TSTP Solution File: LCL770-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL770-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.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 07:57:45 EDT 2022
% Result : Unsatisfiable 0.87s 1.24s
% Output : Refutation 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL770-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Jul 3 12:41:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.87/1.23 *** allocated 10000 integers for termspace/termends
% 0.87/1.23 *** allocated 10000 integers for clauses
% 0.87/1.23 *** allocated 10000 integers for justifications
% 0.87/1.23 *** allocated 15000 integers for termspace/termends
% 0.87/1.23 Bliksem 1.12
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 Automatic Strategy Selection
% 0.87/1.23
% 0.87/1.23 Clauses:
% 0.87/1.23 [
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.87/1.23 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.87/1.23 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 X ), Y ), Z ) ), T ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.23 , Y, X ) ) ],
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.23 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.23 , Y, X ) ) ],
% 0.87/1.23 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( X, Y, Z ),
% 0.87/1.23 'tc_List_Olist'( Z ) ), 'c_Suc'( 'c_Nat_Osize__class_Osize'( Y,
% 0.87/1.23 'tc_List_Olist'( Z ) ) ) ) ],
% 0.87/1.23 [ =( 'c_Suc'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ) ),
% 0.87/1.23 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( Z, X, Y ),
% 0.87/1.23 'tc_List_Olist'( Y ) ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.23 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 Y, T, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 Y, Z, X ) ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.23 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 Y, T, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 Y, Z, X ) ) ) ],
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.23 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.23 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( X, Y, Z ),
% 0.87/1.23 'tc_List_Olist'( Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.87/1.23 ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ) ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.87/1.23 [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U, 'c_List_Olist_OCons'(
% 0.87/1.23 Y, T, W ), 'c_List_Olist_OCons'( X, Z, W ), W ) ) ],
% 0.87/1.23 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), 'c_ListOrder_Ostep1'( X,
% 0.87/1.23 'c_List_Olist_OCons'( Y, T, U ), 'c_List_Olist_OCons'( Z, T, U ), U ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.23 'c_Transitive__Closure_Ortranclp'( X, Z ), Y ), T ) ) ), ~(
% 0.87/1.23 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.87/1.23 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( 'c_Wellfounded_Oaccp'( X, T, Z )
% 0.87/1.23 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Z ), Y )
% 0.87/1.23 , T ) ) ) ],
% 0.87/1.23 [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.87/1.23 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X, Y, T ), Z,
% 0.87/1.23 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.87/1.23 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.87/1.23 'tc_Lambda_OdB' ), Z ) ) ],
% 0.87/1.23 [ 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.87/1.23 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ), ~( hBOOL( hAPP(
% 0.87/1.23 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.23 [ hBOOL( hAPP( 'c_InductTermi_OIT', X ) ), ~( 'c_Wellfounded_Oaccp'(
% 0.87/1.23 'c_Predicate_Oconversep'( 'c_Lambda_Obeta', 'tc_Lambda_OdB',
% 0.87/1.23 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ) ) ],
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 0.87/1.23 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 0.87/1.23 ) ) ) ],
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.87/1.23 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.87/1.23 Y ) ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 0.87/1.23 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.87/1.23 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 X, T, 'tc_nat' ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.23 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ =( 'c_List_Ofoldr'( X, 'c_List_Oappend'( Y, Z, T ), U, T, W ),
% 0.87/1.23 'c_List_Ofoldr'( X, Y, 'c_List_Ofoldr'( X, Z, U, T, W ), T, W ) ) ],
% 0.87/1.23 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.23 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.87/1.23 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 0.87/1.23 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.87/1.23 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.87/1.23 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( 'c_List_Ofoldr'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), 'c_List_Ofoldl'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.23 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.23 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.23 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.23 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.23 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.23 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.23 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 X ), Y ), Z ) ), T ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.87/1.23 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.87/1.23 [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T ), U ) ),
% 0.87/1.23 ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ],
% 0.87/1.23 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.23 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ],
% 0.87/1.23 [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T ), U ) ),
% 0.87/1.23 ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ],
% 0.87/1.23 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.23 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.87/1.23 [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T ), Z ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 0.87/1.23 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.87/1.23 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 0.87/1.23 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 0.87/1.23 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.23 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 0.87/1.23 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.87/1.23 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 0.87/1.23 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.23 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 0.87/1.23 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.87/1.23 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ) ), =( Y, Z ) ],
% 0.87/1.23 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.23 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.87/1.23 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_OCons'( Z, T, U ), W, U ),
% 0.87/1.23 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, W, U ) ) ],
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.87/1.23 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 0.87/1.23 Y ) ) ) ],
% 0.87/1.23 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.87/1.23 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.23 'c_Predicate_Oconversep'( X, Y, Y ), Y ), T ), Z ) ) ) ],
% 0.87/1.23 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.23 'c_Predicate_Oconversep'( X, Y, Y ), Y ), Z ), T ) ), ~( hBOOL( hAPP(
% 0.87/1.23 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), T ), Z ) ) ) ],
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.23 Y, 'tc_nat' ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.87/1.23 ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), T ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.23 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ), U ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ), U ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.23 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 0.87/1.23 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.87/1.23 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 0.87/1.23 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.87/1.23 ) ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 0.87/1.23 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 0.87/1.23 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.87/1.23 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.87/1.23 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.87/1.23 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.87/1.23 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.23 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.87/1.23 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.87/1.23 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 0.87/1.23 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.87/1.23 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 0.87/1.23 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ =( X, Y ), hBOOL( hAPP( hAPP( Z, Y ), X ) ), ~( 'c_ListOrder_Ostep1'(
% 0.87/1.23 Z, 'c_List_Olist_OCons'( Y, T, U ), 'c_List_Olist_OCons'( X, W, U ), U )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.87/1.23 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.87/1.23 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.87/1.23 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.87/1.23 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.87/1.23 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.87/1.23 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.23 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.23 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ],
% 0.87/1.23 [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ],
% 0.87/1.23 [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.87/1.23 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X, Y, T ), Z,
% 0.87/1.23 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.87/1.23 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.87/1.23 'tc_Lambda_OdB' ), Z ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.23 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.23 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.23 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.23 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.23 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.23 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.23 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.23 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.23 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.87/1.23 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.23 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.23 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.23 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.23 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 X ), T, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.23 ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.87/1.23 , Y ), T ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.87/1.23 Y ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.87/1.23 Y ) ],
% 0.87/1.23 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 0.87/1.23 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.23 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.87/1.23 Y ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.87/1.23 Y ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.87/1.23 Y ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.87/1.23 Y ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.87/1.23 Y ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), X ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.23 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 0.87/1.23 , 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.23 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.87/1.23 , 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.23 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.23 ) ), X, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.87/1.23 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.23 ) ), X, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.23 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.87/1.23 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ), hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ), hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.87/1.23 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.23 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 T, U, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, U, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.23 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 T, U, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, U, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ],
% 0.87/1.23 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.23 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 0.87/1.23 =( Y, T ), =( X, Z ) ],
% 0.87/1.23 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.23 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 0.87/1.23 =( Y, T ), =( X, Z ) ],
% 0.87/1.23 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ),
% 0.87/1.23 'tc_List_Olist'( X ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ =( 'c_Predicate_Oconversep'( 'c_fequal'( X ), X, X ), 'c_fequal'( X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 0.87/1.23 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.23 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ) ) ) ],
% 0.87/1.23 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Oappend'( X, Y, Z ),
% 0.87/1.23 'tc_List_Olist'( Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.87/1.23 ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) ) ),
% 0.87/1.23 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ) ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), =( Z, Y ), ~( 'c_ListOrder_Ostep1'(
% 0.87/1.23 X, 'c_List_Olist_OCons'( U, Y, T ), 'c_List_Olist_OCons'( W, Z, T ), T )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.23 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.23 T, X ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.87/1.23 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X
% 0.87/1.23 ), 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X, X ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.87/1.23 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.87/1.23 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.23 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_List_Olist_ONil'( Y
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.87/1.23 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_OCons'( Y, Z, T ), U, T, W ),
% 0.87/1.23 hAPP( hAPP( X, Y ), 'c_List_Ofoldr'( X, Z, U, T, W ) ) ) ],
% 0.87/1.23 [ =( 'c_Predicate_Oconversep'( 'c_Predicate_Oconversep'( X, Y, Z ), Z, Y
% 0.87/1.23 ), X ) ],
% 0.87/1.23 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.23 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.23 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Otimes__class_Otimes'( Z, U
