~(
% 0.98/1.34 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.98/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 0.98/1.34 , clause( 802, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 803, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.98/1.34 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.98/1.34 , Z ), Y ), 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 804, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.98/1.34 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 0.98/1.34 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 0.98/1.34 , clause( 805, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.34 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.98/1.34 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.34 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.98/1.34 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.98/1.34 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.34 , clause( 806, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 0.98/1.34 'c_List_Olist_OCons'( T, U, Z ) ) ), =( X, T ) ] )
% 0.98/1.34 , clause( 807, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 0.98/1.34 'c_List_Olist_OCons'( T, U, Z ) ) ), =( Y, U ) ] )
% 0.98/1.34 , clause( 808, [ 'c_Type_Otyping'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.34 'c_Lambda_Obeta', T ), Y ) ) ), ~( 'c_Type_Otyping'( X, T, Z ) ) ] )
% 0.98/1.34 , clause( 809, [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), hBOOL( hAPP( hAPP( X,
% 0.98/1.34 U ), W ) ), ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( U, Y, T ),
% 0.98/1.34 'c_List_Olist_OCons'( W, Z, T ), T ) ) ] )
% 0.98/1.34 , clause( 810, [ 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 0.98/1.34 'c_List_Olist_OCons'( Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T
% 0.98/1.34 ) ) ] )
% 0.98/1.34 , clause( 811, [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.98/1.35 'c_List_Olist_OCons'( Y, T, Z ), Z ), 'c_List_Olist_OCons'( Y,
% 0.98/1.35 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ), T, Z ), Z ) ) ] )
% 0.98/1.35 , clause( 812, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.98/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.98/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.98/1.35 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.98/1.35 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ] )
% 0.98/1.35 , clause( 813, [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T
% 0.98/1.35 ) ) ), =( Y, 'c_List_Olist_ONil'( Z ) ) ] )
% 0.98/1.35 , clause( 814, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.98/1.35 'c_List_Olistsum'( 'c_List_Oappend'( Y, Z, X ), X ), hAPP( hAPP(
% 0.98/1.35 'c_HOL_Oplus__class_Oplus'( X ), 'c_List_Olistsum'( Y, X ) ),
% 0.98/1.35 'c_List_Olistsum'( Z, X ) ) ) ] )
% 0.98/1.35 , clause( 815, [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.98/1.35 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.98/1.35 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( X, T
% 0.98/1.35 ) ] )
% 0.98/1.35 , clause( 816, [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.98/1.35 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.98/1.35 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( Y, U
% 0.98/1.35 ) ] )
% 0.98/1.35 , clause( 817, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ),
% 0.98/1.35 'c_List_Olist_ONil'( X ), X ), 'c_List_Olist_ONil'( X ) ) ] )
% 0.98/1.35 , clause( 818, [ 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'(
% 0.98/1.35 'c_COMBC'( 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.98/1.35 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), ~( 'c_List_Olistsp'(
% 0.98/1.35 'c_InductTermi_OIT', X, 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.35 , clause( 819, [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.98/1.35 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.98/1.35 , clause( 820, [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.98/1.35 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ] )
% 0.98/1.35 , clause( 821, [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.98/1.35 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.98/1.35 , clause( 822, [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.98/1.35 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ] )
% 0.98/1.35 , clause( 823, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.98/1.35 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.98/1.35 Y, X ) ) ] )
% 0.98/1.35 , clause( 824, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.98/1.35 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.35 X, Y ), U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ) ] )
% 0.98/1.35 , clause( 825, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.98/1.35 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP(
% 0.98/1.35 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ] )
% 0.98/1.35 , clause( 826, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.98/1.35 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.98/1.35 Y, X ) ) ] )
% 0.98/1.35 , clause( 827, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X
