TSTP Solution File: LCL762-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL762-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 07:57:39 EDT 2022
% Result : Unsatisfiable 0.80s 1.20s
% Output : Refutation 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL762-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n020.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 : Sat Jul 2 14:20:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.80/1.19 *** allocated 10000 integers for termspace/termends
% 0.80/1.19 *** allocated 10000 integers for clauses
% 0.80/1.19 *** allocated 10000 integers for justifications
% 0.80/1.19 Bliksem 1.12
% 0.80/1.19
% 0.80/1.19
% 0.80/1.19 Automatic Strategy Selection
% 0.80/1.19
% 0.80/1.19 Clauses:
% 0.80/1.19 [
% 0.80/1.19 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP( hAPP(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.80/1.19 ) ) ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X
% 0.80/1.19 ), 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y,
% 0.80/1.19 'c_HOL_Ozero__class_Ozero'( X ), X, X ) ) ],
% 0.80/1.19 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.19 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.80/1.19 'tc_nat' ) ],
% 0.80/1.19 [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T ), Z ) ],
% 0.80/1.19 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.19 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ), 'tc_List_Olist'( X
% 0.80/1.19 ) ), 'tc_nat' ) ) ],
% 0.80/1.19 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 0.80/1.19 ), =( Y, U ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.19 [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.80/1.19 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X, Y, T ), Z,
% 0.80/1.19 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.80/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.80/1.19 'tc_Lambda_OdB' ), Z ) ) ],
% 0.80/1.19 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist__update'( X, Y, Z, T ),
% 0.80/1.19 'tc_List_Olist'( T ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T
% 0.80/1.19 ) ) ) ],
% 0.80/1.19 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 0.80/1.19 , 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, Y ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.19 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ), 'tc_nat' ), =( X,
% 0.80/1.19 'c_List_Olist_ONil'( Y ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.19 'c_Predicate_Oconversep'( X, Y, Y ), Y ), Z ), T ) ), ~( hBOOL( hAPP(
% 0.80/1.19 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), T ), Z ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.80/1.19 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.19 'c_Predicate_Oconversep'( X, Y, Y ), Y ), T ), Z ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.19 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T ), U ) ),
% 0.80/1.19 ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.19 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T ), U ) ),
% 0.80/1.19 ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ],
% 0.80/1.19 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.19 ), 'tc_nat' ) ) ],
% 0.80/1.19 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.19 ), 'tc_nat' ) ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.80/1.19 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.19 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.80/1.19 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 0.80/1.19 ), =( X, T ) ],
% 0.80/1.19 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.19 'c_Transitive__Closure_Ortranclp'( X, Z ), Y ), T ) ) ), ~(
% 0.80/1.19 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.80/1.19 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( 'c_Wellfounded_Oaccp'( X, T, Z )
% 0.80/1.19 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Z ), Y )
% 0.80/1.19 , T ) ) ) ],
% 0.80/1.19 [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.80/1.19 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X, Y, T ), Z,
% 0.80/1.19 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.80/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.80/1.19 'tc_Lambda_OdB' ), Z ) ) ],
% 0.80/1.19 [ 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.80/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ), ~( hBOOL( hAPP(
% 0.80/1.19 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', X ) ), ~( 'c_Wellfounded_Oaccp'(
% 0.80/1.19 'c_Predicate_Oconversep'( 'c_Lambda_Obeta', 'tc_Lambda_OdB',
% 0.80/1.19 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ) ) ],
% 0.80/1.19 [ ~( =( 'c_Nat_Osize__class_Osize'( 'c_List_Oremdups'( X, Y ),
% 0.80/1.19 'tc_List_Olist'( Y ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y
% 0.80/1.19 ) ) ) ), =( 'c_List_Oremdups'( X, Y ), X ) ],
% 0.80/1.19 [ ~( =( 'c_List_Oremdups'( X, Y ), X ) ), =( 'c_Nat_Osize__class_Osize'(
% 0.80/1.19 'c_List_Oremdups'( X, Y ), 'tc_List_Olist'( Y ) ),
% 0.80/1.19 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ) ) ],
% 0.80/1.19 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Omap'( X, Y, Z, T ),
% 0.80/1.19 'tc_List_Olist'( T ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z
% 0.80/1.19 ) ) ) ],
% 0.80/1.19 [ =( 'c_List_Omap'( X, 'c_List_Oreplicate'( Y, Z, T ), T, U ),
% 0.80/1.19 'c_List_Oreplicate'( Y, hAPP( X, Z ), U ) ) ],
% 0.80/1.19 [ =( 'c_List_Orev'( 'c_List_Oreplicate'( X, Y, Z ), Z ),
% 0.80/1.19 'c_List_Oreplicate'( X, Y, Z ) ) ],
% 0.80/1.19 [ =( 'c_List_Ofoldr'( X, 'c_List_Oappend'( Y, Z, T ), U, T, W ),
% 0.80/1.19 'c_List_Ofoldr'( X, Y, 'c_List_Ofoldr'( X, Z, U, T, W ), T, W ) ) ],
% 0.80/1.19 [ =( 'c_List_Ofilter'( X, 'c_List_Oreplicate'( Y, Z, T ), T ),
% 0.80/1.19 'c_List_Oreplicate'( Y, Z, T ) ), ~( hBOOL( hAPP( X, Z ) ) ) ],
% 0.80/1.19 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Omap'( X, U, Z, T ) ) ),
% 0.80/1.19 =( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ),
% 0.80/1.19 'c_Nat_Osize__class_Osize'( U, 'tc_List_Olist'( Z ) ) ) ],
% 0.80/1.19 [ =( 'c_Predicate_Oconversep'( 'c_fequal'( X ), X, X ), 'c_fequal'( X )
% 0.80/1.19 ) ],
% 0.80/1.19 [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T, U, Z ),
% 0.80/1.19 'c_List_Oappend'( 'c_List_Olist__update'( X, T, U, Z ), Y, Z ) ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 0.80/1.19 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ],
% 0.80/1.19 [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T, U, Z ),
% 0.80/1.19 'c_List_Oappend'( 'c_List_Olist__update'( X, T, U, Z ), Y, Z ) ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 0.80/1.19 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ],
% 0.80/1.19 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Orotate'( X, Y, Z ),
% 0.80/1.19 'tc_List_Olist'( Z ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z
% 0.80/1.19 ) ) ) ],
% 0.80/1.19 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.80/1.19 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.80/1.19 , X ) ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.19 , Y, X ) ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.19 , Y, X ) ) ],
% 0.80/1.19 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.80/1.19 ), =( Z, Y ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.80/1.19 ) ],
% 0.80/1.19 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.80/1.19 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.80/1.19 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 0.80/1.19 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 0.80/1.19 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.80/1.19 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.19 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.80/1.19 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.80/1.19 'c_List_Oreplicate'( T, Y, Z ), Z ), 'c_List_Oappend'(
% 0.80/1.19 'c_List_Oreplicate'( T, Y, Z ), 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.19 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.80/1.19 ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.19 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.80/1.19 T, X ) ) ],
% 0.80/1.19 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.19 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.19 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.19 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.80/1.19 'tc_List_Olist'( Z ) ), X ) ],
% 0.80/1.19 [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_OCons'( Y, Z, T ), U, T, W ),
% 0.80/1.19 hAPP( hAPP( X, Y ), 'c_List_Ofoldr'( X, Z, U, T, W ) ) ) ],
% 0.80/1.19 [ =( 'c_Predicate_Oconversep'( 'c_Predicate_Oconversep'( X, Y, Z ), Z, Y
% 0.80/1.19 ), X ) ],
% 0.80/1.19 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP( hAPP(
% 0.80/1.19 'c_Type_Otype_OFun', Z ), T ) ) ), =( Y, T ) ],
% 0.80/1.19 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP( hAPP(
% 0.80/1.19 'c_Type_Otype_OFun', Z ), T ) ) ), =( X, Z ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.19 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.80/1.19 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.80/1.19 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 0.80/1.19 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.80/1.19 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.19 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.80/1.19 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.80/1.19 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 0.80/1.19 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.80/1.19 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.80/1.19 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Orev'( X, Y ), 'tc_List_Olist'(
% 0.80/1.19 Y ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ) ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.19 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.19 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.80/1.19 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) )
% 0.80/1.19 ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.19 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.80/1.19 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) )
% 0.80/1.19 ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.19 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.19 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.19 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.19 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.19 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.19 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.19 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.19 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.19 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.80/1.19 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.80/1.19 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 0.80/1.19 , 'c_List_Olist_ONil'( Y ) ) ],