% 0.87/1.23 , X ) ) ) ), =( T, U ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.87/1.23 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.23 Y, T, 'tc_nat' ) ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.87/1.23 , X ) ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 0.87/1.23 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.87/1.23 , X ) ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.23 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.87/1.23 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 0.87/1.24 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.24 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.87/1.24 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 0.87/1.24 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.24 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.87/1.24 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.87/1.24 , Z ), Y ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.87/1.24 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 0.87/1.24 ) ), =( X, T ) ],
% 0.87/1.24 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 0.87/1.24 ) ), =( Y, U ) ],
% 0.87/1.24 [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), hBOOL( hAPP( hAPP( X, U ), W ) ),
% 0.87/1.24 ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( U, Y, T ),
% 0.87/1.24 'c_List_Olist_OCons'( W, Z, T ), T ) ) ],
% 0.87/1.24 [ 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 0.87/1.24 'c_List_Olist_OCons'( Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 0.87/1.24 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Y, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.24 , T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.24 , T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.24 , Y, X ), X ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.87/1.24 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 0.87/1.24 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.87/1.24 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.87/1.24 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.24 T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.87/1.24 X ), Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.24 T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.24 X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.87/1.24 T, X ), X ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.87/1.24 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.24 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.24 X ), T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.87/1.24 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 Z, T, X ) ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.87/1.24 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 Z, T, X ) ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.87/1.24 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ) ) ],
% 0.87/1.24 [ =( 'c_HOL_Otimes__class_Otimes'( X, hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.24 Y, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 X ), Z ), T ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.24 Y, T, X ) ) ) ],
% 0.87/1.24 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) )
% 0.87/1.24 ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.87/1.24 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) )
% 0.87/1.24 ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.87/1.24 [ =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Oappend'(
% 0.87/1.24 'c_List_Olist_ONil'( Z ), 'c_List_Olist_OCons'( X, Y, Z ), Z ) ) ],
% 0.87/1.24 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y
% 0.87/1.24 , Z, X ), X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.87/1.24 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.87/1.24 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( X, T
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.87/1.24 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.87/1.24 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( Y, U
% 0.87/1.24 ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.87/1.24 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ), 'tc_nat' ), =( X,
% 0.87/1.24 'c_List_Olist_ONil'( Y ) ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ), 'tc_List_Olist'( X
% 0.87/1.24 ) ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.87/1.24 , 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z,
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ), ~(
% 0.87/1.24 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB' ) ),
% 0.87/1.24 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.87/1.24 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ],
% 0.87/1.24 [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U, 'c_List_Oappend'( X
% 0.87/1.24 , 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W ), W ),
% 0.87/1.24 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( T, 'c_List_Olist_ONil'( W ), W
% 0.87/1.24 ), W ), W ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), =( Y, Z ), ~( 'c_ListOrder_Ostep1'(
% 0.87/1.24 X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( U )
% 0.87/1.24 , U ), U ), 'c_List_Oappend'( W, 'c_List_Olist_OCons'( Z,
% 0.87/1.24 'c_List_Olist_ONil'( U ), U ), U ), U ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_ListOrder_Ostep1'( X, T, U, W ),
% 0.87/1.24 ~( 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y
% 0.87/1.24 , 'c_List_Olist_ONil'( W ), W ), W ), 'c_List_Oappend'( U,
% 0.87/1.24 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W ), W ), W ) ) ],
% 0.87/1.24 [ =( X, Y ), 'c_ListOrder_Ostep1'( Z, X, Y, T ), ~( 'c_ListOrder_Ostep1'(
% 0.87/1.24 Z, 'c_List_Oappend'( X, 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( T )
% 0.87/1.24 , T ), T ), 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( W,
% 0.87/1.24 'c_List_Olist_ONil'( T ), T ), T ), T ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.87/1.24 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.24 Y ), X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.24 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.24 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeD__1__1'(
% 0.87/1.24 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeE__1__1'(
% 0.87/1.24 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, Z,
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ), ~( 'c_Type_Otypings'( X, Z, U )
% 0.87/1.24 ), ~( 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun', U, T
% 0.87/1.24 , 'tc_Type_Otype', 'tc_Type_Otype' ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.87/1.24 'v_sko__List__Xlistsp__Xinduct__1'( Z, X ),
% 0.87/1.24 'v_sko__List__Xlistsp__Xinduct__2'( Z, X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.87/1.24 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'(
% 0.87/1.24 Z, 't_a' ), Y ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.87/1.24 'v_sko__List__Xlistsp__Xinducts__1'( Z, X ),
% 0.87/1.24 'v_sko__List__Xlistsp__Xinducts__2'( Z, X ), 't_a' ) ) ) ), ~( hBOOL(
% 0.87/1.24 hAPP( X, 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.87/1.24 'c_List_Olistsp'( Z, 't_a' ), Y ) ) ) ],
% 0.87/1.24 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), 'c_List_Ofoldr'(
% 0.87/1.24 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X,
% 0.87/1.24 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.87/1.24 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), T,
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ],
% 0.87/1.24 [ =( X, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.87/1.24 'c_Type_Osko__Type__Xvar__app__types__1__1'( Y, X, Z, T ), Y,
% 0.87/1.24 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( Z,
% 0.87/1.24 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ), ~( 'c_Type_Otypings'( Z, W, V0
% 0.87/1.24 ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.24 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.87/1.24 , Y ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( 'c_List_Olistsp'( Z, 't_a' ),
% 0.87/1.24 'v_sko__List__Xlistsp__Xinducts__2'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.87/1.24 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( Z,
% 0.87/1.24 't_a' ), Y ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( 'c_List_Olistsp'( Z, 't_a' ),
% 0.87/1.24 'v_sko__List__Xlistsp__Xinduct__2'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.87/1.24 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( Z,
% 0.87/1.24 't_a' ), Y ) ) ) ],
% 0.87/1.24 [ 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', X,
% 0.87/1.24 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, X, Z ),
% 0.87/1.24 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.87/1.24 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), X,
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.87/1.24 , 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ), 'c_Lambda_Osubst'( X
% 0.87/1.24 , T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.24 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y ), T ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.87/1.24 , 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ), 'c_Lambda_Osubst'( T
% 0.87/1.24 , Y, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.24 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), T ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.87/1.24 , 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ), 'c_Lambda_Osubst'( X
% 0.87/1.24 , T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', Y ), T ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.87/1.24 , 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ), 'c_Lambda_OdB_OAbs'( Y )
% 0.87/1.24 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.24 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Y ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.87/1.24 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.87/1.24 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.24 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.87/1.24 ), Z ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.87/1.24 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.87/1.24 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.24 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.87/1.24 ), Z ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.87/1.24 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.87/1.24 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.24 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.87/1.24 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.24 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubstn'(
% 0.87/1.24 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'( X, Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.24 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.24 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.24 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.87/1.24 ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.24 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.87/1.24 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), U )
% 0.87/1.24 , T ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.87/1.24 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP( hAPP(
% 0.87/1.24 'c_Type_Otype_OFun', Z ), T ) ) ), =( X, Z ) ],
% 0.87/1.24 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP( hAPP(
% 0.87/1.24 'c_Type_Otype_OFun', Z ), T ) ) ), =( Y, T ) ],
% 0.87/1.24 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 0.87/1.24 X ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.24 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.24 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.24 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.24 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 0.87/1.24 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.24 ), =( Z, Y ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.24 , Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.24 , Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.87/1.24 , X ) ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.87/1.24 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.87/1.24 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.87/1.24 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.87/1.24 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.87/1.24 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.87/1.24 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ],
% 0.87/1.24 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), hAPP( hAPP(
% 0.87/1.24 'c_Type_Otype_OFun', Z ), T ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( X
% 0.87/1.24 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_Type_Otype' ), Y, T ) )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'c_ListOrder_Ostep1'( X, Y, 'c_List_Olist_ONil'( Z ), Z ) ) ],
% 0.87/1.24 [ ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_ONil'( Y ), Z, Y ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.87/1.24 ), ~( hBOOL( hAPP( hAPP( X, Z ), T ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.87/1.24 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.87/1.24 [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 0.87/1.24 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 0.87/1.24 'c_Suc'( Y ), Z, T ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.87/1.24 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), U )
% 0.87/1.24 , T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.87/1.24 ), Z ), U ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), Z )
% 0.87/1.24 ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), Z )
% 0.87/1.24 ) ],
% 0.87/1.24 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( Y, Z, T ), 'c_List_Oappend'(
% 0.87/1.24 Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T ) ) ],
% 0.87/1.24 [ ~( 'c_ListOrder_Ostep1'( X, Y, Z, T ) ), 'c_ListOrder_Ostep1'( X,
% 0.87/1.24 'c_List_Oappend'( Y, U, T ), 'c_List_Oappend'( Z, U, T ), T ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.24 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.24 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.24 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.24 ), 'tc_nat' ) ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.24 ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.24 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.87/1.24 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.24 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.24 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.87/1.24 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.87/1.24 [ =( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.24 'c_Transitive__Closure_Ortranclp'( X, Y ), Y ),
% 0.87/1.24 'c_Transitive__Closure_Ortranclp'( X, Y ) ) ],
% 0.87/1.24 [ 'c_Type_Otyping'( X, Y, hAPP( hAPP( 'c_Type_Otype_OFun',
% 0.87/1.24 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, Y, T ) ), Z ) ), ~(
% 0.87/1.24 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), T ), Z ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.87/1.24 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.87/1.24 'v_sko__List__Xlistsp__Xinduct__2'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.87/1.24 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( Z,
% 0.87/1.24 't_a' ), Y ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z,
% 0.87/1.24 'v_sko__List__Xlistsp__Xinduct__1'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.87/1.24 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( Z,
% 0.87/1.24 't_a' ), Y ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.87/1.24 'v_sko__List__Xlistsp__Xinducts__2'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.87/1.24 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( Z,
% 0.87/1.24 't_a' ), Y ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z,
% 0.87/1.24 'v_sko__List__Xlistsp__Xinducts__1'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.87/1.24 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( Z,
% 0.87/1.24 't_a' ), Y ) ) ) ],
% 0.87/1.24 [ 'c_Type_Otyping'( X, Y, 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z,