% 0.98/1.35 , Y ), T ) ) ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 0.98/1.35 , clause( 828, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.98/1.35 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.98/1.35 Y, X ) ) ] )
% 0.98/1.35 , clause( 829, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X
% 0.98/1.35 , Y ), T ) ) ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 0.98/1.35 , clause( 830, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.98/1.35 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.98/1.35 Y, X ) ) ] )
% 0.98/1.35 , clause( 831, [ =( 'c_Nat_Osize__class_Osize'( X, 'tc_String_Ochar' ),
% 0.98/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.98/1.35 , clause( 832, [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.35 'tc_nat' ), X, Y ), 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.35 'tc_nat' ), Z, Y ) ) ] )
% 0.98/1.35 , clause( 833, [ =( 'c_Orderings_Oord__class_Omax'( X,
% 0.98/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 0.98/1.35 , clause( 834, [ =( 'c_Orderings_Oord__class_Omax'(
% 0.98/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 0.98/1.35 , clause( 835, [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'(
% 0.98/1.35 T, U, Z ) ) ), =( Y, U ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.98/1.35 ] )
% 0.98/1.35 , clause( 836, [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.35 X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.98/1.35 , clause( 837, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.98/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ] )
% 0.98/1.35 , clause( 838, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.98/1.35 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ] )
% 0.98/1.35 , clause( 839, [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.35 'tc_nat' ) ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z,
% 0.98/1.35 V0 ) ) ] )
% 0.98/1.35 , clause( 840, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.98/1.35 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.98/1.35 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ), 'c_List_Ofoldr'(
% 0.98/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.98/1.35 ) ) ] )
% 0.98/1.35 , clause( 841, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.98/1.35 'c_List_Olistsum'( Y, X ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X
% 0.98/1.35 ), 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ) ) ] )
% 0.98/1.35 , clause( 842, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.98/1.35 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP(
% 0.98/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 0.98/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.98/1.35 ) ) ) ] )
% 0.98/1.35 , clause( 843, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.98/1.35 'c_Lambda_OdB_OAbs'( Z ) ) ) ] )
% 0.98/1.35 , clause( 844, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 0.98/1.35 , clause( 845, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP(
% 0.98/1.35 hAPP( 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP(
% 0.98/1.35 hAPP( Z, U ), W ) ) ) ] )
% 0.98/1.35 , clause( 846, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP(
% 0.98/1.35 hAPP( 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP(
% 0.98/1.35 hAPP( Z, U ), W ) ) ) ] )
% 0.98/1.35 , clause( 847, [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.98/1.35 hAPP( hAPP( 'c_Lambda_Olift', X ), Z ) ), hAPP( hAPP( 'c_Lambda_Olift', Y
% 0.98/1.35 ), Z ) ) ) ] )
% 0.98/1.35 , clause( 848, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', T ), U ), W ), hAPP( hAPP( Y, T ), U ) ) ] )
% 0.98/1.35 , clause( 849, [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', T ), U ), W ), hAPP( hAPP( hAPP( hAPP( Y, T ), U ),
% 0.98/1.35 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, W ) ), 'c_Lambda_OdB_OdB__rec'( X, Y
% 0.98/1.35 , Z, U, W ) ) ) ] )
% 0.98/1.35 , clause( 850, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z
% 0.98/1.35 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', Y ), Z ) ) ) ] )
% 0.98/1.35 , clause( 851, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y
% 0.98/1.35 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ] )
% 0.98/1.35 , clause( 852, [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.98/1.35 Y ), Z ), T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y,
% 0.98/1.35 T ) ), 'c_Lambda_Oliftn'( X, Z, T ) ) ) ] )
% 0.98/1.35 , clause( 853, [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 0.98/1.35 ), Y ), Z, T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X,
% 0.98/1.35 Z, T ) ), 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ] )
% 0.98/1.35 , clause( 854, [ =( 'c_Lambda_Osubstn'( X, Y, Z ), hAPP( hAPP( hAPP(
% 0.98/1.35 'c_Lambda_Osubst', X ), 'c_Lambda_Oliftn'( Z, Y,
% 0.98/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), Z ) ) ] )
% 0.98/1.35 , clause( 855, [ ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'(
% 0.98/1.35 'c_Lambda_Obeta', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.98/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ), ~( 'c_Wellfounded_Oaccp'(
% 0.98/1.35 'c_Predicate_Oconversep'( 'c_Lambda_Obeta', 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB' ) ), 'c_Wellfounded_Oaccp'(
% 0.98/1.35 'c_Predicate_Oconversep'( 'c_Lambda_Obeta', 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z, 'tc_Lambda_OdB'