% 0.80/1.19 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ),
% 0.80/1.19 'tc_List_Olist'( X ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.19 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'(
% 0.80/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, X ) ) ],
% 0.80/1.19 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ),
% 0.80/1.19 =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.19 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'( Y, Z, X ) ) ),
% 0.80/1.19 =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.19 [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ),
% 0.80/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_List_Olist_ONil'( Y
% 0.80/1.19 ) ) ],
% 0.80/1.19 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.80/1.19 'c_List_Olist_OCons'( Y, T, Z ), Z ), 'c_List_Olist_OCons'( Y,
% 0.80/1.19 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ), T, Z ), Z ) ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( 'c_List_Ofoldr'(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), 'c_List_Ofoldl'(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ],
% 0.80/1.19 [ =( 'c_List_Ofilter'( X, 'c_List_Oreplicate'( Y, Z, T ), T ),
% 0.80/1.19 'c_List_Olist_ONil'( T ) ), hBOOL( hAPP( X, Z ) ) ],
% 0.80/1.19 [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T ),
% 0.80/1.19 ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y, hAPP( hAPP(
% 0.80/1.19 'c_Type_Otype_OFun', U ), T ) ) ) ],
% 0.80/1.19 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubst'(
% 0.80/1.19 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.80/1.19 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.19 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.80/1.19 'tc_nat' ) ],
% 0.80/1.19 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.19 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.80/1.19 ) ) ],
% 0.80/1.19 [ 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, Z,
% 0.80/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ), ~( 'c_Type_Otypings'( X, Z, U )
% 0.80/1.19 ), ~( 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun', U, T
% 0.80/1.19 , 'tc_Type_Otype', 'tc_Type_Otype' ) ) ) ],
% 0.80/1.19 [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ),
% 0.80/1.19 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( T ) ) ) ), =(
% 0.80/1.19 'c_Map_Omap__upds'( U, 'c_List_Oappend'( X, W, Y ), Z, Y, T ),
% 0.80/1.19 'c_Map_Omap__upds'( U, X, Z, Y, T ) ) ],
% 0.80/1.19 [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ),
% 0.80/1.19 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( T ) ) ) ), =(
% 0.80/1.19 'c_Map_Omap__upds'( U, X, 'c_List_Oappend'( Z, W, T ), Y, T ),
% 0.80/1.19 'c_Map_Omap__upds'( U, X, Z, Y, T ) ) ],
% 0.80/1.19 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.80/1.19 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.80/1.19 ) ) ],
% 0.80/1.19 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.80/1.19 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.80/1.19 ) ) ],
% 0.80/1.19 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.80/1.19 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( Z ), Z ), Z ),
% 0.80/1.19 'c_List_Olist_OCons'( Y, 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ],
% 0.80/1.19 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 0.80/1.19 'c_List_Osko__List__XCons__eq__filter__iff__1__3'( X, Z, T ) ) ), =(
% 0.80/1.19 'c_List_Olist_OCons'( Y, 'c_List_Ofilter'( X, U, T ), T ),
% 0.80/1.19 'c_List_Ofilter'( X, 'c_List_Oappend'( Z, 'c_List_Olist_OCons'( Y, U, T )
% 0.80/1.19 , T ), T ) ) ],
% 0.80/1.19 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 0.80/1.19 'c_List_Osko__List__Xfilter__eq__Cons__iff__1__3'( X, Z, T ) ) ), =(
% 0.80/1.19 'c_List_Ofilter'( X, 'c_List_Oappend'( Z, 'c_List_Olist_OCons'( Y, U, T )
% 0.80/1.19 , T ), T ), 'c_List_Olist_OCons'( Y, 'c_List_Ofilter'( X, U, T ), T ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.80/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.19 , 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z,
% 0.80/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ), ~(
% 0.80/1.19 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.80/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB' ) ),
% 0.80/1.19 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.80/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.19 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.80/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ],
% 0.80/1.19 [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, 'c_List_Olist_OCons'(
% 0.80/1.19 Y, Z, T ), T ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T ) ), U
% 0.80/1.19 , T ), 'c_List_Oappend'( X, 'c_List_Olist_OCons'( U, Z, T ), T ) ) ],
% 0.80/1.19 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), 'c_List_Ofoldr'(
% 0.80/1.19 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X,
% 0.80/1.19 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.80/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), T,
% 0.80/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ],
% 0.80/1.19 [ =( X, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.80/1.19 'c_Type_Osko__Type__Xvar__app__types__1__1'( Y, X, Z, T ), Y,
% 0.80/1.19 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( Z,
% 0.80/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.80/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ), ~( 'c_Type_Otypings'( Z, W, V0
% 0.80/1.19 ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.80/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.80/1.19 , Y ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.80/1.19 'v_sko__List__Xconcat__Xinduct__1'( X ),
% 0.80/1.19 'v_sko__List__Xconcat__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X
% 0.80/1.19 , 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.80/1.19 'v_sko__List__Xtake__Xinduct__1'( X ), 'v_sko__List__Xtake__Xinduct__2'(
% 0.80/1.19 X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_ONil'( 't_a' ) ) ) )
% 0.80/1.19 ],
% 0.80/1.19 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.80/1.19 'v_sko__List__Xmap__Xinduct__1'( X ), 'v_sko__List__Xmap__Xinduct__2'( X
% 0.80/1.19 ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_ONil'( 't_a' ) ) ) )
% 0.80/1.19 ],
% 0.80/1.19 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.80/1.19 'v_sko__List__Xlist__Xinduct__1'( X ), 'v_sko__List__Xlist__Xinduct__2'(
% 0.80/1.19 X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_ONil'( 't_a' ) ) ) )
% 0.80/1.19 ],
% 0.80/1.19 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.80/1.19 'v_sko__List__XdropWhile__Xinduct__1'( X ),
% 0.80/1.19 'v_sko__List__XdropWhile__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.80/1.19 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.80/1.19 'v_sko__List__Xremove1__Xinduct__1'( X ),
% 0.80/1.19 'v_sko__List__Xremove1__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.80/1.19 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_OCons'(
% 0.80/1.19 'v_sko__List__Xdistinct__Xinduct__1'( X ),
% 0.80/1.19 'v_sko__List__Xdistinct__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.80/1.19 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.80/1.19 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeD__1__1'(
% 0.80/1.19 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.80/1.19 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeE__1__1'(
% 0.80/1.19 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.80/1.19 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubstn'(
% 0.80/1.19 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'( X, Y,
% 0.80/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.19 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.80/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.80/1.19 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.80/1.19 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.80/1.19 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.19 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.80/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.80/1.19 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.80/1.19 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.80/1.19 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.19 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xtypes__snocE__1__1'( Z,
% 0.80/1.19 X, T, Y ) ), ~( 'c_Type_Otypings'( X, 'c_List_Oappend'( Y,
% 0.80/1.19 'c_List_Olist_OCons'( T, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.80/1.19 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), Z ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.19 , 'c_Lambda_Osubst'( 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.19 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.80/1.19 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.80/1.19 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.80/1.19 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.19 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.80/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.80/1.19 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.80/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.80/1.19 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.19 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.80/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.80/1.19 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.80/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.80/1.19 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.19 , 'c_Lambda_Osubst'( 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.19 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.80/1.19 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.80/1.19 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.80/1.19 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.19 , 'c_Lambda_Osubst'( 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.19 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.80/1.19 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.80/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.80/1.19 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.19 [ 'c_Type_Otyping'( X, Y, 'c_Type_Osko__Type__Xtypes__snocE__1__2'( Z, X