% 0.87/1.24 X, T, Y ) ), ~( 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', T )
% 0.87/1.24 , Y ), Z ) ) ],
% 0.87/1.24 [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T ),
% 0.87/1.24 ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y, hAPP( hAPP(
% 0.87/1.24 'c_Type_Otype_OFun', U ), T ) ) ) ],
% 0.87/1.24 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubst'(
% 0.87/1.24 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.87/1.24 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.87/1.24 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.87/1.24 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__types__1__1'(
% 0.87/1.24 Z, T, X, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ), T ) ), ~( 'c_Type_Otypings'( X, W, V0 ) ), ~(
% 0.87/1.24 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.24 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.87/1.24 , Z ) ) ],
% 0.87/1.24 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__typesE__1__1'(
% 0.87/1.24 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ), Z ) ) ],
% 0.87/1.24 [ =( 'c_List_Olistsp'( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.87/1.24 Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_List_Olistsp'( X, Z ),
% 0.87/1.24 'c_List_Olistsp'( Y, Z ), 'tc_fun'( 'tc_List_Olist'( Z ), 'tc_bool' ) ) )
% 0.87/1.24 ],
% 0.87/1.24 [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Type_Otyping'( X, T, Z ) ), ~(
% 0.87/1.24 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.87/1.24 'tc_Lambda_OdB' ), T ), Y ) ) ) ],
% 0.87/1.24 [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 0.87/1.24 X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'( X,
% 0.87/1.24 'c_Lambda_Osubst'( U, Y, T ), W ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.87/1.24 , 'tc_Lambda_OdB' ), 'c_Lambda_Olift'( X, Y ) ), 'c_Lambda_Olift'( Z, Y )
% 0.87/1.24 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.24 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.87/1.24 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ),
% 0.87/1.24 'c_Lambda_Olift'( T, Y ), U ), ~( 'c_Type_Otyping'( X, T, U ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.87/1.24 , 'c_Lambda_Osubst'( 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.87/1.24 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.87/1.24 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.87/1.24 , 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.87/1.24 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.87/1.24 'tc_nat' ) ],
% 0.87/1.24 [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ), 'c_Lambda_Olift'(
% 0.87/1.24 'c_Lambda_Oliftn'( X, Y, Z ), Z ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.87/1.24 , 'c_Lambda_Osubst'( 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.87/1.24 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.87/1.24 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Z, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ) ), ~( 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', Y, Z,
% 0.87/1.24 'tc_Lambda_OdB' ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.87/1.24 , 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~(
% 0.87/1.24 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.87/1.24 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.87/1.24 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.87/1.24 , 'c_Lambda_Osubst'( 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.87/1.24 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), hBOOL( hAPP(
% 0.87/1.24 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__1'( X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.24 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', Z, T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X,
% 0.87/1.24 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z,
% 0.87/1.24 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1'( X
% 0.87/1.24 , Y, Z, T ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), =( T,
% 0.87/1.24 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.87/1.24 , 'c_Lambda_Osubst'( 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.87/1.24 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), hBOOL( hAPP(
% 0.87/1.24 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__1'( X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.24 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 0.87/1.24 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 0.87/1.24 ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.87/1.24 'c_Lambda_OdB_OAbs'( X ) ), Y ) ), 'c_Lambda_Osubst'( X, Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.87/1.24 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ),
% 0.87/1.24 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.24 'c_Lambda_Obeta', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.24 'c_Lambda_OdB_OVar'( Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ) )
% 0.87/1.24 ) ],
% 0.87/1.24 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), hBOOL( hAPP(
% 0.87/1.24 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__1'( X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.24 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), hBOOL( hAPP(
% 0.87/1.24 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__1'( X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.24 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.87/1.24 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.87/1.24 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.24 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y,
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.87/1.24 X ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.87/1.24 X ) ) ), =( X, 'c_Lambda_OdB_OAbs'( 'v_sko__InductTermi__XIT__Xcases__3'(
% 0.87/1.24 X ) ) ), =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Oappend'( Z, T, U ), W, U ),
% 0.87/1.24 'c_List_Ofoldl'( X, 'c_List_Ofoldl'( X, Y, Z, W, U ), T, W, U ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'( X ) ),
% 0.87/1.24 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X )
% 0.87/1.24 , Y ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.87/1.24 'tc_bool' ) ), Y ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 0.87/1.24 'tc_bool' ) ), Y ) ) ) ],
% 0.87/1.24 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( 'c_List_Olist_ONil'( X
% 0.87/1.24 ), 'c_List_Olist_ONil'( X ), X ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Olift'( X, Y ) ),
% 0.87/1.24 'c_Lambda_Olift'( Z, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X )
% 0.87/1.24 , Z ) ) ) ],
% 0.87/1.24 [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.87/1.24 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.87/1.24 ), 'c_Lambda_OdB_OAbs'( X ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X ) ],
% 0.87/1.24 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.87/1.24 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.87/1.24 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.24 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 0.87/1.24 , Y ) ],
% 0.87/1.24 [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.24 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.87/1.24 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 0.87/1.24 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.87/1.24 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 0.87/1.24 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OAbs'( T ), U ),
% 0.87/1.24 hAPP( Z, T ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.87/1.24 'c_Lambda_Osubst'( T, Y, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta'
% 0.87/1.24 , X ), T ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, Y, Z ) ) ),
% 0.87/1.24 =( X, T ) ],
% 0.87/1.24 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( X, T, Z ) ) ),
% 0.87/1.24 =( Y, T ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.87/1.24 X ) ) ), =( X, 'c_Lambda_OdB_OAbs'( 'v_sko__InductTermi__XIT__Xcases__3'(
% 0.87/1.24 X ) ) ), hBOOL( hAPP( 'c_List_Olistsp'( 'c_InductTermi_OIT',
% 0.87/1.24 'tc_Lambda_OdB' ), 'v_sko__InductTermi__XIT__Xcases__1'( X ) ) ), ~(
% 0.87/1.24 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ =( 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ), X ) ],
% 0.87/1.24 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 0.87/1.24 [ =( X, 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 0.87/1.24 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), Y, X ), Y ) ],
% 0.87/1.24 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 0.87/1.24 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), Y ) ],
% 0.87/1.24 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 0.87/1.24 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.87/1.24 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.87/1.24 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.24 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.87/1.24 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.87/1.24 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Y
% 0.87/1.24 , 'c_List_Olist_ONil'( X ) ) ],
% 0.87/1.24 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Z
% 0.87/1.24 , 'c_List_Olist_ONil'( X ) ) ],
% 0.87/1.24 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( X
% 0.87/1.24 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.87/1.24 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y
% 0.87/1.24 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.87/1.24 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.24 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.87/1.24 'tc_Lambda_OdB' ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.87/1.24 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) )
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.87/1.24 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.87/1.24 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.87/1.24 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.87/1.24 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.87/1.24 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 0.87/1.24 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.87/1.24 'c_Lambda_OdB_OApp', X ), Y ), Z ) ],
% 0.87/1.24 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OAbs'( T ), U ),
% 0.87/1.24 hAPP( hAPP( Z, T ), 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, U ) ) ) ],
% 0.87/1.24 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 0.87/1.24 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 0.87/1.24 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.87/1.24 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.87/1.24 'tc_bool' ) ) ) ],
% 0.87/1.24 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.87/1.24 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.87/1.24 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( =( 'c_List_Oappend'( X, Y, Z ), X ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( =( X, 'c_List_Oappend'( X, Y, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( =( 'c_List_Oappend'( X, Y, Z ), Y ) ), =( X, 'c_List_Olist_ONil'( Z
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( =( X, 'c_List_Oappend'( Y, X, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 0.87/1.24 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 0.87/1.24 'tc_bool' ) ), X ) ],
% 0.87/1.24 [ 'c_Type_Otyping'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', T
% 0.87/1.24 ), Y ) ) ), ~( 'c_Type_Otyping'( X, T, Z ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 0.87/1.24 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 0.87/1.24 hAPP( X, T ) ) ) ],
% 0.87/1.24 [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.87/1.24 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.87/1.24 ) ) ],
% 0.87/1.24 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_ONil'( X
% 0.87/1.24 ), X ), 'c_List_Olist_ONil'( X ) ) ],
% 0.87/1.24 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.87/1.24 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.87/1.24 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.87/1.24 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 0.87/1.24 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.87/1.24 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.87/1.24 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.87/1.24 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_Osubst'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 0.87/1.24 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Z, T ) ),
% 0.87/1.24 'c_Lambda_Osubst'( Y, Z, T ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.87/1.24 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 0.87/1.24 Z ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.87/1.24 ) ],
% 0.87/1.24 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.87/1.24 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.87/1.24 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.87/1.24 ],
% 0.87/1.24 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.87/1.24 Z ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.87/1.24 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.87/1.24 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.87/1.24 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.87/1.24 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.87/1.24 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP( hAPP(
% 0.87/1.24 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.87/1.24 Z, U ), W ) ) ) ],
% 0.87/1.24 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP( hAPP(
% 0.87/1.24 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.87/1.24 Z, U ), W ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( X,
% 0.87/1.24 'c_Lambda_OdB_OVar'( Y ), Z ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.87/1.24 ) ) ) ],
% 0.87/1.24 [ =( 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W ),
% 0.87/1.24 'c_Set_Oimage'( 'c_COMBB'( X, Y, U, W, T ), Z, T, W ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_List_Olistsp'( X, Y ), 'c_List_Oappend'( Z, T, Y ) ) )
% 0.87/1.24 , ~( hBOOL( hAPP( 'c_List_Olistsp'( X, Y ), T ) ) ), ~( hBOOL( hAPP(
% 0.87/1.24 'c_List_Olistsp'( X, Y ), Z ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_List_Olistsp'( X, Y ), Z ) ), ~( hBOOL( hAPP( X,
% 0.87/1.24 'c_List_Osko__List__Xin__listsp__conv__set__1__1'( X, Z, Y ) ) ) ) ],
% 0.87/1.24 [ ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.87/1.24 ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.87/1.24 , 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ),
% 0.87/1.24 ~( hBOOL( hAPP( 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' )
% 0.87/1.24 , Y ) ) ) ],
% 0.87/1.24 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.87/1.24 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 0.87/1.24 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.87/1.24 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 0.87/1.24 [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ), X ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_List_Olistsp'(
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.87/1.24 'tc_bool' ) ), Z ), T ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( Y, Z ), T )
% 0.87/1.24 ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( X, Z ), T ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.24 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OVar'( X )
% 0.87/1.24 , Y ) ],
% 0.87/1.24 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OVar'( T ), U ),
% 0.87/1.24 hAPP( X, T ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.87/1.24 X ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), hBOOL( hAPP(