% 0.98/1.35 , 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ] )
% 0.98/1.35 , clause( 856, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.98/1.35 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.98/1.35 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~(
% 0.98/1.35 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.98/1.35 'tc_Lambda_OdB' ), X ), Z ) ) ) ] )
% 0.98/1.35 , clause( 857, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Z, 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ) ) ), ~( 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', Y, Z,
% 0.98/1.35 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.35 , clause( 858, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 0.98/1.35 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.35 , clause( 859, [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'(
% 0.98/1.35 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.35 , clause( 860, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, T, 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ) ) ), =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z,
% 0.98/1.35 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1'( X
% 0.98/1.35 , Y, Z, T ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), =( T,
% 0.98/1.35 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.35 , clause( 861, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.35 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2'( X ),
% 0.98/1.35 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1'( X ),
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.35 , clause( 862, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.98/1.35 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.35 , clause( 863, [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.35 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ) ] )
% 0.98/1.35 , clause( 864, [ =( 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, U, U )
% 0.98/1.35 , hAPP( hAPP( X, Y ), 'c_List_Ofoldl'( X, Z, T, U, U ) ) ), ~(
% 0.98/1.35 'c_OrderedGroup_Osemigroup__add'( X, U ) ) ] )
% 0.98/1.35 , clause( 865, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z )
% 0.98/1.35 , Y ) ] )
% 0.98/1.35 , clause( 866, [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =(
% 0.98/1.35 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.98/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), T, X, X ), hAPP( hAPP(
% 0.98/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.98/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ] )
% 0.98/1.35 , clause( 867, [ =( hAPP( hAPP( X, Y ), 'c_List_Ofoldl'( X, Z, T, U, U ) )
% 0.98/1.35 , 'c_List_Ofoldl'( X, Y, T, U, U ) ), ~( 'c_OrderedGroup_Omonoid__add'( Z
% 0.98/1.35 , X, U ) ) ] )
% 0.98/1.35 , clause( 868, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_OCons'( Z, T, U )
% 0.98/1.35 , W, U ), 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, W, U ) ) ] )
% 0.98/1.35 , clause( 869, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Oappend'( Z, T, U ), W,
% 0.98/1.35 U ), 'c_List_Ofoldl'( X, 'c_List_Ofoldl'( X, Y, Z, W, U ), T, W, U ) ) ]
% 0.98/1.35 )
% 0.98/1.35 , clause( 870, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), T )
% 0.98/1.35 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP(
% 0.98/1.35 'c_Lambda_Osubst', X ), Z ), T ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.98/1.35 'c_Lambda_Osubst', Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.98/1.35 'tc_nat', 'tc_Lambda_OdB' ) ), T, 'tc_Lambda_OdB', 'tc_nat',
% 0.98/1.35 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB'
% 0.98/1.35 , 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.35 , clause( 871, [ hBOOL( hAPP( X,
% 0.98/1.35 'c_ListApplication_Osko__ListApplication__Xlem__1__3'( X ) ) ), ~( hBOOL(
% 0.98/1.35 hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.35 'c_ListApplication_Osko__ListApplication__Xlem__1__1'( X ) ),
% 0.98/1.35 'c_ListApplication_Osko__ListApplication__Xlem__1__2'( X ),
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( X, Y ) ) ] )
% 0.98/1.35 , clause( 872, [ 'c_Type_Otypings'( X, Y,
% 0.98/1.35 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X, T, Y ) ), ~(
% 0.98/1.35 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.35 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.98/1.35 )
% 0.98/1.35 , clause( 873, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.98/1.35 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3'( X ) )
% 0.98/1.35 ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.35 'c_Lambda_OdB_OVar'(
% 0.98/1.35 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1'( X ) )
% 0.98/1.35 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2'( X )
% 0.98/1.35 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.98/1.35 , clause( 874, [ 'c_Type_Otypings'( X, Y,
% 0.98/1.35 'c_Type_Osko__Type__Xvar__app__types__1__1'( Z, T, X, Y ) ), ~(
% 0.98/1.35 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.35 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ) ),
% 0.98/1.35 ~( 'c_Type_Otypings'( X, W, V0 ) ), ~( 'c_Type_Otyping'( X,
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.98/1.35 , clause( 875, [ 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', X,