% 0.80/1.19 , Y, T ) ), ~( 'c_Type_Otypings'( X, 'c_List_Oappend'( T,
% 0.80/1.19 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.80/1.19 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), Z ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.19 , 'c_Lambda_Osubst'( 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.19 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.80/1.19 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.80/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.80/1.19 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.80/1.19 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.19 [ ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.19 'c_Lambda_OdB_OAbs'(
% 0.80/1.19 'c_ListApplication_Osko__ListApplication__Xlem__1__3'( X ) ),
% 0.80/1.19 'c_ListApplication_Osko__ListApplication__Xlem__1__4'( X ),
% 0.80/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.19 'c_ListApplication_Osko__ListApplication__Xlem__1__1'( X ) ),
% 0.80/1.19 'c_ListApplication_Osko__ListApplication__Xlem__1__2'( X ),
% 0.80/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( X, Y ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'(
% 0.80/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.19 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3'( X ) )
% 0.80/1.19 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4'( X )
% 0.80/1.19 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.19 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1'( X ) )
% 0.80/1.19 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2'( X )
% 0.80/1.19 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.19 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.80/1.19 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.19 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.80/1.19 ), Z ) ) ) ],
% 0.80/1.19 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 0.80/1.19 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ =( 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U
% 0.80/1.19 ), 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ) ) ],
% 0.80/1.19 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 0.80/1.19 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ =( 'c_List_Olist_Olist__case'( X, Y, 'c_List_Olist_OCons'( Z, T, U ),
% 0.80/1.19 W, U ), hAPP( hAPP( Y, Z ), T ) ) ],
% 0.80/1.19 [ =( 'c_List_Oremove1'( X, 'c_List_Olist_OCons'( X, Y, Z ), Z ), Y ) ]
% 0.80/1.19 ,
% 0.80/1.19 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.19 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.80/1.19 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.80/1.19 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.80/1.19 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.80/1.19 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.80/1.19 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.80/1.19 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.80/1.19 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 0.80/1.19 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.80/1.19 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 0.80/1.19 [ =( X, Y ), hBOOL( hAPP( hAPP( Z, Y ), X ) ), ~( 'c_ListOrder_Ostep1'(
% 0.80/1.19 Z, 'c_List_Olist_OCons'( Y, T, U ), 'c_List_Olist_OCons'( X, W, U ), U )
% 0.80/1.19 ) ],
% 0.80/1.19 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.19 'c_List_Olinorder__class_Osorted'( Y, X ), ~(
% 0.80/1.19 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Z, Y, X ), X ) )
% 0.80/1.19 ],
% 0.80/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.19 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.80/1.19 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.80/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.80/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.19 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.80/1.19 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.19 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.80/1.19 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.19 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.80/1.19 [ =( 'c_List_Orev'( 'c_List_Oappend'( 'c_List_Orev'( X, Y ),
% 0.80/1.20 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( Y ), Y ), Y ), Y ),
% 0.80/1.20 'c_List_Olist_OCons'( Z, X, Y ) ) ],
% 0.80/1.20 [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Type_Otyping'( X, T, Z ) ), ~(
% 0.80/1.20 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.80/1.20 'tc_Lambda_OdB' ), T ), Y ) ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Olift'( X, Y ) ),
% 0.80/1.20 'c_Lambda_Olift'( Z, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X )
% 0.80/1.20 , Z ) ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ],
% 0.80/1.20 [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ],
% 0.80/1.20 [ =( 'c_List_Olist__update'( 'c_List_Olist_OCons'( X, Y, Z ),
% 0.80/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, Z ), 'c_List_Olist_OCons'( T,
% 0.80/1.20 Y, Z ) ) ],
% 0.80/1.20 [ =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Oappend'(
% 0.80/1.20 'c_List_Olist_ONil'( Z ), 'c_List_Olist_OCons'( X, Y, Z ), Z ) ) ],
% 0.80/1.20 [ =( 'c_List_Omap'( X, 'c_List_Olist__update'( Y, Z, T, U ), U, W ),
% 0.80/1.20 'c_List_Olist__update'( 'c_List_Omap'( X, Y, U, W ), Z, hAPP( X, T ), W )
% 0.80/1.20 ) ],
% 0.80/1.20 [ =( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.80/1.20 'c_List_Orev'( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ), Y
% 0.80/1.20 ) ) ],
% 0.80/1.20 [ =( X, Y ), 'c_ListOrder_Ostep1'( Z, X, Y, T ), ~( 'c_ListOrder_Ostep1'(
% 0.80/1.20 Z, 'c_List_Oappend'( X, 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( T )
% 0.80/1.20 , T ), T ), 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( W,
% 0.80/1.20 'c_List_Olist_ONil'( T ), T ), T ), T ) ) ],
% 0.80/1.20 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Y,
% 0.80/1.20 'c_List_Olist_ONil'( X ), X ), X ) ],
% 0.80/1.20 [ =( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.20 'c_Transitive__Closure_Ortranclp'( X, Y ), Y ),
% 0.80/1.20 'c_Transitive__Closure_Ortranclp'( X, Y ) ) ],
% 0.80/1.20 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.80/1.20 Y ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.80/1.20 Y ) ],
% 0.80/1.20 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.20 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.80/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.80/1.20 Y ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.80/1.20 Y ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.80/1.20 Y ) ],
% 0.80/1.20 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.80/1.20 Y ) ],
% 0.80/1.20 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.80/1.20 Y ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'( X ) ),
% 0.80/1.20 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X )
% 0.80/1.20 , Y ) ) ) ],
% 0.80/1.20 [ =( 'c_List_Orev'( 'c_List_Oappend'( X, Y, Z ), Z ), 'c_List_Oappend'(
% 0.80/1.20 'c_List_Orev'( Y, Z ), 'c_List_Orev'( X, Z ), Z ) ) ],
% 0.80/1.20 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_OrderedGroup_Omonoid__add'( Z,
% 0.80/1.20 X, T ) ) ],
% 0.80/1.20 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_OrderedGroup_Omonoid__add'( Y,
% 0.80/1.20 X, T ) ) ],
% 0.80/1.20 [ =( 'c_List_Ofilter'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.80/1.20 'c_List_Oappend'( 'c_List_Ofilter'( X, Y, T ), 'c_List_Ofilter'( X, Z, T
% 0.80/1.20 ), T ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.80/1.20 X ) ) ), =( X, 'c_Lambda_OdB_OAbs'( 'v_sko__InductTermi__XIT__Xcases__3'(
% 0.80/1.20 X ) ) ), =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.20 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_ONil'( X
% 0.80/1.20 ), X ), 'c_List_Olist_ONil'( X ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) ) ), =( Y
% 0.80/1.20 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.80/1.20 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Orev'( 'c_List_Olist_ONil'( X ),
% 0.80/1.20 X ) ) ],
% 0.80/1.20 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oremdups'( 'c_List_Olist_ONil'( X
% 0.80/1.20 ), X ) ) ],
% 0.80/1.20 [ ~( =( X, 'c_List_Oappend'( Y, X, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.80/1.20 ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Oappend'( X, Y, Z ), Y ) ), =( X, 'c_List_Olist_ONil'( Z
% 0.80/1.20 ) ) ],
% 0.80/1.20 [ ~( =( X, 'c_List_Oappend'( X, Y, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.80/1.20 ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Oappend'( X, Y, Z ), X ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.80/1.20 ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Oremdups'( X, Y ), 'c_List_Olist_ONil'( Y ) ) ), =( X,
% 0.80/1.20 'c_List_Olist_ONil'( Y ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Orotate'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y
% 0.80/1.20 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Orev'( Y, X ) ) ), =( Y,
% 0.80/1.20 'c_List_Olist_ONil'( X ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y
% 0.80/1.20 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( X
% 0.80/1.20 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Z
% 0.80/1.20 , 'c_List_Olist_ONil'( X ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Y
% 0.80/1.20 , 'c_List_Olist_ONil'( X ) ) ],
% 0.80/1.20 [ ~( 'c_ListOrder_Ostep1'( X, Y, 'c_List_Olist_ONil'( Z ), Z ) ) ],
% 0.80/1.20 [ ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_ONil'( Y ), Z, Y ) ) ],
% 0.80/1.20 [ =( 'c_List_Oremdups'( 'c_List_Olist_ONil'( X ), X ),
% 0.80/1.20 'c_List_Olist_ONil'( X ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X ) ) ), =( Z
% 0.80/1.20 , 'c_List_Olist_ONil'( T ) ) ],
% 0.80/1.20 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 0.80/1.20 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), Y, X ), Y ) ],
% 0.80/1.20 [ =( X, 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 0.80/1.20 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 0.80/1.20 [ =( 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ), X ) ],
% 0.80/1.20 [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ],
% 0.80/1.20 [ ~( hBOOL( hAPP( X, 'c_List_Olist_Olist__case'( Y, Z,
% 0.80/1.20 'c_List_Olist_ONil'( 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X, Y ) )
% 0.80/1.20 ],
% 0.80/1.20 [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 0.80/1.20 'c_List_Olist_ONil'( Z ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.20 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.80/1.20 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.20 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.80/1.20 ), Z ) ) ) ],