% 0.87/1.24 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' ),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__1'( X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.24 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.87/1.24 Z ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.87/1.24 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.87/1.24 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Olift'( X, Y ) ) ), ~(
% 0.87/1.24 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X ) ) ) ],
% 0.87/1.24 [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y )
% 0.87/1.24 , Z ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_Olift'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z ),
% 0.87/1.24 hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Olift'( X, Z ) ),
% 0.87/1.24 'c_Lambda_Olift'( Y, Z ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_List_Olistsp'( X, Y ), 'c_List_Olist_ONil'( Y ) ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ hBOOL( hAPP( 'c_List_Olistsp'( X, Y ), Z ) ), ~( hBOOL( hAPP(
% 0.87/1.24 'c_List_Olistsp'( X, Y ), 'c_List_Oappend'( T, Z, Y ) ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_List_Olistsp'( X, Y ), Z ) ), ~( hBOOL( hAPP(
% 0.87/1.24 'c_List_Olistsp'( X, Y ), 'c_List_Oappend'( Z, T, Y ) ) ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, hAPP( hAPP( 'c_Lambda_OdB_OApp'
% 0.87/1.24 , T ), U ), W ), hAPP( hAPP( Y, T ), U ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.24 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OVar'( T ), U ),
% 0.87/1.24 hAPP( X, T ) ) ],
% 0.87/1.24 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.87/1.24 T ), U ), W ), hAPP( hAPP( hAPP( hAPP( Y, T ), U ),
% 0.87/1.24 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, W ) ), 'c_Lambda_OdB_OdB__rec'( X, Y
% 0.87/1.24 , Z, U, W ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.87/1.24 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X ) ) ), ~(
% 0.87/1.24 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.87/1.24 X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP(
% 0.87/1.24 hAPP( 'c_Lambda_Obeta', Y ), Z ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.87/1.24 X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP(
% 0.87/1.24 hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T
% 0.87/1.24 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y, T ) ),
% 0.87/1.24 'c_Lambda_Oliftn'( X, Z, T ) ) ) ],
% 0.87/1.24 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.24 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.87/1.24 'tc_Lambda_OdB' ) ) ],
% 0.87/1.24 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y )
% 0.87/1.24 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.87/1.24 [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 0.87/1.24 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X, Z, T ) ),
% 0.87/1.24 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ],
% 0.87/1.24 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OVar'(
% 0.87/1.24 Z ) ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' )
% 0.87/1.24 , 'v_rs' ) ) ],
% 0.87/1.24 [ hBOOL( hAPP( 'c_List_Olistsp'( 'c_COMBB'( 'c_InductTermi_OIT',
% 0.87/1.24 'c_COMBC'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( 'v_i' ),
% 0.87/1.24 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 0.87/1.24 'tc_bool', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), 'v_rs' ) ) ],
% 0.87/1.24 [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( 'v_i' ) ) )
% 0.87/1.24 ) ],
% 0.87/1.24 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 0.87/1.24 'class_Lattices_Olattice'( Y ) ) ],
% 0.87/1.24 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.87/1.24 'class_Orderings_Opreorder'( Y ) ) ],
% 0.87/1.24 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 0.87/1.24 'class_Lattices_Olattice'( Y ) ) ],
% 0.87/1.24 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.87/1.24 'class_Orderings_Oorder'( Y ) ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.87/1.24 ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.87/1.24 ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.87/1.24 ],
% 0.87/1.24 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 0.87/1.24 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 0.87/1.24 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 0.87/1.24 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 0.87/1.24 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 0.87/1.24 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 0.87/1.24 ] .
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 percentage equality = 0.356464, percentage horn = 0.860606
% 0.87/1.24 This is a problem with some equality
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 Options Used:
% 0.87/1.24
% 0.87/1.24 useres = 1
% 0.87/1.24 useparamod = 1
% 0.87/1.24 useeqrefl = 1
% 0.87/1.24 useeqfact = 1
% 0.87/1.24 usefactor = 1
% 0.87/1.24 usesimpsplitting = 0
% 0.87/1.24 usesimpdemod = 5
% 0.87/1.24 usesimpres = 3
% 0.87/1.24
% 0.87/1.24 resimpinuse = 1000
% 0.87/1.24 resimpclauses = 20000
% 0.87/1.24 substype = eqrewr
% 0.87/1.24 backwardsubs = 1
% 0.87/1.24 selectoldest = 5
% 0.87/1.24
% 0.87/1.24 litorderings [0] = split
% 0.87/1.24 litorderings [1] = extend the termordering, first sorting on arguments
% 0.87/1.24
% 0.87/1.24 termordering = kbo
% 0.87/1.24
% 0.87/1.24 litapriori = 0
% 0.87/1.24 termapriori = 1
% 0.87/1.24 litaposteriori = 0
% 0.87/1.24 termaposteriori = 0
% 0.87/1.24 demodaposteriori = 0
% 0.87/1.24 ordereqreflfact = 0
% 0.87/1.24
% 0.87/1.24 litselect = negord
% 0.87/1.24
% 0.87/1.24 maxweight = 15
% 0.87/1.24 maxdepth = 30000
% 0.87/1.24 maxlength = 115
% 0.87/1.24 maxnrvars = 195
% 0.87/1.24 excuselevel = 1
% 0.87/1.24 increasemaxweight = 1
% 0.87/1.24
% 0.87/1.24 maxselected = 10000000
% 0.87/1.24 maxnrclauses = 10000000
% 0.87/1.24
% 0.87/1.24 showgenerated = 0
% 0.87/1.24 showkept = 0
% 0.87/1.24 showselected = 0
% 0.87/1.24 showdeleted = 0
% 0.87/1.24 showresimp = 1
% 0.87/1.24 showstatus = 2000
% 0.87/1.24
% 0.87/1.24 prologoutput = 1
% 0.87/1.24 nrgoals = 5000000
% 0.87/1.24 totalproof = 1
% 0.87/1.24
% 0.87/1.24 Symbols occurring in the translation:
% 0.87/1.24
% 0.87/1.24 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.87/1.24 . [1, 2] (w:1, o:153, a:1, s:1, b:0),
% 0.87/1.24 ! [4, 1] (w:0, o:99, a:1, s:1, b:0),
% 0.87/1.24 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.87/1.24 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.87/1.24 'class_OrderedGroup_Oab__semigroup__add' [40, 1] (w:1, o:105, a:1, s:
% 0.87/1.24 1, b:0),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus' [41, 1] (w:1, o:106, a:1, s:1, b:0),
% 0.87/1.24 hAPP [43, 2] (w:1, o:178, a:1, s:1, b:0),
% 0.87/1.24 'class_OrderedGroup_Ocomm__monoid__add' [46, 1] (w:1, o:107, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'tc_nat' [47, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.87/1.24 'class_OrderedGroup_Oab__group__add' [54, 1] (w:1, o:108, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'class_Ring__and__Field_Ocomm__semiring__1' [55, 1] (w:1, o:109, a:1
% 0.87/1.24 , s:1, b:0),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes' [56, 3] (w:1, o:189, a:1, s:1, b:0),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero' [57, 1] (w:1, o:110, a:1, s:1, b:0),
% 0.87/1.24 'class_OrderedGroup_Olordered__ab__group__add' [58, 1] (w:1, o:111
% 0.87/1.24 , a:1, s:1, b:0),
% 0.87/1.24 'c_List_Olist_OCons' [60, 3] (w:1, o:190, a:1, s:1, b:0),
% 0.87/1.24 'tc_List_Olist' [61, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.87/1.24 'c_Nat_Osize__class_Osize' [62, 2] (w:1, o:179, a:1, s:1, b:0),
% 0.87/1.24 'c_Suc' [63, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.87/1.24 'class_Ring__and__Field_Oidom' [64, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.87/1.24 'class_Int_Onumber__ring' [65, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.87/1.24 'c_ListOrder_Ostep1' [71, 4] (w:1, o:203, a:1, s:1, b:0),
% 0.87/1.24 hBOOL [72, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.87/1.24 'c_Wellfounded_Oaccp' [73, 3] (w:1, o:191, a:1, s:1, b:0),
% 0.87/1.24 'c_Transitive__Closure_Ortranclp' [74, 2] (w:1, o:180, a:1, s:1, b:0)
% 0.87/1.24 ,
% 0.87/1.24 'c_Type_Otype_OFun' [77, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.87/1.24 'c_Type_Osko__Type__Xlist__app__typeE__1__1' [80, 4] (w:1, o:206, a:1
% 0.87/1.24 , s:1, b:0),
% 0.87/1.24 'tc_Type_Otype' [81, 0] (w:1, o:56, a:1, s:1, b:0),
% 0.87/1.24 'c_List_Ofoldr' [82, 5] (w:1, o:212, a:1, s:1, b:0),
% 0.87/1.24 'c_Type_Otyping' [83, 3] (w:1, o:192, a:1, s:1, b:0),
% 0.87/1.24 'c_Lambda_OdB_OApp' [84, 0] (w:1, o:57, a:1, s:1, b:0),
% 0.87/1.24 'tc_Lambda_OdB' [85, 0] (w:1, o:58, a:1, s:1, b:0),
% 0.87/1.24 'c_List_Ofoldl' [86, 5] (w:1, o:213, a:1, s:1, b:0),
% 0.87/1.24 'c_Lambda_Obeta' [87, 0] (w:1, o:59, a:1, s:1, b:0),
% 0.87/1.24 'c_Predicate_Oconversep' [88, 3] (w:1, o:193, a:1, s:1, b:0),
% 0.87/1.24 'c_InductTermi_OIT' [89, 0] (w:1, o:60, a:1, s:1, b:0),
% 0.87/1.24 'c_HOL_Oord__class_Oless' [91, 3] (w:1, o:194, a:1, s:1, b:0),
% 0.87/1.24 'class_OrderedGroup_Osemigroup__add' [94, 1] (w:1, o:117, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'c_List_Oappend' [98, 3] (w:1, o:195, a:1, s:1, b:0),
% 0.87/1.24 'class_Nat_Osemiring__char__0' [99, 1] (w:1, o:104, a:1, s:1, b:0),
% 0.87/1.24 'c_Nat_Osemiring__1__class_Oof__nat' [100, 2] (w:1, o:181, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'class_Ring__and__Field_Oring__no__zero__divisors' [101, 1] (w:1, o:
% 0.87/1.24 118, a:1, s:1, b:0),
% 0.87/1.24 'class_Ring__and__Field_Ono__zero__divisors' [102, 1] (w:1, o:120, a:
% 0.87/1.24 1, s:1, b:0),
% 0.87/1.24 'class_Ring__and__Field_Oordered__idom' [103, 1] (w:1, o:121, a:1, s:
% 0.87/1.24 1, b:0),
% 0.87/1.24 'c_List_Olist_ONil' [107, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.87/1.24 'class_OrderedGroup_Olordered__ab__group__add__meet' [108, 1] (w:1
% 0.87/1.24 , o:123, a:1, s:1, b:0),
% 0.87/1.24 'c_Lattices_Olower__semilattice__class_Oinf' [109, 3] (w:1, o:196, a:
% 0.87/1.24 1, s:1, b:0),
% 0.87/1.24 'class_Ring__and__Field_Osemiring' [110, 1] (w:1, o:124, a:1, s:1, b:
% 0.87/1.24 0),
% 0.87/1.24 'class_Ring__and__Field_Osemiring__1' [111, 1] (w:1, o:125, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'class_OrderedGroup_Opordered__comm__monoid__add' [112, 1] (w:1, o:
% 0.87/1.24 126, a:1, s:1, b:0),
% 0.87/1.24 'class_OrderedGroup_Omonoid__add' [113, 1] (w:1, o:127, a:1, s:1, b:0
% 0.87/1.24 ),
% 0.87/1.24 'class_Ring__and__Field_Oordered__ring__strict' [114, 1] (w:1, o:128
% 0.87/1.24 , a:1, s:1, b:0),
% 0.87/1.24 'class_OrderedGroup_Ocancel__ab__semigroup__add' [115, 1] (w:1, o:129
% 0.87/1.24 , a:1, s:1, b:0),
% 0.87/1.24 'class_OrderedGroup_Ocancel__semigroup__add' [116, 1] (w:1, o:130, a:
% 0.87/1.24 1, s:1, b:0),
% 0.87/1.24 'class_Ring__and__Field_Oordered__semidom' [120, 1] (w:1, o:131, a:1
% 0.87/1.24 , s:1, b:0),
% 0.87/1.24 'c_Type_Osko__Type__Xlist__app__typeD__1__1' [121, 4] (w:1, o:205, a:
% 0.87/1.24 1, s:1, b:0),
% 0.87/1.24 'class_Ring__and__Field_Oordered__semiring__strict' [122, 1] (w:1, o:
% 0.87/1.24 132, a:1, s:1, b:0),
% 0.87/1.24 'class_Ring__and__Field_Oordered__comm__semiring__strict' [123, 1]
% 0.87/1.24 (w:1, o:133, a:1, s:1, b:0),
% 0.87/1.24 'c_fequal' [125, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.87/1.24 'class_Ring__and__Field_Omult__zero' [130, 1] (w:1, o:119, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [131, 1]
% 0.87/1.24 (w:1, o:135, a:1, s:1, b:0),
% 0.87/1.24 'class_OrderedGroup_Oab__semigroup__idem__mult' [132, 1] (w:1, o:136
% 0.87/1.24 , a:1, s:1, b:0),
% 0.87/1.24 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [133, 1]
% 0.87/1.24 (w:1, o:137, a:1, s:1, b:0),
% 0.87/1.24 'class_OrderedGroup_Oab__semigroup__mult' [134, 1] (w:1, o:138, a:1
% 0.87/1.24 , s:1, b:0),
% 0.87/1.24 'class_Ring__and__Field_Ocomm__semiring' [135, 1] (w:1, o:139, a:1
% 0.87/1.24 , s:1, b:0),
% 0.87/1.24 'c_Lambda_Osubst' [137, 3] (w:1, o:197, a:1, s:1, b:0),
% 0.87/1.24 'c_Lambda_OdB_OAbs' [139, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.87/1.24 'c_Lambda_OdB_OVar' [140, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.87/1.24 'c_Lambda_Oliftn' [141, 3] (w:1, o:198, a:1, s:1, b:0),
% 0.87/1.24 'c_Type_Otypings' [142, 3] (w:1, o:199, a:1, s:1, b:0),
% 0.87/1.24 'v_sko__List__Xlistsp__Xinduct__1' [146, 2] (w:1, o:182, a:1, s:1, b:
% 0.87/1.24 0),
% 0.87/1.24 'v_sko__List__Xlistsp__Xinduct__2' [147, 2] (w:1, o:183, a:1, s:1, b:
% 0.87/1.24 0),
% 0.87/1.24 't_a' [148, 0] (w:1, o:78, a:1, s:1, b:0),
% 0.87/1.24 'c_List_Olistsp' [149, 2] (w:1, o:184, a:1, s:1, b:0),
% 0.87/1.24 'v_sko__List__Xlistsp__Xinducts__1' [150, 2] (w:1, o:185, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'v_sko__List__Xlistsp__Xinducts__2' [151, 2] (w:1, o:186, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'c_Type_Osko__Type__Xvar__app__typesE__1__1' [152, 4] (w:1, o:207, a:
% 0.87/1.24 1, s:1, b:0),
% 0.87/1.24 'c_Type_Osko__Type__Xvar__app__types__1__1' [155, 4] (w:1, o:208, a:1
% 0.87/1.24 , s:1, b:0),
% 0.87/1.24 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1' [158, 3] (w:
% 0.87/1.24 1, o:200, a:1, s:1, b:0),
% 0.87/1.24 'c_Lambda_Osubstn' [161, 3] (w:1, o:201, a:1, s:1, b:0),
% 0.87/1.24 'class_Orderings_Opreorder' [162, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.87/1.24 'class_Orderings_Olinorder' [163, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.87/1.24 'class_Orderings_Oorder' [164, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.87/1.24 'c_Type_Oshift' [169, 4] (w:1, o:209, a:1, s:1, b:0),
% 0.87/1.24 'class_Lattices_Olower__semilattice' [171, 1] (w:1, o:145, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'c_Type_Osko__Type__Xtyping__elims__2__1' [175, 4] (w:1, o:210, a:1
% 0.87/1.24 , s:1, b:0),
% 0.87/1.24 'tc_bool' [177, 0] (w:1, o:84, a:1, s:1, b:0),
% 0.87/1.24 'tc_fun' [178, 2] (w:1, o:187, a:1, s:1, b:0),
% 0.87/1.24 'c_Lambda_Olift' [180, 2] (w:1, o:188, a:1, s:1, b:0),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__4' [181, 1] (w:1, o:149, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__5' [182, 1] (w:1, o:150, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__6' [183, 1] (w:1, o:151, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__3' [184, 1] (w:1, o:148, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__2' [185, 1] (w:1, o:147, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'v_sko__InductTermi__XIT__Xcases__1' [186, 1] (w:1, o:146, a:1, s:1
% 0.87/1.24 , b:0),
% 0.87/1.24 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1' [
% 0.87/1.24 187, 4] (w:1, o:211, a:1, s:1, b:0),
% 0.87/1.24 'class_Lattices_Olattice' [188, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.87/1.24 'c_Lambda_OdB_OdB__case' [193, 5] (w:1, o:214, a:1, s:1, b:0),
% 0.87/1.24 'c_Lambda_OdB_OdB__rec' [196, 5] (w:1, o:215, a:1, s:1, b:0),
% 0.87/1.24 'c_Set_Oimage' [204, 4] (w:1, o:204, a:1, s:1, b:0),
% 0.87/1.24 'c_COMBB' [205, 5] (w:1, o:216, a:1, s:1, b:0),
% 0.87/1.24 'c_List_Osko__List__Xin__listsp__conv__set__1__1' [206, 3] (w:1, o:
% 0.87/1.24 202, a:1, s:1, b:0),
% 0.87/1.24 'c_COMBC' [211, 5] (w:1, o:217, a:1, s:1, b:0),
% 0.87/1.24 'v_rs' [212, 0] (w:1, o:93, a:1, s:1, b:0),
% 0.87/1.24 'v_i' [213, 0] (w:1, o:94, a:1, s:1, b:0).
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 Starting Search:
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 Bliksems!, er is een bewijs:
% 0.87/1.24 % SZS status Unsatisfiable
% 0.87/1.24 % SZS output start Refutation
% 0.87/1.24
% 0.87/1.24 clause( 397, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X ) )
% 0.87/1.24 ) ] )
% 0.87/1.24 .
% 0.87/1.24 clause( 419, [] )
% 0.87/1.24 .
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 % SZS output end Refutation
% 0.87/1.24 found a proof!