% 0.98/1.35 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, X, Z ),
% 0.98/1.35 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), X,
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ) ) ) ] )
% 0.98/1.35 , clause( 876, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.35 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 0.98/1.35 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.35 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.98/1.35 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.35 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.35 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.98/1.35 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.35 , clause( 877, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( hAPP(
% 0.98/1.35 'c_Lambda_Osubst', X ), Y ), Z ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.35 T ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), T ) ) ) ]
% 0.98/1.35 )
% 0.98/1.35 , clause( 878, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.98/1.35 'c_Lambda_Olift', X ), Y ) ), Z ), Y ), X ) ] )
% 0.98/1.35 , clause( 879, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.35 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), hBOOL( hAPP(
% 0.98/1.35 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X
% 0.98/1.35 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.98/1.35 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.98/1.35 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.35 , clause( 880, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) )
% 0.98/1.35 ) ] )
% 0.98/1.35 , clause( 881, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.98/1.35 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.98/1.35 ] )
% 0.98/1.35 , clause( 882, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.98/1.35 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.98/1.35 ] )
% 0.98/1.35 , clause( 883, [ ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.98/1.35 'c_Lambda_OdB_OVar'( X ) ), Y ) ) ) ] )
% 0.98/1.35 , clause( 884, [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OVar'(
% 0.98/1.35 T ), U ), hAPP( X, T ) ) ] )
% 0.98/1.35 , clause( 885, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.98/1.35 ) ] )
% 0.98/1.35 , clause( 886, [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X,
% 0.98/1.35 'c_Lambda_OdB_OVar'( Y ), Z ) ) ] )
% 0.98/1.35 , clause( 887, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OVar'(
% 0.98/1.35 T ), U ), hAPP( X, T ) ) ] )
% 0.98/1.35 , clause( 888, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y
% 0.98/1.35 ) ) ] )
% 0.98/1.35 , clause( 889, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.35 'c_Lambda_Olift', X ), Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X )
% 0.98/1.35 ) ) ] )
% 0.98/1.35 , clause( 890, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X )
% 0.98/1.35 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.35 , clause( 891, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ) ), hAPP( hAPP( hAPP(
% 0.98/1.35 'c_Lambda_Osubst', X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 0.98/1.35 ] )
% 0.98/1.35 , clause( 892, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.35 'c_Lambda_OdB_OVar'( Y ),
% 0.98/1.35 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( hAPP(
% 0.98/1.35 'c_Lambda_Obeta', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.35 'c_Lambda_OdB_OVar'( Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ) )
% 0.98/1.35 ) ] )
% 0.98/1.35 , clause( 893, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.98/1.35 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.98/1.35 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.98/1.35 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.98/1.35 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.98/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.98/1.35 , clause( 894, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.98/1.35 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.98/1.35 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.98/1.35 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.98/1.35 , clause( 895, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.98/1.35 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.98/1.35 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.98/1.35 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.35 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 0.98/1.35 , clause( 896, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.98/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.35 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.98/1.35 , clause( 897, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.98/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.98/1.35 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.98/1.35 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.98/1.35 )
% 0.98/1.35 , clause( 898, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.35 'tc_nat' ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.98/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.98/1.35 , clause( 899, [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OVar'( X ),