% 0.80/1.20 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 0.80/1.20 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.80/1.20 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 0.80/1.20 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.80/1.20 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Y, Z, X ), X ),
% 0.80/1.20 ~( 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( T,
% 0.80/1.20 'c_List_Olist_OCons'( Y, Z, X ), X ), X ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_OCons'( Z, T, Y ) ) ), =( X
% 0.80/1.20 , 'c_List_Oappend'( 'c_List_Orev'( T, Y ), 'c_List_Olist_OCons'( Z,
% 0.80/1.20 'c_List_Olist_ONil'( Y ), Y ), Y ) ) ],
% 0.80/1.20 [ =( 'c_List_Orev'( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y
% 0.80/1.20 ), Y ), 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_ListOrder_Ostep1'( X, T, U, W ),
% 0.80/1.20 ~( 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y
% 0.80/1.20 , 'c_List_Olist_ONil'( W ), W ), W ), 'c_List_Oappend'( U,
% 0.80/1.20 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W ), W ), W ) ) ],
% 0.80/1.20 [ =( 'c_List_Orev'( 'c_List_Olist_OCons'( X, Y, Z ), Z ),
% 0.80/1.20 'c_List_Oappend'( 'c_List_Orev'( Y, Z ), 'c_List_Olist_OCons'( X,
% 0.80/1.20 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Ofilter'( T, U, Z ) ) )
% 0.80/1.20 , hBOOL( hAPP( T, X ) ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.80/1.20 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.20 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.80/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.80/1.20 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.80/1.20 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.20 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.80/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.80/1.20 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.20 X ), Y ), Z ) ), T ) ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.20 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.80/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.20 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.80/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.80/1.20 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.20 X ), Y ), Z ) ), T ) ) ],
% 0.80/1.20 [ =( 'c_List_Oremdups'( 'c_List_Ofilter'( X, Y, Z ), Z ),
% 0.80/1.20 'c_List_Ofilter'( X, 'c_List_Oremdups'( Y, Z ), Z ) ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.80/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.80/1.20 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ =( 'c_List_Ofilter'( X, 'c_List_Olist_OCons'( Y, Z, T ), T ),
% 0.80/1.20 'c_List_Olist_OCons'( Y, 'c_List_Ofilter'( X, Z, T ), T ) ), ~( hBOOL(
% 0.80/1.20 hAPP( X, Y ) ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.80/1.20 'c_List_Orev'( Z, Y ) ) ), =( Z, 'c_List_Olist_OCons'( X,
% 0.80/1.20 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 0.80/1.20 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 0.80/1.20 ],
% 0.80/1.20 [ ~( 'c_ListOrder_Ostep1'( X, Y, Z, T ) ), 'c_ListOrder_Ostep1'( X,
% 0.80/1.20 'c_List_Oappend'( Y, U, T ), 'c_List_Oappend'( Z, U, T ), T ) ],
% 0.80/1.20 [ 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( Y, Z, T ), 'c_List_Oappend'(
% 0.80/1.20 Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.20 , 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ), 'c_Lambda_OdB_OAbs'( Y )
% 0.80/1.20 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Y ) ) ) ],
% 0.80/1.20 [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X, 'c_List_Oappend'(
% 0.80/1.20 Y, T, Z ), Z ) ) ],
% 0.80/1.20 [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X, 'c_List_Oappend'(
% 0.80/1.20 T, Y, Z ), Z ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OAbs'( T ), U ),
% 0.80/1.20 hAPP( Z, T ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.80/1.20 'c_Lambda_Osubst'( T, Y, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta'
% 0.80/1.20 , X ), T ) ) ) ],
% 0.80/1.20 [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U, 'c_List_Olist_OCons'(
% 0.80/1.20 Y, T, W ), 'c_List_Olist_OCons'( X, Z, W ), W ) ) ],
% 0.80/1.20 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), 'c_ListOrder_Ostep1'( X,
% 0.80/1.20 'c_List_Olist_OCons'( Y, T, U ), 'c_List_Olist_OCons'( Z, T, U ), U ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ =( 'c_List_Orev'( 'c_List_Omap'( X, Y, Z, T ), T ), 'c_List_Omap'( X,
% 0.80/1.20 'c_List_Orev'( Y, Z ), Z, T ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, Y, Z ) ) ),
% 0.80/1.20 =( X, T ) ],
% 0.80/1.20 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( X, T, Z ) ) ),
% 0.80/1.20 =( Y, T ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), Z )
% 0.80/1.20 ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), Z )
% 0.80/1.20 ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.80/1.20 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), U )
% 0.80/1.20 , T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.80/1.20 ), Z ), U ) ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Ofilter'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z ) ) )
% 0.80/1.20 , hBOOL( hAPP( X, T ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.80/1.20 X ) ) ), =( X, 'c_Lambda_OdB_OAbs'( 'v_sko__InductTermi__XIT__Xcases__3'(
% 0.80/1.20 X ) ) ), 'c_List_Olistsp'( 'c_InductTermi_OIT',
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB' ), ~( hBOOL(
% 0.80/1.20 hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.20 [ =( 'c_List_Orotate'( X, 'c_List_Omap'( Y, Z, T, U ), U ),
% 0.80/1.20 'c_List_Omap'( Y, 'c_List_Orotate'( X, Z, T ), T, U ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.20 , 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ), 'c_Lambda_Osubst'( X
% 0.80/1.20 , T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', Y ), T ) ) ) ],
% 0.80/1.20 [ =( X, 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ) ) ],
% 0.80/1.20 [ =( 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ), X ) ],
% 0.80/1.20 [ =( 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ), X ) ],
% 0.80/1.20 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.80/1.20 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), =( Y, Z ), ~( 'c_ListOrder_Ostep1'(
% 0.80/1.20 X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( U )
% 0.80/1.20 , U ), U ), 'c_List_Oappend'( W, 'c_List_Olist_OCons'( Z,
% 0.80/1.20 'c_List_Olist_ONil'( U ), U ), U ), U ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_OCons'( Z,
% 0.80/1.20 'c_List_Olist_ONil'( Y ), Y ) ) ), =( X, 'c_List_Olist_OCons'( Z,
% 0.80/1.20 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 0.80/1.20 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.20 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.80/1.20 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.20 , 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ), 'c_Lambda_Osubst'( T
% 0.80/1.20 , Y, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), T ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.20 , 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ), 'c_Lambda_Osubst'( X
% 0.80/1.20 , T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y ), T ) ) ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.80/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.80/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.80/1.20 ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.80/1.20 ), ~( hBOOL( hAPP( hAPP( X, Z ), T ) ) ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.80/1.20 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ 'c_List_Olistrelp'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 0.80/1.20 'c_List_Olist_OCons'( U, W, T ), T ), ~( 'c_List_Olistrelp'( X, Z, W, T )
% 0.80/1.20 ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ) ],
% 0.80/1.20 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.80/1.20 ) ],
% 0.80/1.20 [ =( 'c_List_Oremove1'( X, 'c_List_Olist_OCons'( Y, Z, T ), T ),
% 0.80/1.20 'c_List_Olist_OCons'( Y, 'c_List_Oremove1'( X, Z, T ), T ) ), =( X, Y ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.80/1.20 X ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.80/1.20 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.80/1.20 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.80/1.20 'c_Lambda_OdB_OAbs'( X ) ), Y ) ), 'c_Lambda_Osubst'( X, Y,
% 0.80/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.20 , 'tc_Lambda_OdB' ), 'c_Lambda_Olift'( X, Y ) ), 'c_Lambda_Olift'( Z, Y )
% 0.80/1.20 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.80/1.20 [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), =( Z, Y ), ~( 'c_ListOrder_Ostep1'(
% 0.80/1.20 X, 'c_List_Olist_OCons'( U, Y, T ), 'c_List_Olist_OCons'( W, Z, T ), T )
% 0.80/1.20 ) ],
% 0.80/1.20 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.80/1.20 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_OrderedGroup_Osemigroup__add'( X, U )
% 0.80/1.20 ) ],
% 0.80/1.20 [ =( 'c_List_Omap'( X, 'c_List_Oappend'( Y, Z, T ), T, U ),
% 0.80/1.20 'c_List_Oappend'( 'c_List_Omap'( X, Y, T, U ), 'c_List_Omap'( X, Z, T, U
% 0.80/1.20 ), U ) ) ],
% 0.80/1.20 [ =( 'c_List_Oremove1'( X, 'c_List_Ofilter'( Y, Z, T ), T ),
% 0.80/1.20 'c_List_Ofilter'( Y, Z, T ) ), hBOOL( hAPP( Y, X ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Orev'( Z, Y ) ) ), =( X, Z ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U, 'c_List_Oappend'( X
% 0.80/1.20 , 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W ), W ),
% 0.80/1.20 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( T, 'c_List_Olist_ONil'( W ), W
% 0.80/1.20 ), W ), W ) ) ],
% 0.80/1.20 [ 'c_List_Olistsp'( X, 'c_List_Oappend'( Y, Z, T ), T ), ~(
% 0.80/1.20 'c_List_Olistsp'( X, Z, T ) ), ~( 'c_List_Olistsp'( X, Y, T ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OAbs'( T ), U ),
% 0.80/1.20 hAPP( hAPP( Z, T ), 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, U ) ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 0.80/1.20 X ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ),
% 0.80/1.20 'c_OrderedGroup_Osemigroup__add'( 'c_HOL_Oplus__class_Oplus'( X ), X ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.80/1.20 , 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.80/1.20 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.80/1.20 ],
% 0.80/1.20 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.80/1.20 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.80/1.20 ],