% 0.87/1.24
% 0.87/1.24 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.87/1.24
% 0.87/1.24 initialclauses(
% 0.87/1.24 [ clause( 421, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.87/1.24 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.87/1.24 , clause( 422, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.87/1.24 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.87/1.24 , clause( 423, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.87/1.24 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.87/1.24 , clause( 424, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.24 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP(
% 0.87/1.24 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ] )
% 0.87/1.24 , clause( 425, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.87/1.24 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP(
% 0.87/1.24 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ] )
% 0.87/1.24 , clause( 426, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 0.87/1.24 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.87/1.24 , clause( 427, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 X ), Y ), Z ) ), T ) ) ] )
% 0.87/1.24 , clause( 428, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.24 , Y, X ) ) ] )
% 0.87/1.24 , clause( 429, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.24 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.24 , clause( 430, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.24 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.87/1.24 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.24 , clause( 431, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 0.87/1.24 , clause( 432, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.24 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.24 , Y, X ) ) ] )
% 0.87/1.24 , clause( 433, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( X, Y
% 0.87/1.24 , Z ), 'tc_List_Olist'( Z ) ), 'c_Suc'( 'c_Nat_Osize__class_Osize'( Y,
% 0.87/1.24 'tc_List_Olist'( Z ) ) ) ) ] )
% 0.87/1.24 , clause( 434, [ =( 'c_Suc'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'(
% 0.87/1.24 Y ) ) ), 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( Z, X, Y ),
% 0.87/1.24 'tc_List_Olist'( Y ) ) ) ] )
% 0.87/1.24 , clause( 435, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.87/1.24 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.24 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), hAPP( hAPP(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 0.87/1.24 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ) ] )
% 0.87/1.24 , clause( 436, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.87/1.24 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.25 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 0.87/1.25 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ) ] )
% 0.87/1.25 , clause( 437, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.25 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 438, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.25 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 439, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 440, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( X, Y
% 0.87/1.25 , Z ), 'tc_List_Olist'( Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.25 'tc_nat' ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ) ),
% 0.87/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.87/1.25 , clause( 441, [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U,
% 0.87/1.25 'c_List_Olist_OCons'( Y, T, W ), 'c_List_Olist_OCons'( X, Z, W ), W ) ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 442, [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ),
% 0.87/1.25 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( Y, T, U ),
% 0.87/1.25 'c_List_Olist_OCons'( Z, T, U ), U ) ] )
% 0.87/1.25 , clause( 443, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Transitive__Closure_Ortranclp'( X, Z ), Y ), T ) ) ), ~(
% 0.87/1.25 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 0.87/1.25 , clause( 444, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( 'c_Wellfounded_Oaccp'(
% 0.87/1.25 X, T, Z ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X,
% 0.87/1.25 Z ), Y ), T ) ) ) ] )
% 0.87/1.25 , clause( 445, [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 0.87/1.25 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X,
% 0.87/1.25 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.87/1.25 , clause( 446, [ 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'(
% 0.87/1.25 'c_Lambda_Obeta', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB'
% 0.87/1.25 ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 447, [ hBOOL( hAPP( 'c_InductTermi_OIT', X ) ), ~(
% 0.87/1.25 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ) ) ] )
% 0.87/1.25 , clause( 448, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.87/1.25 , 'c_Suc'( Y ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.25 'tc_nat' ), X ), Y ) ) ) ] )
% 0.87/1.25 , clause( 449, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 'c_Suc'( X ) ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.25 'tc_nat' ), X ), Y ) ) ) ] )
% 0.87/1.25 , clause( 450, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ] )
% 0.87/1.25 , clause( 451, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ] )
% 0.87/1.25 , clause( 452, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ] )
% 0.87/1.25 , clause( 453, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 454, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 455, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.25 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 456, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 457, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 458, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.87/1.25 , clause( 459, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.87/1.25 , clause( 460, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.87/1.25 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 461, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) )
% 0.87/1.25 ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( X, T, 'tc_nat' ) ] )
% 0.87/1.25 , clause( 462, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.87/1.25 , clause( 463, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 464, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 465, [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =(
% 0.87/1.25 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), T, X, X ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ] )
% 0.87/1.25 , clause( 466, [ =( 'c_List_Ofoldr'( X, 'c_List_Oappend'( Y, Z, T ), U, T,
% 0.87/1.25 W ), 'c_List_Ofoldr'( X, Y, 'c_List_Ofoldr'( X, Z, U, T, W ), T, W ) ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 467, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.87/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 0.87/1.25 , clause( 468, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.87/1.25 'class_Int_Onumber__ring'( X ) ), ~( =( Y, hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), =( Z,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 469, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), Y ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 470, [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.87/1.25 ), X ), Y ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 471, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 472, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 0.87/1.25 , clause( 473, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 0.87/1.25 , clause( 474, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 475, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 476, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.25 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 477, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.87/1.25 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ),
% 0.87/1.25 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ] )
% 0.87/1.25 , clause( 478, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.87/1.25 ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.25 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 479, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 0.87/1.25 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 480, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 0.87/1.25 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 481, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 482, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.25 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 483, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.25 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 484, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.25 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 485, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.25 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 486, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 0.87/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 487, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.25 X ), Y ), Z ) ), T ) ) ] )
% 0.87/1.25 , clause( 488, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.25 X ), Y ), T ) ), Z ) ) ] )
% 0.87/1.25 , clause( 489, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.87/1.25 , clause( 490, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.87/1.25 , clause( 491, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 492, [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T
% 0.87/1.25 ), U ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ] )
% 0.87/1.25 , clause( 493, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ] )
% 0.87/1.25 , clause( 494, [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T
% 0.87/1.25 ), U ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ] )
% 0.87/1.25 , clause( 495, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ] )
% 0.87/1.25 , clause( 496, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ] )
% 0.87/1.25 , clause( 497, [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T )
% 0.87/1.25 , Z ) ] )
% 0.87/1.25 , clause( 498, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X
% 0.87/1.25 ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ] )
% 0.87/1.25 , clause( 499, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X
% 0.87/1.25 ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 0.87/1.25 , clause( 500, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.25 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ] )
% 0.87/1.25 , clause( 501, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.25 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 0.87/1.25 , clause( 502, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.87/1.25 , clause( 503, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.25 'tc_nat' ) ), =( Y, Z ) ] )
% 0.87/1.25 , clause( 504, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 0.87/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 505, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 506, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 507, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 508, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_OCons'( Z, T, U )
% 0.87/1.25 , W, U ), 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, W, U ) ) ] )
% 0.87/1.25 , clause( 509, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), 'c_Suc'( Y ) ) ) ] )
% 0.87/1.25 , clause( 510, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.87/1.25 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Predicate_Oconversep'( X, Y, Y ), Y ), T ), Z ) ) ) ] )
% 0.87/1.25 , clause( 511, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Predicate_Oconversep'( X, Y, Y ), Y ), Z ), T ) ), ~( hBOOL( hAPP(
% 0.87/1.25 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), T ), Z ) ) ) ] )
% 0.87/1.25 , clause( 512, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.25 Y, 'tc_nat' ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.87/1.25 ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.25 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), T ) ) ] )
% 0.87/1.25 , clause( 513, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.87/1.25 , X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ), U ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ), U ) ) ] )
% 0.87/1.25 , clause( 514, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.87/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 515, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.87/1.25 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 516, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.25 Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 517, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.87/1.25 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.87/1.25 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 518, [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z
% 0.87/1.25 ), 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.87/1.25 , clause( 519, [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z
% 0.87/1.25 ), 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.87/1.25 , clause( 520, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.87/1.25 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.87/1.25 ) ) ) ] )
% 0.87/1.25 , clause( 521, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 522, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 'c_Suc'( X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 0.87/1.25 Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 523, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.87/1.25 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.87/1.25 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 524, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) )
% 0.87/1.25 ), =( Y, Z ) ] )
% 0.87/1.25 , clause( 525, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) )
% 0.87/1.25 ), =( X, Z ) ] )
% 0.87/1.25 , clause( 526, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) )
% 0.87/1.25 ), =( Y, Z ) ] )
% 0.87/1.25 , clause( 527, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.87/1.25 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.87/1.25 , clause( 528, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) )
% 0.87/1.25 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.87/1.25 , clause( 529, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.87/1.25 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.87/1.25 , clause( 530, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.87/1.25 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ] )
% 0.87/1.25 , clause( 531, [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T
% 0.87/1.25 ), 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ] )
% 0.87/1.25 , clause( 532, [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T
% 0.87/1.25 ), 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ] )
% 0.87/1.25 , clause( 533, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'(
% 0.87/1.25 Z ) ) ) ] )
% 0.87/1.25 , clause( 534, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'(
% 0.87/1.25 Z ) ) ) ] )
% 0.87/1.25 , clause( 535, [ =( X, Y ), hBOOL( hAPP( hAPP( Z, Y ), X ) ), ~(
% 0.87/1.25 'c_ListOrder_Ostep1'( Z, 'c_List_Olist_OCons'( Y, T, U ),
% 0.87/1.25 'c_List_Olist_OCons'( X, W, U ), U ) ) ] )
% 0.87/1.25 , clause( 536, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y,
% 0.87/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 537, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 538, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.87/1.25 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 539, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.87/1.25 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Z,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 540, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.25 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) )
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 541, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 542, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 0.87/1.25 , clause( 543, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y,
% 0.87/1.25 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 0.87/1.25 ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 0.87/1.25 , clause( 544, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 0.87/1.25 , clause( 545, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y,
% 0.87/1.25 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 0.87/1.25 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 0.87/1.25 , clause( 546, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ] )
% 0.87/1.25 , clause( 547, [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ] )
% 0.87/1.25 , clause( 548, [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 0.87/1.25 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X,
% 0.87/1.25 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.87/1.25 , clause( 549, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.87/1.25 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat'
% 0.87/1.25 ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.25 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 550, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.87/1.25 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.87/1.25 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.25 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 551, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.87/1.25 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.87/1.25 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.25 , X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 552, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.87/1.25 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat'
% 0.87/1.25 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.25 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 553, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.87/1.25 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.87/1.25 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 554, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.87/1.25 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.87/1.25 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.25 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 555, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.25 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 556, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 557, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.25 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 X ), T, X ) ) ] )
% 0.87/1.25 , clause( 558, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.87/1.25 , clause( 559, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.87/1.25 , clause( 560, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.87/1.25 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.25 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.87/1.25 , clause( 561, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.87/1.25 , clause( 562, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 563, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 0.87/1.25 , clause( 564, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.87/1.25 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.25 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.87/1.25 , clause( 565, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.87/1.25 , clause( 566, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 567, [ ~(
% 0.87/1.25 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.87/1.25 , clause( 568, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.87/1.25 , Y ), T ), Z, X ) ) ] )
% 0.87/1.25 , clause( 569, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 X ) ), Y ), Y ) ] )