% 0.98/1.35 'tc_Lambda_OdB' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.98/1.35 , clause( 900, [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OVar'( X ) ),
% 0.98/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.98/1.35 , clause( 901, [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 0.98/1.35 ), Y ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.35 , clause( 902, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'(
% 0.98/1.35 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', X ), Y ), Z ) ] )
% 0.98/1.35 , clause( 903, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.98/1.35 'c_Lambda_OdB_OAbs'( Z ) ) ] )
% 0.98/1.35 , clause( 904, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.35 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.98/1.35 , clause( 905, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.35 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 0.98/1.35 , clause( 906, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) )
% 0.98/1.35 ) ] )
% 0.98/1.35 , clause( 907, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 0.98/1.35 'c_Lambda_OdB_OAbs'( X ), Y ) ] )
% 0.98/1.35 , clause( 908, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.35 'c_Lambda_OdB_OVar'( X ) ), Y ), Z ), 'c_Lambda_OdB_OVar'( X ) ), ~(
% 0.98/1.35 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.98/1.35 , clause( 909, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.35 'c_Lambda_OdB_OVar'( X ) ), Y ), Z ), 'c_Lambda_OdB_OVar'( X ) ), =( X, Z
% 0.98/1.35 ), 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ] )
% 0.98/1.35 , clause( 910, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( hAPP( hAPP(
% 0.98/1.35 hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y ) ] )
% 0.98/1.35 , clause( 911, [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ), X ) ) ] )
% 0.98/1.35 , clause( 912, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.35 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.98/1.35 , clause( 913, [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'(
% 0.98/1.35 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.35 , clause( 914, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 0.98/1.35 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.35 , clause( 915, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.98/1.35 X ) ), Y ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z
% 0.98/1.35 ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.98/1.35 , clause( 916, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ) ) ), ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y,
% 0.98/1.35 'tc_Lambda_OdB' ) ) ] )
% 0.98/1.35 , clause( 917, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.98/1.35 X ) ), Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.98/1.35 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.98/1.35 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB'
% 0.98/1.35 , 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.98/1.35 , clause( 918, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), T ), hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Z ), T ) )
% 0.98/1.35 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', Y ), Z ), T ) ) ) ] )
% 0.98/1.35 , clause( 919, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) )
% 0.98/1.35 ), =( X, Y ) ] )
% 0.98/1.35 , clause( 920, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.35 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.98/1.35 , clause( 921, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.35 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.98/1.35 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 0.98/1.35 , clause( 922, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.98/1.35 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y ) ] )
% 0.98/1.35 , clause( 923, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 0.98/1.35 'c_Lambda_Osubst', X ), 'c_Lambda_OdB_OVar'( Y ) ), Z ) ) ), ~( hBOOL(
% 0.98/1.35 hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.98/1.35 , clause( 924, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.98/1.35 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ] )
% 0.98/1.35 , clause( 925, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.98/1.35 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ] )
% 0.98/1.35 , clause( 926, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 0.98/1.35 'c_Lambda_OdB_OVar'( X ), Y ) ] )
% 0.98/1.35 , clause( 927, [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 0.98/1.35 , clause( 928, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X )
% 0.98/1.35 ) ) ] )
% 0.98/1.35 , clause( 929, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.98/1.35 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.98/1.35 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.98/1.35 , clause( 930, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.98/1.35 'c_Lambda_OdB_OVar'( Z ) ) ) ] )
% 0.98/1.35 , clause( 931, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.98/1.35 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'v_r' ), 'v_s'
% 0.98/1.35 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_ss', 'tc_Lambda_OdB',
% 0.98/1.35 'tc_Lambda_OdB' ) ) ) ] )