% 0.80/1.20 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y
% 0.80/1.20 , Z, X ), X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 0.80/1.20 ) ), =( X, T ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 0.80/1.20 ) ), =( Y, U ) ],
% 0.80/1.20 [ 'c_Type_Otyping'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', T
% 0.80/1.20 ), Y ) ) ), ~( 'c_Type_Otyping'( X, T, Z ) ) ],
% 0.80/1.20 [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), hBOOL( hAPP( hAPP( X, U ), W ) ),
% 0.80/1.20 ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( U, Y, T ),
% 0.80/1.20 'c_List_Olist_OCons'( W, Z, T ), T ) ) ],
% 0.80/1.20 [ 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 0.80/1.20 'c_List_Olist_OCons'( Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T
% 0.80/1.20 ) ) ],
% 0.80/1.20 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( Y, X ), ~(
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( 'c_List_Oappend'( Y, Z, X ), X ) ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( Y, X ), ~(
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( 'c_List_Oappend'( Z, Y, X ), X ) ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ =( 'c_List_Olist__update'( 'c_List_Olist__update'( X, Y, Z, T ), U, W
% 0.80/1.20 , T ), 'c_List_Olist__update'( 'c_List_Olist__update'( X, U, W, T ), Y, Z
% 0.80/1.20 , T ) ), =( Y, U ) ],
% 0.80/1.20 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( 'c_List_Oremdups'( Y, X ), X ), ~(
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( Y, X ) ) ],
% 0.80/1.20 [ =( 'c_List_Ofilter'( X, 'c_List_Olist_OCons'( Y, Z, T ), T ),
% 0.80/1.20 'c_List_Ofilter'( X, Z, T ) ), hBOOL( hAPP( X, Y ) ) ],
% 0.80/1.20 [ =( 'c_List_Orev'( 'c_List_Ofilter'( X, Y, Z ), Z ), 'c_List_Ofilter'(
% 0.80/1.20 X, 'c_List_Orev'( Y, Z ), Z ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.80/1.20 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.80/1.20 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( X, T
% 0.80/1.20 ) ],
% 0.80/1.20 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.80/1.20 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.80/1.20 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( Y, U
% 0.80/1.20 ) ],
% 0.80/1.20 [ ~( hBOOL( hAPP( X, 'c_List_Olist_Olist__case'( Y, Z,
% 0.80/1.20 'c_List_Olist_OCons'( T, U, 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X
% 0.80/1.20 , hAPP( hAPP( Z, T ), U ) ) ) ],
% 0.80/1.20 [ ~( hBOOL( hAPP( X, 'c_List_Olist_Olist__case'( Y, Z,
% 0.80/1.20 'c_List_Olist_OCons'( T, U, 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X
% 0.80/1.20 , hAPP( hAPP( Z, T ), U ) ) ) ],
% 0.80/1.20 [ =( 'c_List_Olist__update'( 'c_List_Olist__update'( X, Y, Z, T ), Y, U
% 0.80/1.20 , T ), 'c_List_Olist__update'( X, Y, U, T ) ) ],
% 0.80/1.20 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.80/1.20 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.80/1.20 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.80/1.20 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 0.80/1.20 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.80/1.20 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.80/1.20 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.80/1.20 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 0.80/1.20 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( 'c_List_Oremove1'( Y, Z, X ), X ), ~(
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( Z, X ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.80/1.20 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), U )
% 0.80/1.20 , T ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.80/1.20 ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.20 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.20 'v_sko__List__XdropWhile__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.20 'v_sko__List__Xtake__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.80/1.20 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_ONil'( X ), X ) ],
% 0.80/1.20 [ =( 'c_List_Ofiltermap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 0.80/1.20 'c_List_Olist_ONil'( Z ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oremdups'( Y, X ) ) ), =( Y,
% 0.80/1.20 'c_List_Olist_ONil'( X ) ) ],
% 0.80/1.20 [ =( 'c_List_Ofilter'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.80/1.20 'c_List_Olist_ONil'( Y ) ) ],
% 0.80/1.20 [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z, X ),
% 0.80/1.20 'c_List_Olist_ONil'( X ) ) ],
% 0.80/1.20 [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z, X ),
% 0.80/1.20 'c_List_Olist_ONil'( X ) ) ],
% 0.80/1.20 [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z, X ),
% 0.80/1.20 'c_List_Olist_ONil'( X ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.20 'v_sko__List__Xconcat__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ =( 'c_List_Oremove1'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.80/1.20 'c_List_Olist_ONil'( Y ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.20 'v_sko__List__Xdistinct__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.80/1.20 [ =( 'c_Map_Omap__upds'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), X ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ =( 'c_Map_Omap__upds'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T ), X ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.20 'v_sko__List__Xremove1__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.80/1.20 [ =( 'c_List_Olist_Olist__case'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z )
% 0.80/1.20 , X ) ],
% 0.80/1.20 [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_ONil'( Y ) ) ), =( X,
% 0.80/1.20 'c_List_Olist_ONil'( Y ) ) ],
% 0.80/1.20 [ =( 'c_List_Orotate'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.80/1.20 'c_List_Olist_ONil'( Y ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.20 'v_sko__List__Xlist__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.80/1.20 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, 'c_List_Olist_ONil'( Z
% 0.80/1.20 ), Z, X ) ) ],
% 0.80/1.20 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( 'c_List_Olist_ONil'( X
% 0.80/1.20 ), 'c_List_Olist_ONil'( X ), X ) ) ],
% 0.80/1.20 [ 'c_List_Olistrelp'( X, 'c_List_Olist_ONil'( Y ), 'c_List_Olist_ONil'(
% 0.80/1.20 Y ), Y ) ],
% 0.80/1.20 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__List__Xmap__Xinduct__2'(
% 0.80/1.20 X ) ) ), ~( hBOOL( hAPP( X, 'c_List_Olist_ONil'( 't_a' ) ) ) ) ],
% 0.80/1.20 [ =( 'c_List_Orev'( 'c_List_Olist_ONil'( X ), X ), 'c_List_Olist_ONil'(
% 0.80/1.20 X ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Olist__update'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) )
% 0.80/1.20 ), =( X, 'c_List_Olist_ONil'( T ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_Osubst'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 0.80/1.20 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Z, T ) ),
% 0.80/1.20 'c_Lambda_Osubst'( Y, Z, T ) ) ) ],
% 0.80/1.20 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 Z ) ) ) ],
% 0.80/1.20 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.80/1.20 Z ) ) ) ],
% 0.80/1.20 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP( hAPP(
% 0.80/1.20 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.80/1.20 Z, U ), W ) ) ) ],
% 0.80/1.20 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP( hAPP(
% 0.80/1.20 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.80/1.20 Z, U ), W ) ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_Olift'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z ),
% 0.80/1.20 hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Olift'( X, Z ) ),
% 0.80/1.20 'c_Lambda_Olift'( Y, Z ) ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, hAPP( hAPP( 'c_Lambda_OdB_OApp'
% 0.80/1.20 , T ), U ), W ), hAPP( hAPP( Y, T ), U ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.80/1.20 T ), U ), W ), hAPP( hAPP( hAPP( hAPP( Y, T ), U ),
% 0.80/1.20 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, W ) ), 'c_Lambda_OdB_OdB__rec'( X, Y
% 0.80/1.20 , Z, U, W ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.80/1.20 X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP(
% 0.80/1.20 hAPP( 'c_Lambda_Obeta', Y ), Z ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.80/1.20 X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP(
% 0.80/1.20 hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T
% 0.80/1.20 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y, T ) ),
% 0.80/1.20 'c_Lambda_Oliftn'( X, Z, T ) ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 0.80/1.20 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X, Z, T ) ),
% 0.80/1.20 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.20 , 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~(
% 0.80/1.20 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.80/1.20 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Z, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ) ), ~( 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', Y, Z,
% 0.80/1.20 'tc_Lambda_OdB' ) ) ],
% 0.80/1.20 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2'( X ),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1'( X ),
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.80/1.20 [ =( 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, U, U ), hAPP( hAPP(
% 0.80/1.20 X, Y ), 'c_List_Ofoldl'( X, Z, T, U, U ) ) ), ~(
% 0.80/1.20 'c_OrderedGroup_Osemigroup__add'( X, U ) ) ],
% 0.80/1.20 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.20 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.20 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 0.80/1.20 ,
% 0.80/1.20 [ =( hAPP( hAPP( X, Y ), 'c_List_Ofoldl'( X, Z, T, U, U ) ),
% 0.80/1.20 'c_List_Ofoldl'( X, Y, T, U, U ) ), ~( 'c_OrderedGroup_Omonoid__add'( Z,
% 0.80/1.20 X, U ) ) ],
% 0.80/1.20 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_OCons'( Z, T, U ), W, U ),
% 0.80/1.20 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, W, U ) ) ],
% 0.80/1.20 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Oappend'( Z, T, U ), W, U ),
% 0.80/1.20 'c_List_Ofoldl'( X, 'c_List_Ofoldl'( X, Y, Z, W, U ), T, W, U ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( X, 'c_ListApplication_Osko__ListApplication__Xlem__1__3'(
% 0.80/1.20 X ) ) ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 'c_Lambda_OdB_OVar'(
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xlem__1__1'( X ) ),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xlem__1__2'( X ),
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( X, Y ) ) ],