% 0.87/1.25 , clause( 570, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.25 , Y ), Y ) ] )
% 0.87/1.25 , clause( 571, [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 572, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ] )
% 0.87/1.25 , clause( 573, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.87/1.25 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ] )
% 0.87/1.25 , clause( 574, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.87/1.25 'class_Int_Onumber__ring'( X ) ), =( Y, hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 575, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.25 ) ), Y ) ] )
% 0.87/1.25 , clause( 576, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.87/1.25 Y ) ] )
% 0.87/1.25 , clause( 577, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.87/1.25 Y ) ] )
% 0.87/1.25 , clause( 578, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 0.87/1.25 , clause( 579, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 X ) ), Y ), Y ) ] )
% 0.87/1.25 , clause( 580, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ), X ) ) ] )
% 0.87/1.25 , clause( 581, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.87/1.25 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 582, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.87/1.25 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 583, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 0.87/1.25 , clause( 584, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.87/1.25 , clause( 585, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 X, Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.25 ) ), X, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 586, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.25 ) ), X, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 587, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.25 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 588, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.87/1.25 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.87/1.25 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.87/1.25 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 0.87/1.25 , clause( 589, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.87/1.25 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.87/1.25 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.87/1.25 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 0.87/1.25 , clause( 590, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.87/1.25 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.87/1.25 , clause( 591, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 592, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.25 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.25 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 593, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.87/1.25 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 594, [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat'
% 0.87/1.25 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 595, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat'
% 0.87/1.25 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 596, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.87/1.25 ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.25 ), X ) ) ] )
% 0.87/1.25 , clause( 597, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.87/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.87/1.25 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 0.87/1.25 , clause( 598, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.87/1.25 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.25 ), 'c_HOL_Otimes__class_Otimes'( T, U, X ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, U, X )
% 0.87/1.25 ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 599, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.87/1.25 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.25 ), 'c_HOL_Otimes__class_Otimes'( T, U, X ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, U, X )
% 0.87/1.25 ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 600, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.25 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 0.87/1.25 =( Y, T ), =( X, Z ) ] )
% 0.87/1.25 , clause( 601, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.25 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 0.87/1.25 =( Y, T ), =( X, Z ) ] )
% 0.87/1.25 , clause( 602, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ),
% 0.87/1.25 'tc_List_Olist'( X ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 603, [ =( 'c_Predicate_Oconversep'( 'c_fequal'( X ), X, X ),
% 0.87/1.25 'c_fequal'( X ) ) ] )
% 0.87/1.25 , clause( 604, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 605, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 0.87/1.25 , clause( 606, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 0.87/1.25 , clause( 607, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 0.87/1.25 , clause( 608, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 609, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 610, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.87/1.25 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.25 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 611, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.87/1.25 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y,
% 0.87/1.25 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 612, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 613, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 614, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 615, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 616, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 617, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 618, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Oappend'( X, Y, Z )
% 0.87/1.25 , 'tc_List_Olist'( Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.25 'tc_nat' ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) ) ),
% 0.87/1.25 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ) ) ) ] )
% 0.87/1.25 , clause( 619, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.87/1.25 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.87/1.25 , clause( 620, [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), =( Z, Y ), ~(
% 0.87/1.25 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( U, Y, T ),
% 0.87/1.25 'c_List_Olist_OCons'( W, Z, T ), T ) ) ] )
% 0.87/1.25 , clause( 621, [ ~(
% 0.87/1.25 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.25 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.25 T, X ) ) ] )
% 0.87/1.25 , clause( 622, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 623, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y, Z
% 0.87/1.25 , X ) ) ) ] )
% 0.87/1.25 , clause( 624, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 625, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 0.87/1.25 , clause( 626, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.87/1.25 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ), 'c_List_Ofoldr'(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 627, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.87/1.25 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 628, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.87/1.25 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 629, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 0.87/1.25 , =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.87/1.25 , X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 0.87/1.25 , clause( 630, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.87/1.25 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.25 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.87/1.25 , clause( 631, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.87/1.25 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.25 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.87/1.25 , clause( 632, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.87/1.25 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.25 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.87/1.25 , clause( 633, [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y )
% 0.87/1.25 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_List_Olist_ONil'(
% 0.87/1.25 Y ) ) ] )
% 0.87/1.25 , clause( 634, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.87/1.25 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.87/1.25 , clause( 635, [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_OCons'( Y, Z, T ), U
% 0.87/1.25 , T, W ), hAPP( hAPP( X, Y ), 'c_List_Ofoldr'( X, Z, U, T, W ) ) ) ] )
% 0.87/1.25 , clause( 636, [ =( 'c_Predicate_Oconversep'( 'c_Predicate_Oconversep'( X,
% 0.87/1.25 Y, Z ), Z, Y ), X ) ] )
% 0.87/1.25 , clause( 637, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.25 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 638, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.25 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 639, [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 640, [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 641, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.87/1.25 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Otimes__class_Otimes'( Z, T
% 0.87/1.25 , X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Z, U, X ) ) ) ), =( T, U ), =( Z,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 642, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 Y, T, 'tc_nat' ) ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 643, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 644, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 645, [ ~(
% 0.87/1.25 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.25 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.87/1.25 , clause( 646, [ ~(
% 0.87/1.25 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.25 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.87/1.25 , clause( 647, [ ~(
% 0.87/1.25 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 0.87/1.25 , clause( 648, [ ~(
% 0.87/1.25 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.25 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.87/1.25 , clause( 649, [ ~(
% 0.87/1.25 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.87/1.25 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.87/1.25 , clause( 650, [ ~(
% 0.87/1.25 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 0.87/1.25 , clause( 651, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 652, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.25 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.87/1.25 , Z ), Y ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 653, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 654, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 0.87/1.25 'c_List_Olist_OCons'( T, U, Z ) ) ), =( X, T ) ] )
% 0.87/1.25 , clause( 655, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 0.87/1.25 'c_List_Olist_OCons'( T, U, Z ) ) ), =( Y, U ) ] )
% 0.87/1.25 , clause( 656, [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), hBOOL( hAPP( hAPP( X,
% 0.87/1.25 U ), W ) ), ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( U, Y, T ),
% 0.87/1.25 'c_List_Olist_OCons'( W, Z, T ), T ) ) ] )
% 0.87/1.25 , clause( 657, [ 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 0.87/1.25 'c_List_Olist_OCons'( Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 658, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 659, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 0.87/1.25 , =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 0.87/1.25 , clause( 660, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.87/1.25 , clause( 661, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.25 , Y, X ), X ) ) ] )
% 0.87/1.25 , clause( 662, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.25 , T, X ), X ) ) ] )
% 0.87/1.25 , clause( 663, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.25 , T, X ), X ) ) ] )
% 0.87/1.25 , clause( 664, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.87/1.25 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.25 , Y, X ), X ) ) ] )
% 0.87/1.25 , clause( 665, [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 0.87/1.25 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) )
% 0.87/1.25 , =( Y, Z ) ] )
% 0.87/1.25 , clause( 666, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.87/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.87/1.25 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ] )
% 0.87/1.25 , clause( 667, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y,
% 0.87/1.25 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 668, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 669, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.25 T, X ), X ) ) ] )
% 0.87/1.25 , clause( 670, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.87/1.25 X ), Z, X ) ) ] )
% 0.87/1.25 , clause( 671, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.25 T, X ), X ) ) ] )
% 0.87/1.25 , clause( 672, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.25 X ), T, X ) ) ] )
% 0.87/1.25 , clause( 673, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.87/1.25 T, X ), X ) ) ] )
% 0.87/1.25 , clause( 674, [ =( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.25 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 675, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.25 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.25 X ), T, X ) ) ] )
% 0.87/1.25 , clause( 676, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.87/1.25 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 Z, T, X ) ) ) ] )
% 0.87/1.25 , clause( 677, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.87/1.25 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 Z, T, X ) ) ) ] )
% 0.87/1.25 , clause( 678, [ =( 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.87/1.25 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 679, [ =( 'c_HOL_Otimes__class_Otimes'( X, hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP( hAPP(
% 0.87/1.25 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.87/1.25 Y, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 680, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.25 X ), Z ), T ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.87/1.25 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.25 Y, T, X ) ) ) ] )
% 0.87/1.25 , clause( 681, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X
% 0.87/1.25 , Y ), T ) ) ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 0.87/1.25 , clause( 682, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X
% 0.87/1.25 , Y ), T ) ) ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 0.87/1.25 , clause( 683, [ =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Oappend'(
% 0.87/1.25 'c_List_Olist_ONil'( Z ), 'c_List_Olist_OCons'( X, Y, Z ), Z ) ) ] )
% 0.87/1.25 , clause( 684, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ),
% 0.87/1.25 'c_List_Olist_OCons'( Y, Z, X ), X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 685, [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.87/1.25 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.87/1.25 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( X, T
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 686, [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.87/1.25 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.87/1.25 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( Y, U
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 687, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 0.87/1.25 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.25 ) ), Y, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 688, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ),
% 0.87/1.25 'tc_nat' ), =( X, 'c_List_Olist_ONil'( Y ) ) ] )
% 0.87/1.25 , clause( 689, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ),
% 0.87/1.25 'tc_List_Olist'( X ) ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 690, [ ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'(
% 0.87/1.25 'c_Lambda_Obeta', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ) ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) )
% 0.87/1.25 , ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB' ) ),
% 0.87/1.25 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.87/1.25 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ] )
% 0.87/1.25 , clause( 691, [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U,
% 0.87/1.25 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W
% 0.87/1.25 ), W ), 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( T,
% 0.87/1.25 'c_List_Olist_ONil'( W ), W ), W ), W ) ) ] )
% 0.87/1.25 , clause( 692, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), =( Y, Z ), ~(
% 0.87/1.25 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y,
% 0.87/1.25 'c_List_Olist_ONil'( U ), U ), U ), 'c_List_Oappend'( W,
% 0.87/1.25 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( U ), U ), U ), U ) ) ] )
% 0.87/1.25 , clause( 693, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_ListOrder_Ostep1'( X
% 0.87/1.25 , T, U, W ), ~( 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( T,
% 0.87/1.25 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( W ), W ), W ),
% 0.87/1.25 'c_List_Oappend'( U, 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W
% 0.87/1.25 ), W ), W ) ) ] )
% 0.87/1.25 , clause( 694, [ =( X, Y ), 'c_ListOrder_Ostep1'( Z, X, Y, T ), ~(
% 0.87/1.25 'c_ListOrder_Ostep1'( Z, 'c_List_Oappend'( X, 'c_List_Olist_OCons'( U,
% 0.87/1.25 'c_List_Olist_ONil'( T ), T ), T ), 'c_List_Oappend'( Y,
% 0.87/1.25 'c_List_Olist_OCons'( W, 'c_List_Olist_ONil'( T ), T ), T ), T ) ) ] )
% 0.87/1.25 , clause( 695, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.87/1.25 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.87/1.25 Y ), X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ] )
% 0.87/1.25 , clause( 696, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.25 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.25 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 0.87/1.25 , clause( 697, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.25 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.25 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 698, [ 'c_Type_Otypings'( X, Y,
% 0.87/1.25 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X, T, Y ) ), ~(
% 0.87/1.25 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', T, Y,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.87/1.25 , clause( 699, [ 'c_Type_Otypings'( X, Y,
% 0.87/1.25 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X, T, Y ) ), ~(
% 0.87/1.25 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', T, Y,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.87/1.25 , clause( 700, [ 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.87/1.25 , Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ), ~( 'c_Type_Otypings'( X
% 0.87/1.25 , Z, U ) ), ~( 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 0.87/1.25 'c_Type_Otype_OFun', U, T, 'tc_Type_Otype', 'tc_Type_Otype' ) ) ) ] )
% 0.87/1.25 , clause( 701, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.87/1.25 'c_List_Olist_OCons'( 'v_sko__List__Xlistsp__Xinduct__1'( Z, X ),
% 0.87/1.25 'v_sko__List__Xlistsp__Xinduct__2'( Z, X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'(
% 0.87/1.25 Z, 't_a' ), Y ) ) ) ] )
% 0.87/1.25 , clause( 702, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.87/1.25 'c_List_Olist_OCons'( 'v_sko__List__Xlistsp__Xinducts__1'( Z, X ),
% 0.87/1.25 'v_sko__List__Xlistsp__Xinducts__2'( Z, X ), 't_a' ) ) ) ), ~( hBOOL(
% 0.87/1.25 hAPP( X, 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 'c_List_Olistsp'( Z, 't_a' ), Y ) ) ) ] )
% 0.87/1.25 , clause( 703, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ),
% 0.87/1.25 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.87/1.25 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X, Y, T ), Z,