% 0.98/1.35 , clause( 932, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.35 hAPP( 'c_Lambda_Osubst', 'v_r' ), 'v_s' ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.35 'tc_nat' ) ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.98/1.35 'c_Lambda_OdB_OVar'( 'v_i' ) ) ) ) ] )
% 0.98/1.35 , clause( 933, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_s' ) ) ] )
% 0.98/1.35 , clause( 934, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', 'v_s' ), 'c_Lambda_OdB_OVar'( 'v_i' ) ) ) ) ] )
% 0.98/1.35 , clause( 935, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.35 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.35 hAPP( 'c_Lambda_Osubst', 'v_r' ), 'v_s' ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.35 'tc_nat' ) ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.98/1.35 'c_Lambda_OdB_OVar'( 'v_i' ) ) ) ) ) ] )
% 0.98/1.35 , clause( 936, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.98/1.35 'class_Orderings_Opreorder'( Y ) ) ] )
% 0.98/1.35 , clause( 937, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.98/1.35 'class_Orderings_Oorder'( Y ) ) ] )
% 0.98/1.35 , clause( 938, [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.98/1.35 'tc_nat' ) ] )
% 0.98/1.35 , clause( 939, [
% 0.98/1.35 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 0.98/1.35 )
% 0.98/1.35 , clause( 940, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 0.98/1.35 'tc_nat' ) ] )
% 0.98/1.35 , clause( 941, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.98/1.35 'tc_nat' ) ] )
% 0.98/1.35 , clause( 942, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat'
% 0.98/1.35 ) ] )
% 0.98/1.35 , clause( 943, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ]
% 0.98/1.35 )
% 0.98/1.35 , clause( 944, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ]
% 0.98/1.35 )
% 0.98/1.35 , clause( 945, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 0.98/1.35 )
% 0.98/1.35 , clause( 946, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ]
% 0.98/1.35 )
% 0.98/1.35 , clause( 947, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 948, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 949, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 950, [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 951, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 952, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 953, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 954, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 955, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 956, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 957, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 958, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 959, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 960, [ 'class_Power_Opower'( 'tc_nat' ) ] )
% 0.98/1.35 , clause( 961, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 0.98/1.35 , clause( 962, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 0.98/1.35 , clause( 963, [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ] )
% 0.98/1.35 , clause( 964, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y )
% 0.98/1.36 ) ) ] )
% 0.98/1.36 ] ).
% 0.98/1.36
% 0.98/1.36
% 0.98/1.36
% 0.98/1.36 eqswap(
% 0.98/1.36 clause( 1366, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.98/1.36 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y,
% 0.98/1.36 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.98/1.36 , clause( 898, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.36 'tc_nat' ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.98/1.36 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.98/1.36 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.98/1.36
% 0.98/1.36
% 0.98/1.36 subsumption(
% 0.98/1.36 clause( 383, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.98/1.36 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y,
% 0.98/1.36 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.98/1.36 , clause( 1366, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.98/1.36 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y,
% 0.98/1.36 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.98/1.36 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.98/1.36 )] ) ).
% 0.98/1.36
% 0.98/1.36
% 0.98/1.36 paramod(
% 0.98/1.36 clause( 2356, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.36 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.36 'c_Lambda_Osubstn'( 'v_r', 'v_s', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.36 ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_Lambda_OdB_OVar'(
% 0.98/1.36 'v_i' ) ) ) ) ] )
% 0.98/1.36 , clause( 383, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.98/1.36 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y,
% 0.98/1.36 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.98/1.36 , 0, clause( 932, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.36 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.36 hAPP( 'c_Lambda_Osubst', 'v_r' ), 'v_s' ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.36 'tc_nat' ) ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.98/1.36 'c_Lambda_OdB_OVar'( 'v_i' ) ) ) ) ] )
% 0.98/1.36 , 0, 8, substitution( 0, [ :=( X, 'v_r' ), :=( Y, 'v_s' )] ),
% 0.98/1.36 substitution( 1, [] )).