% 0.80/1.20 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__typesE__1__1'(
% 0.80/1.20 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ), Z ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3'( X ) )
% 0.80/1.20 ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 'c_Lambda_OdB_OVar'(
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1'( X ) )
% 0.80/1.20 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2'( X )
% 0.80/1.20 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ],
% 0.80/1.20 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__types__1__1'(
% 0.80/1.20 Z, T, X, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ), T ) ), ~( 'c_Type_Otypings'( X, W, V0 ) ), ~(
% 0.80/1.20 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.80/1.20 , Z ) ) ],
% 0.80/1.20 [ 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', X,
% 0.80/1.20 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, X, Z ),
% 0.80/1.20 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), X,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.20 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.80/1.20 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y,
% 0.80/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.80/1.20 X ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.20 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.80/1.20 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.80/1.20 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.80/1.20 ],
% 0.80/1.20 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.80/1.20 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.80/1.20 ],
% 0.80/1.20 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.80/1.20 [ ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.80/1.20 ) ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OVar'( T ), U ),
% 0.80/1.20 hAPP( X, T ) ) ],
% 0.80/1.20 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.80/1.20 [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y )
% 0.80/1.20 , Z ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OVar'( T ), U ),
% 0.80/1.20 hAPP( X, T ) ) ],
% 0.80/1.20 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y ) ) ],
% 0.80/1.20 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', Z, T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( T,
% 0.80/1.20 'c_List_Oappend'(
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1'( X
% 0.80/1.20 , Y, Z, T ), 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'(
% 0.80/1.20 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ), =( T,
% 0.80/1.20 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Olift'( X, Y ) ) ), ~(
% 0.80/1.20 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X ) ) ), ~(
% 0.80/1.20 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.20 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ),
% 0.80/1.20 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.20 'c_Lambda_Obeta', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 'c_Lambda_OdB_OVar'( Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ) )
% 0.80/1.20 ) ],
% 0.80/1.20 [ =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'(
% 0.80/1.20 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ),
% 0.80/1.20 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, X,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Y ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', Z, 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.80/1.20 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ),
% 0.80/1.20 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.80/1.20 [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ),
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, 'c_List_Oappend'( Y,
% 0.80/1.20 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.80/1.20 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.80/1.20 ) ],
% 0.80/1.20 [ ~( =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.80/1.20 'c_Lambda_OdB_OApp', X ), Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) )
% 0.80/1.20 , =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.80/1.20 'c_List_Oappend'( Z, 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'(
% 0.80/1.20 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), 'tc_Lambda_OdB'
% 0.80/1.20 , 'tc_Lambda_OdB' ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.80/1.20 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.80/1.20 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.80/1.20 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.80/1.20 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) )
% 0.80/1.20 ) ],
% 0.80/1.20 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 0.80/1.20 , Y ) ],
% 0.80/1.20 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( X,
% 0.80/1.20 'c_Lambda_OdB_OVar'( Y ), Z ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.80/1.20 ) ) ) ],
% 0.80/1.20 [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ), X ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.80/1.20 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ) ) ],
% 0.80/1.20 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y )
% 0.80/1.20 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.80/1.20 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.80/1.20 'tc_Lambda_OdB' ) ) ],
% 0.80/1.20 [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.80/1.20 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', Z, T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X,
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z,
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1'( X
% 0.80/1.20 , Y, Z, T ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), =( T,
% 0.80/1.20 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.80/1.20 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.80/1.20 [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.80/1.20 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.80/1.20 ), 'c_Lambda_OdB_OAbs'( X ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.20 , 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ),
% 0.80/1.20 ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y, 'tc_Lambda_OdB' ) ) ],
% 0.80/1.20 [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.80/1.20 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.80/1.20 ) ) ],
% 0.80/1.20 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.80/1.20 ) ],
% 0.80/1.20 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.80/1.20 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.80/1.20 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.80/1.20 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.80/1.20 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_Lambda_OdB_OApp', X ), Y ), Z ) ],
% 0.80/1.20 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.80/1.20 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 0.80/1.20 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.80/1.20 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 0.80/1.20 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OVar'( X )
% 0.80/1.20 , Y ) ],
% 0.80/1.20 [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.80/1.20 Z ) ) ) ],
% 0.80/1.20 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), Y ) ],
% 0.80/1.20 [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.80/1.20 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.80/1.20 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.80/1.20 'tc_Lambda_OdB' ) ) ],
% 0.80/1.20 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OVar'(
% 0.80/1.20 Z ) ) ) ],
% 0.80/1.20 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.20 , 'c_Lambda_OdB_OVar'( 'v_n' ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.80/1.20 [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( 'v_n' ) ) )
% 0.80/1.20 ) ],
% 0.80/1.20 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.80/1.20 'class_Orderings_Opreorder'( Y ) ) ],
% 0.80/1.20 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.80/1.20 'class_Orderings_Oorder'( Y ) ) ],
% 0.80/1.20 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.80/1.20 ],
% 0.80/1.20 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.80/1.20 ) ],
% 0.80/1.20 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.80/1.20 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.80/1.20 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.80/1.20 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.80/1.20 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.80/1.20 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.80/1.20 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.80/1.20 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 0.80/1.20 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.80/1.20 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.80/1.20 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.80/1.20 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.80/1.20 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 0.80/1.20 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 0.80/1.20 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 0.80/1.20 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 0.80/1.20 ] .
% 0.80/1.20
% 0.80/1.20
% 0.80/1.20 percentage equality = 0.417755, percentage horn = 0.873385
% 0.80/1.20 This is a problem with some equality
% 0.80/1.20
% 0.80/1.20
% 0.80/1.20
% 0.80/1.20 Options Used:
% 0.80/1.20
% 0.80/1.20 useres = 1
% 0.80/1.20 useparamod = 1
% 0.80/1.20 useeqrefl = 1
% 0.80/1.20 useeqfact = 1
% 0.80/1.20 usefactor = 1
% 0.80/1.20 usesimpsplitting = 0
% 0.80/1.20 usesimpdemod = 5
% 0.80/1.20 usesimpres = 3
% 0.80/1.20
% 0.80/1.20 resimpinuse = 1000
% 0.80/1.20 resimpclauses = 20000
% 0.80/1.20 substype = eqrewr
% 0.80/1.20 backwardsubs = 1
% 0.80/1.20 selectoldest = 5
% 0.80/1.20
% 0.80/1.20 litorderings [0] = split
% 0.80/1.20 litorderings [1] = extend the termordering, first sorting on arguments
% 0.80/1.20
% 0.80/1.20 termordering = kbo
% 0.80/1.20
% 0.80/1.20 litapriori = 0
% 0.80/1.20 termapriori = 1
% 0.80/1.20 litaposteriori = 0
% 0.80/1.20 termaposteriori = 0
% 0.80/1.20 demodaposteriori = 0
% 0.80/1.20 ordereqreflfact = 0
% 0.80/1.20
% 0.80/1.20 litselect = negord
% 0.80/1.20
% 0.80/1.20 maxweight = 15
% 0.80/1.20 maxdepth = 30000
% 0.80/1.20 maxlength = 115
% 0.80/1.20 maxnrvars = 195
% 0.80/1.20 excuselevel = 1
% 0.80/1.20 increasemaxweight = 1
% 0.80/1.20
% 0.80/1.20 maxselected = 10000000
% 0.80/1.20 maxnrclauses = 10000000
% 0.80/1.20
% 0.80/1.20 showgenerated = 0
% 0.80/1.20 showkept = 0
% 0.80/1.20 showselected = 0
% 0.80/1.20 showdeleted = 0