% 0.87/1.25 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), T,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.87/1.25 , clause( 704, [ =( X, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.87/1.25 'c_Type_Osko__Type__Xvar__app__types__1__1'( Y, X, Z, T ), Y,
% 0.87/1.25 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( Z,
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ), ~( 'c_Type_Otypings'( Z, W, V0
% 0.87/1.25 ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.87/1.25 , Y ) ) ] )
% 0.87/1.25 , clause( 705, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( 'c_List_Olistsp'( Z,
% 0.87/1.25 't_a' ), 'v_sko__List__Xlistsp__Xinducts__2'( Z, X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'(
% 0.87/1.25 Z, 't_a' ), Y ) ) ) ] )
% 0.87/1.25 , clause( 706, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( 'c_List_Olistsp'( Z,
% 0.87/1.25 't_a' ), 'v_sko__List__Xlistsp__Xinduct__2'( Z, X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'(
% 0.87/1.25 Z, 't_a' ), Y ) ) ) ] )
% 0.87/1.25 , clause( 707, [ 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', X,
% 0.87/1.25 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, X, Z ),
% 0.87/1.25 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), X,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ) ) ) ] )
% 0.87/1.25 , clause( 708, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.87/1.25 'c_Lambda_Osubst'( X, T, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.87/1.25 ), T ) ) ) ] )
% 0.87/1.25 , clause( 709, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.87/1.25 'c_Lambda_Osubst'( T, Y, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.87/1.25 ), T ) ) ) ] )
% 0.87/1.25 , clause( 710, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.87/1.25 'c_Lambda_Osubst'( X, T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta'
% 0.87/1.25 , Y ), T ) ) ) ] )
% 0.87/1.25 , clause( 711, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ),
% 0.87/1.25 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.87/1.25 ), Y ) ) ) ] )
% 0.87/1.25 , clause( 712, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.87/1.25 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.87/1.25 'tc_Lambda_OdB' ), Y ), Z ) ) ) ] )
% 0.87/1.25 , clause( 713, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.87/1.25 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.87/1.25 'tc_Lambda_OdB' ), X ), Z ) ) ) ] )
% 0.87/1.25 , clause( 714, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.87/1.25 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.87/1.25 'tc_Lambda_OdB' ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.87/1.25 ), Z ) ) ) ] )
% 0.87/1.25 , clause( 715, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 0.87/1.25 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'(
% 0.87/1.25 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 716, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.25 Y, X ) ) ] )
% 0.87/1.25 , clause( 717, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.25 Y, X ) ) ] )
% 0.87/1.25 , clause( 718, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.25 Y, X ) ) ] )
% 0.87/1.25 , clause( 719, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.87/1.25 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ] )
% 0.87/1.25 , clause( 720, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.87/1.25 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 X, Y ), U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ) ] )
% 0.87/1.25 , clause( 721, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.25 Y, X ) ) ] )
% 0.87/1.25 , clause( 722, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.87/1.25 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 723, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 724, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 0.87/1.25 , clause( 725, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 0.87/1.25 , clause( 726, [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP(
% 0.87/1.25 hAPP( 'c_Type_Otype_OFun', Z ), T ) ) ), =( X, Z ) ] )
% 0.87/1.25 , clause( 727, [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP(
% 0.87/1.25 hAPP( 'c_Type_Otype_OFun', Z ), T ) ) ), =( Y, T ) ] )
% 0.87/1.25 , clause( 728, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U )
% 0.87/1.25 ), ~( 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 729, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 730, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.25 ), X, Y ), X ) ] )
% 0.87/1.25 , clause( 731, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 732, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.87/1.25 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 733, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 734, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 735, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 736, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 737, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.25 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.87/1.25 , clause( 738, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.25 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.87/1.25 , clause( 739, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 740, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 0.87/1.25 , clause( 741, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.25 ), =( Z, Y ) ] )
% 0.87/1.25 , clause( 742, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 0.87/1.25 , clause( 743, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), =( Z, Y ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ] )
% 0.87/1.25 , clause( 744, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 0.87/1.25 , clause( 745, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 746, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.25 ), =( Z, Y ) ] )
% 0.87/1.25 , clause( 747, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.87/1.25 , clause( 748, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.87/1.25 , clause( 749, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.87/1.25 , clause( 750, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 751, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 752, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ),
% 0.87/1.25 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 0.87/1.25 , clause( 753, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ),
% 0.87/1.25 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 0.87/1.25 , clause( 754, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.87/1.25 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 755, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ] )
% 0.87/1.25 , clause( 756, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), hAPP( hAPP(
% 0.87/1.25 'c_Type_Otype_OFun', Z ), T ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( X
% 0.87/1.25 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_Type_Otype' ), Y, T ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 757, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 758, [ ~( 'c_ListOrder_Ostep1'( X, Y, 'c_List_Olist_ONil'( Z ), Z
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 759, [ ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_ONil'( Y ), Z, Y
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 760, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.87/1.25 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( X, Z ), T ) ) ) ] )
% 0.87/1.25 , clause( 761, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 0.87/1.25 , clause( 762, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 0.87/1.25 , clause( 763, [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 0.87/1.25 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 0.87/1.25 'c_Suc'( Y ), Z, T ) ) ] )
% 0.87/1.25 , clause( 764, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X )
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 765, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X )
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 766, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.87/1.25 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 X, Y ), U ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ] )
% 0.87/1.25 , clause( 767, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.87/1.25 ), Z ), Z ) ) ] )
% 0.87/1.25 , clause( 768, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.87/1.25 ), Z ), Z ) ) ] )
% 0.87/1.25 , clause( 769, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 770, [ 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( Y, Z, T ),
% 0.87/1.25 'c_List_Oappend'( Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 771, [ ~( 'c_ListOrder_Ostep1'( X, Y, Z, T ) ),
% 0.87/1.25 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( Y, U, T ), 'c_List_Oappend'( Z
% 0.87/1.25 , U, T ), T ) ] )
% 0.87/1.25 , clause( 772, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 0.87/1.25 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.87/1.25 , clause( 773, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.87/1.25 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.87/1.25 , clause( 774, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 775, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 776, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.87/1.25 , clause( 777, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.87/1.25 , clause( 778, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.87/1.25 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 779, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 0.87/1.25 , clause( 780, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 781, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.87/1.25 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 0.87/1.25 , clause( 782, [ =( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Transitive__Closure_Ortranclp'( X, Y ), Y ),
% 0.87/1.25 'c_Transitive__Closure_Ortranclp'( X, Y ) ) ] )
% 0.87/1.25 , clause( 783, [ 'c_Type_Otyping'( X, Y, hAPP( hAPP( 'c_Type_Otype_OFun',
% 0.87/1.25 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, Y, T ) ), Z ) ), ~(
% 0.87/1.25 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), T ), Z ) ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 784, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.87/1.25 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 785, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.25 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 786, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.87/1.25 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 0.87/1.25 , clause( 787, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.87/1.25 'v_sko__List__Xlistsp__Xinduct__2'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.87/1.25 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( Z,
% 0.87/1.25 't_a' ), Y ) ) ) ] )
% 0.87/1.25 , clause( 788, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z,
% 0.87/1.25 'v_sko__List__Xlistsp__Xinduct__1'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.87/1.25 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( Z,
% 0.87/1.25 't_a' ), Y ) ) ) ] )
% 0.87/1.25 , clause( 789, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.87/1.25 'v_sko__List__Xlistsp__Xinducts__2'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.87/1.25 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( Z,
% 0.87/1.25 't_a' ), Y ) ) ) ] )
% 0.87/1.25 , clause( 790, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z,
% 0.87/1.25 'v_sko__List__Xlistsp__Xinducts__1'( Z, X ) ) ), ~( hBOOL( hAPP( X,
% 0.87/1.25 'c_List_Olist_ONil'( 't_a' ) ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( Z,
% 0.87/1.25 't_a' ), Y ) ) ) ] )
% 0.87/1.25 , clause( 791, [ 'c_Type_Otyping'( X, Y,
% 0.87/1.25 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, T, Y ) ), ~(
% 0.87/1.25 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', T ), Y ), Z ) ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 792, [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y )
% 0.87/1.25 , Z ), T ), ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y,
% 0.87/1.25 hAPP( hAPP( 'c_Type_Otype_OFun', U ), T ) ) ) ] )
% 0.87/1.25 , clause( 793, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 0.87/1.25 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ] )
% 0.87/1.25 , clause( 794, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.87/1.25 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.87/1.25 'tc_nat' ) ] )
% 0.87/1.25 , clause( 795, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.87/1.25 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 796, [ 'c_Type_Otypings'( X, Y,
% 0.87/1.25 'c_Type_Osko__Type__Xvar__app__types__1__1'( Z, T, X, Y ) ), ~(
% 0.87/1.25 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.25 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ) ),
% 0.87/1.25 ~( 'c_Type_Otypings'( X, W, V0 ) ), ~( 'c_Type_Otyping'( X,
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.87/1.25 , clause( 797, [ 'c_Type_Otypings'( X, Y,
% 0.87/1.25 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X, T, Y ) ), ~(
% 0.87/1.25 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.25 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 798, [ =( 'c_List_Olistsp'(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.87/1.25 'tc_bool' ) ), Z ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.25 'c_List_Olistsp'( X, Z ), 'c_List_Olistsp'( Y, Z ), 'tc_fun'(
% 0.87/1.25 'tc_List_Olist'( Z ), 'tc_bool' ) ) ) ] )
% 0.87/1.25 , clause( 799, [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Type_Otyping'( X, T, Z
% 0.87/1.25 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), T ), Y ) ) ) ] )
% 0.87/1.25 , clause( 800, [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'(
% 0.87/1.25 'c_Type_Oshift'( X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'(
% 0.87/1.25 X, 'c_Lambda_Osubst'( U, Y, T ), W ) ] )
% 0.87/1.25 , clause( 801, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Olift'( X, Y ) ),
% 0.87/1.25 'c_Lambda_Olift'( Z, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.87/1.25 ), Z ) ) ) ] )
% 0.87/1.25 , clause( 802, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.87/1.25 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 803, [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z,
% 0.87/1.25 'tc_Type_Otype' ), 'c_Lambda_Olift'( T, Y ), U ), ~( 'c_Type_Otyping'( X
% 0.87/1.25 , T, U ) ) ] )
% 0.87/1.25 , clause( 804, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.87/1.25 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 805, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.87/1.25 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 806, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ) ), 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ) ) ) ] )
% 0.87/1.25 , clause( 807, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.87/1.25 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.87/1.25 'tc_nat' ) ] )
% 0.87/1.25 , clause( 808, [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ),
% 0.87/1.25 'c_Lambda_Olift'( 'c_Lambda_Oliftn'( X, Y, Z ), Z ) ) ] )
% 0.87/1.25 , clause( 809, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.87/1.25 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 810, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Z, 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ) ), ~( 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', Y, Z,
% 0.87/1.25 'tc_Lambda_OdB' ) ) ] )
% 0.87/1.25 , clause( 811, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.87/1.25 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.87/1.25 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~(
% 0.87/1.25 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.87/1.25 'tc_Lambda_OdB' ), X ), Z ) ) ) ] )
% 0.87/1.25 , clause( 812, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 813, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 814, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.87/1.25 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), hBOOL( hAPP(
% 0.87/1.25 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__1'( X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 815, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, T, 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ) ), =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z,
% 0.87/1.25 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1'( X
% 0.87/1.25 , Y, Z, T ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), =( T,
% 0.87/1.25 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.87/1.25 , clause( 816, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.25 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.87/1.25 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), hBOOL( hAPP(
% 0.87/1.25 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__1'( X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 817, [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 0.87/1.25 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 818, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ) ), 'c_Lambda_Osubst'(
% 0.87/1.25 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.87/1.25 , clause( 819, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.25 'c_Lambda_OdB_OVar'( Y ),
% 0.87/1.25 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Lambda_Obeta', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.25 'c_Lambda_OdB_OVar'( Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ) )
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 820, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), hBOOL( hAPP(
% 0.87/1.25 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__1'( X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 821, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), hBOOL( hAPP(
% 0.87/1.25 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__1'( X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 822, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 X ) ), Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y,
% 0.87/1.25 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.87/1.25 , clause( 823, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), hBOOL( hAPP(
% 0.87/1.25 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X
% 0.87/1.25 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 824, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 825, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Oappend'( Z, T, U ), W,
% 0.87/1.25 U ), 'c_List_Ofoldl'( X, 'c_List_Ofoldl'( X, Y, Z, W, U ), T, W, U ) ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 826, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 X ) ), 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Lambda_Obeta', X ), Y ) ) ) ] )
% 0.87/1.25 , clause( 827, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.87/1.25 'tc_bool' ) ), Y ) ) ) ] )
% 0.87/1.25 , clause( 828, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 0.87/1.25 'tc_bool' ) ), Y ) ) ) ] )
% 0.87/1.25 , clause( 829, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'(
% 0.87/1.25 'c_List_Olist_ONil'( X ), 'c_List_Olist_ONil'( X ), X ) ) ] )
% 0.87/1.25 , clause( 830, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Olift'( X,
% 0.87/1.25 Y ) ), 'c_Lambda_Olift'( Z, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Lambda_Obeta', X ), Z ) ) ) ] )
% 0.87/1.25 , clause( 831, [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.25 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ) ] )
% 0.87/1.25 , clause( 832, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 833, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.87/1.25 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.87/1.25 , clause( 834, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 0.87/1.25 'c_Lambda_OdB_OAbs'( X ), Y ) ] )
% 0.87/1.25 , clause( 835, [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'(