% 0.98/1.36
% 0.98/1.36
% 0.98/1.36 subsumption(
% 0.98/1.36 clause( 411, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.36 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.36 'c_Lambda_Osubstn'( 'v_r', 'v_s', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.36 ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_Lambda_OdB_OVar'(
% 0.98/1.36 'v_i' ) ) ) ) ] )
% 0.98/1.36 , clause( 2356, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.36 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.36 'c_Lambda_Osubstn'( 'v_r', 'v_s', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.36 ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_Lambda_OdB_OVar'(
% 0.98/1.36 'v_i' ) ) ) ) ] )
% 0.98/1.36 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.98/1.36
% 0.98/1.36
% 0.98/1.36 paramod(
% 0.98/1.36 clause( 3334, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.36 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.36 'c_Lambda_Osubstn'( 'v_r', 'v_s', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.36 ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_Lambda_OdB_OVar'(
% 0.98/1.36 'v_i' ) ) ) ) ) ] )
% 0.98/1.36 , clause( 383, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.98/1.36 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Lambda_Osubstn'( X, Y,
% 0.98/1.36 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.98/1.36 , 0, clause( 935, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.36 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.98/1.36 hAPP( 'c_Lambda_Osubst', 'v_r' ), 'v_s' ), 'c_HOL_Ozero__class_Ozero'(
% 0.98/1.36 'tc_nat' ) ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.98/1.36 'c_Lambda_OdB_OVar'( 'v_i' ) ) ) ) ) ] )
% 0.98/1.36 , 0, 9, substitution( 0, [ :=( X, 'v_r' ), :=( Y, 'v_s' )] ),
% 0.98/1.36 substitution( 1, [] )).
% 0.98/1.36
% 0.98/1.36
% 0.98/1.36 resolution(
% 0.98/1.36 clause( 3335, [] )
% 0.98/1.36 , clause( 3334, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.36 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.36 'c_Lambda_Osubstn'( 'v_r', 'v_s', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.36 ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_Lambda_OdB_OVar'(
% 0.98/1.36 'v_i' ) ) ) ) ) ] )
% 0.98/1.36 , 0, clause( 411, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.98/1.36 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.98/1.36 'c_Lambda_Osubstn'( 'v_r', 'v_s', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.98/1.36 ), 'v_ss', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_Lambda_OdB_OVar'(
% 0.98/1.36 'v_i' ) ) ) ) ] )
% 0.98/1.36 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.98/1.36
% 0.98/1.36
% 0.98/1.36 subsumption(
% 0.98/1.36 clause( 414, [] )
% 0.98/1.36 , clause( 3335, [] )
% 0.98/1.36 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.98/1.36
% 0.98/1.36
% 0.98/1.36 end.
% 0.98/1.36
% 0.98/1.36 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.98/1.36
% 0.98/1.36 Memory use:
% 0.98/1.36
% 0.98/1.36 space for terms: 29810
% 0.98/1.36 space for clauses: 37821
% 0.98/1.36
% 0.98/1.36
% 0.98/1.36 clauses generated: 520
% 0.98/1.36 clauses kept: 415
% 0.98/1.36 clauses selected: 0
% 0.98/1.36 clauses deleted: 0
% 0.98/1.36 clauses inuse deleted: 0
% 0.98/1.36
% 0.98/1.36 subsentry: 10613
% 0.98/1.36 literals s-matched: 4410
% 0.98/1.36 literals matched: 4305
% 0.98/1.36 full subsumption: 547
% 0.98/1.36
% 0.98/1.36 checksum: -2115036976
% 0.98/1.36
% 0.98/1.36
% 0.98/1.36 Bliksem ended
%------------------------------------------------------------------------------