% 0.80/1.20 showresimp = 1
% 0.80/1.20 showstatus = 2000
% 0.80/1.20
% 0.80/1.20 prologoutput = 1
% 0.80/1.20 nrgoals = 5000000
% 0.80/1.20 totalproof = 1
% 0.80/1.20
% 0.80/1.20 Symbols occurring in the translation:
% 0.80/1.20
% 0.80/1.20 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.80/1.20 . [1, 2] (w:1, o:155, a:1, s:1, b:0),
% 0.80/1.20 ! [4, 1] (w:0, o:93, a:1, s:1, b:0),
% 0.80/1.20 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.80/1.20 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.80/1.20 'class_OrderedGroup_Omonoid__add' [40, 1] (w:1, o:99, a:1, s:1, b:0)
% 0.80/1.20 ,
% 0.80/1.20 'c_HOL_Oplus__class_Oplus' [41, 1] (w:1, o:100, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Ofoldl' [44, 5] (w:1, o:220, a:1, s:1, b:0),
% 0.80/1.20 hAPP [45, 2] (w:1, o:180, a:1, s:1, b:0),
% 0.80/1.20 'c_HOL_Ozero__class_Ozero' [46, 1] (w:1, o:101, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Ofoldr' [47, 5] (w:1, o:221, a:1, s:1, b:0),
% 0.80/1.20 'c_Lambda_OdB_OVar' [49, 1] (w:1, o:102, a:1, s:1, b:0),
% 0.80/1.20 'c_Lambda_Osubstn' [52, 3] (w:1, o:189, a:1, s:1, b:0),
% 0.80/1.20 'tc_nat' [53, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.80/1.20 'c_HOL_Oord__class_Oless' [54, 3] (w:1, o:190, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Olist_ONil' [57, 1] (w:1, o:103, a:1, s:1, b:0),
% 0.80/1.20 'tc_List_Olist' [58, 1] (w:1, o:104, a:1, s:1, b:0),
% 0.80/1.20 'c_Nat_Osize__class_Osize' [59, 2] (w:1, o:181, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Oreplicate' [62, 3] (w:1, o:191, a:1, s:1, b:0),
% 0.80/1.20 'c_Type_Otype_OFun' [67, 0] (w:1, o:47, a:1, s:1, b:0),
% 0.80/1.20 'c_Type_Osko__Type__Xlist__app__typeD__1__1' [70, 4] (w:1, o:208, a:1
% 0.80/1.20 , s:1, b:0),
% 0.80/1.20 'tc_Type_Otype' [71, 0] (w:1, o:50, a:1, s:1, b:0),
% 0.80/1.20 'c_Type_Otyping' [72, 3] (w:1, o:192, a:1, s:1, b:0),
% 0.80/1.20 'c_Lambda_OdB_OApp' [73, 0] (w:1, o:51, a:1, s:1, b:0),
% 0.80/1.20 'tc_Lambda_OdB' [74, 0] (w:1, o:52, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Olist__update' [75, 4] (w:1, o:209, a:1, s:1, b:0),
% 0.80/1.20 'c_Predicate_Oconversep' [77, 3] (w:1, o:194, a:1, s:1, b:0),
% 0.80/1.20 'c_Transitive__Closure_Ortranclp' [78, 2] (w:1, o:182, a:1, s:1, b:0)
% 0.80/1.20 ,
% 0.80/1.20 hBOOL [79, 1] (w:1, o:105, a:1, s:1, b:0),
% 0.80/1.20 'class_Orderings_Oorder' [83, 1] (w:1, o:106, a:1, s:1, b:0),
% 0.80/1.20 'class_Orderings_Opreorder' [85, 1] (w:1, o:107, a:1, s:1, b:0),
% 0.80/1.20 'c_Wellfounded_Oaccp' [86, 3] (w:1, o:195, a:1, s:1, b:0),
% 0.80/1.20 'c_Type_Osko__Type__Xlist__app__typeE__1__1' [87, 4] (w:1, o:210, a:1
% 0.80/1.20 , s:1, b:0),
% 0.80/1.20 'c_Lambda_Obeta' [88, 0] (w:1, o:60, a:1, s:1, b:0),
% 0.80/1.20 'c_InductTermi_OIT' [89, 0] (w:1, o:61, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Oremdups' [90, 2] (w:1, o:183, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Omap' [91, 4] (w:1, o:212, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Orev' [92, 2] (w:1, o:184, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Oappend' [94, 3] (w:1, o:196, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Ofilter' [96, 3] (w:1, o:197, a:1, s:1, b:0),
% 0.80/1.20 'c_fequal' [97, 1] (w:1, o:108, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Orotate' [98, 3] (w:1, o:198, a:1, s:1, b:0),
% 0.80/1.20 'class_Orderings_Olinorder' [99, 1] (w:1, o:109, a:1, s:1, b:0),
% 0.80/1.20 'class_Ring__and__Field_Oordered__idom' [100, 1] (w:1, o:110, a:1, s:
% 0.80/1.20 1, b:0),
% 0.80/1.20 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [101, 1]
% 0.80/1.20 (w:1, o:111, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Olist_OCons' [104, 3] (w:1, o:199, a:1, s:1, b:0),
% 0.80/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [109, 1]
% 0.80/1.20 (w:1, o:112, a:1, s:1, b:0),
% 0.80/1.20 'class_OrderedGroup_Olordered__ab__group__add' [110, 1] (w:1, o:98
% 0.80/1.20 , a:1, s:1, b:0),
% 0.80/1.20 'class_OrderedGroup_Opordered__comm__monoid__add' [111, 1] (w:1, o:
% 0.80/1.20 113, a:1, s:1, b:0),
% 0.80/1.20 'class_Ring__and__Field_Oordered__semidom' [112, 1] (w:1, o:114, a:1
% 0.80/1.20 , s:1, b:0),
% 0.80/1.20 'class_OrderedGroup_Oab__semigroup__add' [113, 1] (w:1, o:115, a:1
% 0.80/1.20 , s:1, b:0),
% 0.80/1.20 'c_Lambda_Osubst' [116, 3] (w:1, o:200, a:1, s:1, b:0),
% 0.80/1.20 'c_Type_Otypings' [120, 3] (w:1, o:201, a:1, s:1, b:0),
% 0.80/1.20 'c_Map_Omap__upds' [122, 5] (w:1, o:225, a:1, s:1, b:0),
% 0.80/1.20 'c_Lambda_Olift' [123, 2] (w:1, o:185, a:1, s:1, b:0),
% 0.80/1.20 'c_Lambda_Oliftn' [124, 3] (w:1, o:202, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Osko__List__XCons__eq__filter__iff__1__3' [126, 3] (w:1, o:
% 0.80/1.20 204, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Osko__List__Xfilter__eq__Cons__iff__1__3' [128, 3] (w:1, o:
% 0.80/1.20 205, a:1, s:1, b:0),
% 0.80/1.20 'c_Lambda_OdB_OAbs' [130, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.80/1.20 'c_Type_Osko__Type__Xvar__app__typesE__1__1' [131, 4] (w:1, o:213, a:
% 0.80/1.20 1, s:1, b:0),
% 0.80/1.20 'c_Type_Osko__Type__Xvar__app__types__1__1' [133, 4] (w:1, o:214, a:1
% 0.80/1.20 , s:1, b:0),
% 0.80/1.20 'v_sko__List__Xconcat__Xinduct__1' [135, 1] (w:1, o:117, a:1, s:1, b:
% 0.80/1.20 0),
% 0.80/1.20 'v_sko__List__Xconcat__Xinduct__2' [136, 1] (w:1, o:118, a:1, s:1, b:
% 0.80/1.20 0),
% 0.80/1.20 't_a' [137, 0] (w:1, o:75, a:1, s:1, b:0),
% 0.80/1.20 'v_sko__List__Xtake__Xinduct__1' [138, 1] (w:1, o:119, a:1, s:1, b:0)
% 0.80/1.20 ,
% 0.80/1.20 'v_sko__List__Xtake__Xinduct__2' [139, 1] (w:1, o:120, a:1, s:1, b:0)
% 0.80/1.20 ,
% 0.80/1.20 'v_sko__List__Xmap__Xinduct__1' [140, 1] (w:1, o:123, a:1, s:1, b:0)
% 0.80/1.20 ,
% 0.80/1.20 'v_sko__List__Xmap__Xinduct__2' [141, 1] (w:1, o:124, a:1, s:1, b:0)
% 0.80/1.20 ,
% 0.80/1.20 'v_sko__List__Xlist__Xinduct__1' [142, 1] (w:1, o:121, a:1, s:1, b:0)
% 0.80/1.20 ,
% 0.80/1.20 'v_sko__List__Xlist__Xinduct__2' [143, 1] (w:1, o:122, a:1, s:1, b:0)
% 0.80/1.20 ,
% 0.80/1.20 'v_sko__List__XdropWhile__Xinduct__1' [144, 1] (w:1, o:125, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'v_sko__List__XdropWhile__Xinduct__2' [145, 1] (w:1, o:126, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'v_sko__List__Xremove1__Xinduct__1' [146, 1] (w:1, o:127, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'v_sko__List__Xremove1__Xinduct__2' [147, 1] (w:1, o:128, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'v_sko__List__Xdistinct__Xinduct__1' [148, 1] (w:1, o:129, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'v_sko__List__Xdistinct__Xinduct__2' [149, 1] (w:1, o:130, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__4' [150, 1] (w:1, o:133, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__5' [151, 1] (w:1, o:134, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__6' [152, 1] (w:1, o:135, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__3' [153, 1] (w:1, o:132, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__1' [154, 1] (w:1, o:136, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'c_List_Olistsp' [155, 3] (w:1, o:206, a:1, s:1, b:0),
% 0.80/1.20 'c_Type_Osko__Type__Xtypes__snocE__1__1' [156, 4] (w:1, o:215, a:1
% 0.80/1.20 , s:1, b:0),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__2' [157, 1] (w:1, o:131, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'c_Type_Osko__Type__Xtypes__snocE__1__2' [158, 4] (w:1, o:216, a:1
% 0.80/1.20 , s:1, b:0),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xlem__1__3' [159, 1] (w:1
% 0.80/1.20 , o:138, a:1, s:1, b:0),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xlem__1__4' [160, 1] (w:1
% 0.80/1.20 , o:139, a:1, s:1, b:0),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xlem__1__1' [161, 1] (w:1
% 0.80/1.20 , o:140, a:1, s:1, b:0),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xlem__1__2' [162, 1] (w:1
% 0.80/1.20 , o:137, a:1, s:1, b:0),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3' [163, 1
% 0.80/1.20 ] (w:1, o:142, a:1, s:1, b:0),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4' [164, 1
% 0.80/1.20 ] (w:1, o:143, a:1, s:1, b:0),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1' [165, 1
% 0.80/1.20 ] (w:1, o:144, a:1, s:1, b:0),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2' [166, 1
% 0.80/1.20 ] (w:1, o:141, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Olist_Olist__case' [170, 5] (w:1, o:222, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Oremove1' [171, 3] (w:1, o:203, a:1, s:1, b:0),
% 0.80/1.20 'class_Ring__and__Field_Oidom' [172, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.80/1.20
% 0.80/1.20 'class_Int_Onumber__ring' [173, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.80/1.20 'class_OrderedGroup_Ocancel__ab__semigroup__add' [174, 1] (w:1, o:147
% 0.80/1.20 , a:1, s:1, b:0),
% 0.80/1.20 'class_OrderedGroup_Ocancel__semigroup__add' [175, 1] (w:1, o:148, a:
% 0.80/1.20 1, s:1, b:0),
% 0.80/1.20 'c_ListOrder_Ostep1' [177, 4] (w:1, o:217, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Olinorder__class_Osorted' [178, 2] (w:1, o:186, a:1, s:1, b:0
% 0.80/1.20 ),
% 0.80/1.20 'class_Ring__and__Field_Ocomm__semiring__1' [179, 1] (w:1, o:149, a:1
% 0.80/1.20 , s:1, b:0),
% 0.80/1.20 'class_OrderedGroup_Ocomm__monoid__add' [181, 1] (w:1, o:150, a:1, s:
% 0.80/1.20 1, b:0),
% 0.80/1.20 'c_OrderedGroup_Omonoid__add' [184, 3] (w:1, o:193, a:1, s:1, b:0),
% 0.80/1.20 't_b' [188, 0] (w:1, o:81, a:1, s:1, b:0),
% 0.80/1.20 'class_OrderedGroup_Oab__group__add' [189, 1] (w:1, o:151, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'c_Lambda_OdB_OdB__case' [193, 5] (w:1, o:223, a:1, s:1, b:0),
% 0.80/1.20 'c_List_Olistrelp' [194, 4] (w:1, o:211, a:1, s:1, b:0),
% 0.80/1.20 'c_OrderedGroup_Osemigroup__add' [196, 2] (w:1, o:187, a:1, s:1, b:0)
% 0.80/1.20 ,
% 0.80/1.20 'c_Lambda_OdB_OdB__rec' [197, 5] (w:1, o:224, a:1, s:1, b:0),
% 0.80/1.20 'class_OrderedGroup_Osemigroup__add' [198, 1] (w:1, o:152, a:1, s:1
% 0.80/1.20 , b:0),
% 0.80/1.20 'c_List_Ofiltermap' [202, 4] (w:1, o:218, a:1, s:1, b:0),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2' [210, 1
% 0.80/1.20 ] (w:1, o:154, a:1, s:1, b:0),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1' [211, 1
% 0.80/1.20 ] (w:1, o:153, a:1, s:1, b:0),
% 0.80/1.20 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1' [212, 3] (w:
% 0.80/1.20 1, o:207, a:1, s:1, b:0),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1' [
% 0.80/1.20 215, 4] (w:1, o:219, a:1, s:1, b:0),
% 0.80/1.20 'v_n' [219, 0] (w:1, o:87, a:1, s:1, b:0),
% 0.80/1.20 'tc_fun' [222, 2] (w:1, o:188, a:1, s:1, b:0),
% 0.80/1.20 'tc_bool' [223, 0] (w:1, o:90, a:1, s:1, b:0).