% 0.87/1.25 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.87/1.25 , clause( 836, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ] )
% 0.87/1.25 , clause( 837, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ] )
% 0.87/1.25 , clause( 838, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 0.87/1.25 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.25 Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 0.87/1.25 , clause( 839, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 T ), U ), hAPP( Z, T ) ) ] )
% 0.87/1.25 , clause( 840, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Osubst'( X
% 0.87/1.25 , Y, Z ) ), 'c_Lambda_Osubst'( T, Y, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Lambda_Obeta', X ), T ) ) ) ] )
% 0.87/1.25 , clause( 841, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, Y
% 0.87/1.25 , Z ) ) ), =( X, T ) ] )
% 0.87/1.25 , clause( 842, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( X, T
% 0.87/1.25 , Z ) ) ), =( Y, T ) ] )
% 0.87/1.25 , clause( 843, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), hBOOL( hAPP(
% 0.87/1.25 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__1'( X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 844, [ =( 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ), X )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 845, [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 846, [ =( X, 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 847, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), Y, X ), Y )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 848, [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 849, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z )
% 0.87/1.25 , Y ) ] )
% 0.87/1.25 , clause( 850, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 0.87/1.25 , clause( 851, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 0.87/1.25 , clause( 852, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 0.87/1.25 , clause( 853, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 0.87/1.25 , clause( 854, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.87/1.25 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.87/1.25 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 0.87/1.25 , clause( 855, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.87/1.25 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.87/1.25 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 0.87/1.25 , clause( 856, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X
% 0.87/1.25 ) ) ), =( Y, 'c_List_Olist_ONil'( X ) ) ] )
% 0.87/1.25 , clause( 857, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X
% 0.87/1.25 ) ) ), =( Z, 'c_List_Olist_ONil'( X ) ) ] )
% 0.87/1.25 , clause( 858, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.87/1.25 ), =( X, Y ) ] )
% 0.87/1.25 , clause( 859, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z
% 0.87/1.25 ) ) ), =( X, 'c_List_Olist_ONil'( Z ) ) ] )
% 0.87/1.25 , clause( 860, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z
% 0.87/1.25 ) ) ), =( Y, 'c_List_Olist_ONil'( Z ) ) ] )
% 0.87/1.25 , clause( 861, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 0.87/1.25 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.87/1.25 , clause( 862, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) )
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 863, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.25 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 0.87/1.25 , clause( 864, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.25 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.87/1.25 , clause( 865, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.87/1.25 'c_Lambda_OdB_OAbs'( Z ) ) ] )
% 0.87/1.25 , clause( 866, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'(
% 0.87/1.25 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.87/1.25 'c_Lambda_OdB_OApp', X ), Y ), Z ) ] )
% 0.87/1.25 , clause( 867, [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 T ), U ), hAPP( hAPP( Z, T ), 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, U ) )
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 868, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ] )
% 0.87/1.25 , clause( 869, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ] )
% 0.87/1.25 , clause( 870, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.87/1.25 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.87/1.25 'tc_bool' ) ) ) ] )
% 0.87/1.25 , clause( 871, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.87/1.25 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 872, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.87/1.25 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 873, [ ~( =( 'c_List_Oappend'( X, Y, Z ), X ) ), =( Y,
% 0.87/1.25 'c_List_Olist_ONil'( Z ) ) ] )
% 0.87/1.25 , clause( 874, [ ~( =( X, 'c_List_Oappend'( X, Y, Z ) ) ), =( Y,
% 0.87/1.25 'c_List_Olist_ONil'( Z ) ) ] )
% 0.87/1.25 , clause( 875, [ ~( =( 'c_List_Oappend'( X, Y, Z ), Y ) ), =( X,
% 0.87/1.25 'c_List_Olist_ONil'( Z ) ) ] )
% 0.87/1.25 , clause( 876, [ ~( =( X, 'c_List_Oappend'( Y, X, Z ) ) ), =( Y,
% 0.87/1.25 'c_List_Olist_ONil'( Z ) ) ] )
% 0.87/1.25 , clause( 877, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ] )
% 0.87/1.25 , clause( 878, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X,
% 0.87/1.25 'tc_fun'( Y, 'tc_bool' ) ), X ) ] )
% 0.87/1.25 , clause( 879, [ 'c_Type_Otyping'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.25 'c_Lambda_Obeta', T ), Y ) ) ), ~( 'c_Type_Otyping'( X, T, Z ) ) ] )
% 0.87/1.25 , clause( 880, [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.87/1.25 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~(
% 0.87/1.25 hBOOL( hAPP( X, T ) ) ) ] )
% 0.87/1.25 , clause( 881, [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 0.87/1.25 ), Y ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ) ] )
% 0.87/1.25 , clause( 882, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ),
% 0.87/1.25 'c_List_Olist_ONil'( X ), X ), 'c_List_Olist_ONil'( X ) ) ] )
% 0.87/1.25 , clause( 883, [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.87/1.25 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.87/1.25 , clause( 884, [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.87/1.25 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ] )
% 0.87/1.25 , clause( 885, [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.87/1.25 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.87/1.25 , clause( 886, [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.87/1.25 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ] )
% 0.87/1.25 , clause( 887, [ =( 'c_Lambda_Osubst'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.87/1.25 , Y ), Z, T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Z,
% 0.87/1.25 T ) ), 'c_Lambda_Osubst'( Y, Z, T ) ) ) ] )
% 0.87/1.25 , clause( 888, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) )
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 889, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.87/1.25 'c_Lambda_OdB_OAbs'( Z ) ) ) ] )
% 0.87/1.25 , clause( 890, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) )
% 0.87/1.25 ), =( X, Y ) ] )
% 0.87/1.25 , clause( 891, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.87/1.25 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 892, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.87/1.25 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 893, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP(
% 0.87/1.25 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 0.87/1.25 , clause( 894, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.25 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.87/1.25 , clause( 895, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.25 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 0.87/1.25 , clause( 896, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 897, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP(
% 0.87/1.25 hAPP( 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP(
% 0.87/1.25 hAPP( Z, U ), W ) ) ) ] )
% 0.87/1.25 , clause( 898, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP(
% 0.87/1.25 hAPP( 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP(
% 0.87/1.25 hAPP( Z, U ), W ) ) ) ] )
% 0.87/1.25 , clause( 899, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( X,
% 0.87/1.25 'c_Lambda_OdB_OVar'( Y ), Z ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.87/1.25 ) ) ) ] )
% 0.87/1.25 , clause( 900, [ =( 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W )
% 0.87/1.25 , 'c_Set_Oimage'( 'c_COMBB'( X, Y, U, W, T ), Z, T, W ) ) ] )
% 0.87/1.25 , clause( 901, [ hBOOL( hAPP( 'c_List_Olistsp'( X, Y ), 'c_List_Oappend'( Z
% 0.87/1.25 , T, Y ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( X, Y ), T ) ) ), ~( hBOOL(
% 0.87/1.25 hAPP( 'c_List_Olistsp'( X, Y ), Z ) ) ) ] )
% 0.87/1.25 , clause( 902, [ hBOOL( hAPP( 'c_List_Olistsp'( X, Y ), Z ) ), ~( hBOOL(
% 0.87/1.25 hAPP( X, 'c_List_Osko__List__Xin__listsp__conv__set__1__1'( X, Z, Y ) ) )
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 903, [ ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.87/1.25 'c_Lambda_OdB_OVar'( X ) ), Y ) ) ) ] )
% 0.87/1.25 , clause( 904, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'(
% 0.87/1.25 'c_InductTermi_OIT', 'tc_Lambda_OdB' ), Y ) ) ) ] )
% 0.87/1.25 , clause( 905, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.87/1.25 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ] )
% 0.87/1.25 , clause( 906, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.87/1.25 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ] )
% 0.87/1.25 , clause( 907, [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.87/1.25 'tc_Lambda_OdB' ), X ) ) ] )
% 0.87/1.25 , clause( 908, [ hBOOL( hAPP( 'c_List_Olistsp'(
% 0.87/1.25 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.87/1.25 'tc_bool' ) ), Z ), T ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( Y, Z ), T )
% 0.87/1.25 ) ), ~( hBOOL( hAPP( 'c_List_Olistsp'( X, Z ), T ) ) ) ] )
% 0.87/1.25 , clause( 909, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 0.87/1.25 'c_Lambda_OdB_OVar'( X ), Y ) ] )
% 0.87/1.25 , clause( 910, [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OVar'(
% 0.87/1.25 T ), U ), hAPP( X, T ) ) ] )
% 0.87/1.25 , clause( 911, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), hBOOL( hAPP(
% 0.87/1.25 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), hBOOL(
% 0.87/1.25 hAPP( 'c_List_Olistsp'( 'c_InductTermi_OIT', 'tc_Lambda_OdB' ),
% 0.87/1.25 'v_sko__InductTermi__XIT__Xcases__1'( X ) ) ), ~( hBOOL( hAPP(
% 0.87/1.25 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 912, [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP(
% 0.87/1.25 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 0.87/1.25 , clause( 913, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.87/1.25 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.87/1.25 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.87/1.25 , clause( 914, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Olift'( X, Y )
% 0.87/1.25 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 915, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 916, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X )
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 917, [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X,
% 0.87/1.25 'c_Lambda_OdB_OVar'( Y ), Z ) ) ] )
% 0.87/1.25 , clause( 918, [ =( 'c_Lambda_Olift'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.87/1.25 , Y ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Olift'( X, Z ) ),
% 0.87/1.25 'c_Lambda_Olift'( Y, Z ) ) ) ] )
% 0.87/1.25 , clause( 919, [ hBOOL( hAPP( 'c_List_Olistsp'( X, Y ), 'c_List_Olist_ONil'(
% 0.87/1.25 Y ) ) ) ] )
% 0.87/1.25 , clause( 920, [ hBOOL( hAPP( 'c_List_Olistsp'( X, Y ), Z ) ), ~( hBOOL(
% 0.87/1.25 hAPP( 'c_List_Olistsp'( X, Y ), 'c_List_Oappend'( T, Z, Y ) ) ) ) ] )
% 0.87/1.25 , clause( 921, [ hBOOL( hAPP( 'c_List_Olistsp'( X, Y ), Z ) ), ~( hBOOL(
% 0.87/1.25 hAPP( 'c_List_Olistsp'( X, Y ), 'c_List_Oappend'( Z, T, Y ) ) ) ) ] )
% 0.87/1.25 , clause( 922, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, hAPP( hAPP(
% 0.87/1.25 'c_Lambda_OdB_OApp', T ), U ), W ), hAPP( hAPP( Y, T ), U ) ) ] )
% 0.87/1.25 , clause( 923, [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'(
% 0.87/1.25 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.87/1.25 , clause( 924, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OVar'(
% 0.87/1.25 T ), U ), hAPP( X, T ) ) ] )
% 0.87/1.25 , clause( 925, [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y
% 0.87/1.25 , W ) ) ) ] )
% 0.87/1.25 , clause( 926, [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W
% 0.87/1.25 ), Y ) ) ] )
% 0.87/1.25 , clause( 927, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 928, [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, hAPP( hAPP(
% 0.87/1.25 'c_Lambda_OdB_OApp', T ), U ), W ), hAPP( hAPP( hAPP( hAPP( Y, T ), U ),
% 0.87/1.25 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, W ) ), 'c_Lambda_OdB_OdB__rec'( X, Y
% 0.87/1.25 , Z, U, W ) ) ) ] )
% 0.87/1.25 , clause( 929, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.87/1.25 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.87/1.25 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.87/1.25 , clause( 930, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X )
% 0.87/1.25 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.87/1.25 , clause( 931, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.87/1.25 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z
% 0.87/1.25 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', Y ), Z ) ) ) ] )
% 0.87/1.25 , clause( 932, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.87/1.25 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y
% 0.87/1.25 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ] )
% 0.87/1.25 , clause( 933, [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.87/1.25 Y ), Z ), T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y,
% 0.87/1.25 T ) ), 'c_Lambda_Oliftn'( X, Z, T ) ) ) ] )
% 0.87/1.25 , clause( 934, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.87/1.25 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 0.87/1.25 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.87/1.25 , clause( 935, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.87/1.25 X ) ), Y ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z
% 0.87/1.25 ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.87/1.25 , clause( 936, [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 0.87/1.25 ), Y ), Z, T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X,
% 0.87/1.25 Z, T ) ), 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ] )
% 0.87/1.25 , clause( 937, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.87/1.25 'c_Lambda_OdB_OVar'( Z ) ) ) ] )
% 0.87/1.25 , clause( 938, [ hBOOL( hAPP( 'c_List_Olistsp'( 'c_InductTermi_OIT',
% 0.87/1.25 'tc_Lambda_OdB' ), 'v_rs' ) ) ] )
% 0.87/1.25 , clause( 939, [ hBOOL( hAPP( 'c_List_Olistsp'( 'c_COMBB'(
% 0.87/1.25 'c_InductTermi_OIT', 'c_COMBC'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.87/1.25 'v_i' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.87/1.25 'tc_Lambda_OdB', 'tc_bool', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), 'v_rs'
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 940, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'(
% 0.87/1.25 'v_i' ) ) ) ) ] )
% 0.87/1.25 , clause( 941, [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ),
% 0.87/1.25 ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 0.87/1.25 , clause( 942, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.87/1.25 'class_Orderings_Opreorder'( Y ) ) ] )
% 0.87/1.25 , clause( 943, [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 0.87/1.25 'class_Lattices_Olattice'( Y ) ) ] )
% 0.87/1.25 , clause( 944, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.87/1.25 'class_Orderings_Oorder'( Y ) ) ] )
% 0.87/1.25 , clause( 945, [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.87/1.25 'tc_nat' ) ] )
% 0.87/1.25 , clause( 946, [
% 0.87/1.25 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 947, [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.87/1.25 'tc_nat' ) ] )
% 0.87/1.25 , clause( 948, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.87/1.25 'tc_nat' ) ] )
% 0.87/1.25 , clause( 949, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.87/1.25 'tc_nat' ) ] )
% 0.87/1.25 , clause( 950, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat'
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 951, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 952, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 953, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 954, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 955, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 956, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 957, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 958, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 959, [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 960, [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 961, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 962, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 963, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 964, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 965, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 966, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 967, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 968, [ 'class_Lattices_Olattice'( 'tc_nat' ) ] )
% 0.87/1.25 , clause( 969, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 0.87/1.26 , clause( 970, [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ] )
% 0.87/1.26 , clause( 971, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 0.87/1.26 , clause( 972, [ 'class_Lattices_Olattice'( 'tc_bool' ) ] )
% 0.87/1.26 , clause( 973, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 0.87/1.26 , clause( 974, [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W
% 0.87/1.26 ), Y ) ) ] )
% 0.87/1.26 , clause( 975, [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y
% 0.87/1.26 , W ) ) ) ] )
% 0.87/1.26 , clause( 976, [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ] )
% 0.87/1.26 , clause( 977, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y )
% 0.87/1.26 ) ) ] )
% 0.87/1.26 ] ).
% 0.87/1.26
% 0.87/1.26
% 0.87/1.26
% 0.87/1.26 subsumption(
% 0.87/1.26 clause( 397, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X ) )
% 0.87/1.26 ) ] )
% 0.87/1.26 , clause( 916, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X )
% 0.87/1.26 ) ) ] )
% 0.87/1.26 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.87/1.26
% 0.87/1.26
% 0.87/1.26 resolution(
% 0.87/1.26 clause( 2156, [] )
% 0.87/1.26 , clause( 940, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'(
% 0.87/1.26 'v_i' ) ) ) ) ] )
% 0.87/1.26 , 0, clause( 397, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'(
% 0.87/1.26 X ) ) ) ] )
% 0.87/1.26 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_i' )] )).
% 0.87/1.26
% 0.87/1.26
% 0.87/1.26 subsumption(
% 0.87/1.26 clause( 419, [] )
% 0.87/1.26 , clause( 2156, [] )
% 0.87/1.26 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.87/1.26
% 0.87/1.26
% 0.87/1.26 end.
% 0.87/1.26
% 0.87/1.26 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.87/1.26
% 0.87/1.26 Memory use:
% 0.87/1.26
% 0.87/1.26 space for terms: 29378
% 0.87/1.26 space for clauses: 39191
% 0.87/1.26
% 0.87/1.26
% 0.87/1.26 clauses generated: 520
% 0.87/1.26 clauses kept: 420
% 0.87/1.26 clauses selected: 0
% 0.87/1.26 clauses deleted: 0
% 0.87/1.26 clauses inuse deleted: 0
% 0.87/1.26
% 0.87/1.26 subsentry: 9769
% 0.87/1.26 literals s-matched: 4156
% 0.87/1.26 literals matched: 4102
% 0.87/1.26 full subsumption: 1006
% 0.87/1.26
% 0.87/1.26 checksum: -841744685
% 0.87/1.26
% 0.87/1.26
% 0.87/1.26 Bliksem ended
%------------------------------------------------------------------------------