% 0.80/1.20
% 0.80/1.20
% 0.80/1.20 Starting Search:
% 0.80/1.20
% 0.80/1.20
% 0.80/1.20 Bliksems!, er is een bewijs:
% 0.80/1.20 % SZS status Unsatisfiable
% 0.80/1.20 % SZS output start Refutation
% 0.80/1.20
% 0.80/1.20 clause( 328, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ),
% 0.80/1.20 Y ) ] )
% 0.80/1.20 .
% 0.80/1.20 clause( 331, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( 'v_n'
% 0.80/1.20 ) ) ) ] )
% 0.80/1.20 .
% 0.80/1.20 clause( 332, [] )
% 0.80/1.20 .
% 0.80/1.20
% 0.80/1.20
% 0.80/1.20 % SZS output end Refutation
% 0.80/1.20 found a proof!
% 0.80/1.20
% 0.80/1.20 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.80/1.20
% 0.80/1.20 initialclauses(
% 0.80/1.20 [ clause( 334, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.80/1.20 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP(
% 0.80/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.80/1.20 ) ) ) ] )
% 0.80/1.20 , clause( 335, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.80/1.20 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.80/1.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ), 'c_List_Ofoldr'(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.80/1.20 ) ) ] )
% 0.80/1.20 , clause( 336, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.20 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.80/1.20 'tc_nat' ) ] )
% 0.80/1.20 , clause( 337, [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T )
% 0.80/1.20 , Z ) ] )
% 0.80/1.20 , clause( 338, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 'tc_nat' ), 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ),
% 0.80/1.20 'tc_List_Olist'( X ) ), 'tc_nat' ) ) ] )
% 0.80/1.20 , clause( 339, [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'(
% 0.80/1.20 T, U, Z ) ) ), =( Y, U ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.80/1.20 ] )
% 0.80/1.20 , clause( 340, [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 0.80/1.20 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X,
% 0.80/1.20 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.80/1.20 , clause( 341, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist__update'( X,
% 0.80/1.20 Y, Z, T ), 'tc_List_Olist'( T ) ), 'c_Nat_Osize__class_Osize'( X,
% 0.80/1.20 'tc_List_Olist'( T ) ) ) ] )
% 0.80/1.20 , clause( 342, [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 'tc_nat' ), X, Y ), 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 'tc_nat' ), Z, Y ) ) ] )
% 0.80/1.20 , clause( 343, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 'tc_nat' ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ),
% 0.80/1.20 'tc_nat' ), =( X, 'c_List_Olist_ONil'( Y ) ) ] )
% 0.80/1.20 , clause( 344, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.20 'c_Predicate_Oconversep'( X, Y, Y ), Y ), Z ), T ) ), ~( hBOOL( hAPP(
% 0.80/1.20 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), T ), Z ) ) ) ] )
% 0.80/1.20 , clause( 345, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.80/1.20 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.20 'c_Predicate_Oconversep'( X, Y, Y ), Y ), T ), Z ) ) ) ] )
% 0.80/1.20 , clause( 346, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.20 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ] )
% 0.80/1.20 , clause( 347, [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T
% 0.80/1.20 ), U ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ] )
% 0.80/1.20 , clause( 348, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.20 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ] )
% 0.80/1.20 , clause( 349, [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T
% 0.80/1.20 ), U ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ] )
% 0.80/1.20 , clause( 350, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 0.80/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.80/1.20 , clause( 351, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 0.80/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.80/1.20 , clause( 352, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.80/1.20 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.80/1.20 , clause( 353, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 0.80/1.20 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.80/1.20 , clause( 354, [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'(
% 0.80/1.20 T, U, Z ) ) ), =( X, T ) ] )
% 0.80/1.20 , clause( 355, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.20 'c_Transitive__Closure_Ortranclp'( X, Z ), Y ), T ) ) ), ~(
% 0.80/1.20 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 0.80/1.20 , clause( 356, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( 'c_Wellfounded_Oaccp'(
% 0.80/1.20 X, T, Z ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X,
% 0.80/1.20 Z ), Y ), T ) ) ) ] )
% 0.80/1.20 , clause( 357, [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 0.80/1.20 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X,
% 0.80/1.20 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.80/1.20 , clause( 358, [ 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'(
% 0.80/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB'
% 0.80/1.20 ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.20 , clause( 359, [ hBOOL( hAPP( 'c_InductTermi_OIT', X ) ), ~(
% 0.80/1.20 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.20 , clause( 360, [ ~( =( 'c_Nat_Osize__class_Osize'( 'c_List_Oremdups'( X, Y
% 0.80/1.20 ), 'tc_List_Olist'( Y ) ), 'c_Nat_Osize__class_Osize'( X,
% 0.80/1.20 'tc_List_Olist'( Y ) ) ) ), =( 'c_List_Oremdups'( X, Y ), X ) ] )
% 0.80/1.20 , clause( 361, [ ~( =( 'c_List_Oremdups'( X, Y ), X ) ), =(
% 0.80/1.20 'c_Nat_Osize__class_Osize'( 'c_List_Oremdups'( X, Y ), 'tc_List_Olist'( Y
% 0.80/1.20 ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ) ) ] )
% 0.80/1.20 , clause( 362, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Omap'( X, Y, Z, T )
% 0.80/1.20 , 'tc_List_Olist'( T ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'(
% 0.80/1.20 Z ) ) ) ] )
% 0.80/1.20 , clause( 363, [ =( 'c_List_Omap'( X, 'c_List_Oreplicate'( Y, Z, T ), T, U
% 0.80/1.20 ), 'c_List_Oreplicate'( Y, hAPP( X, Z ), U ) ) ] )
% 0.80/1.20 , clause( 364, [ =( 'c_List_Orev'( 'c_List_Oreplicate'( X, Y, Z ), Z ),
% 0.80/1.20 'c_List_Oreplicate'( X, Y, Z ) ) ] )
% 0.80/1.20 , clause( 365, [ =( 'c_List_Ofoldr'( X, 'c_List_Oappend'( Y, Z, T ), U, T,
% 0.80/1.20 W ), 'c_List_Ofoldr'( X, Y, 'c_List_Ofoldr'( X, Z, U, T, W ), T, W ) ) ]
% 0.80/1.20 )
% 0.80/1.20 , clause( 366, [ =( 'c_List_Ofilter'( X, 'c_List_Oreplicate'( Y, Z, T ), T
% 0.80/1.20 ), 'c_List_Oreplicate'( Y, Z, T ) ), ~( hBOOL( hAPP( X, Z ) ) ) ] )
% 0.80/1.20 , clause( 367, [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Omap'( X, U, Z
% 0.80/1.20 , T ) ) ), =( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ),
% 0.80/1.20 'c_Nat_Osize__class_Osize'( U, 'tc_List_Olist'( Z ) ) ) ] )
% 0.80/1.20 , clause( 368, [ =( 'c_Predicate_Oconversep'( 'c_fequal'( X ), X, X ),
% 0.80/1.20 'c_fequal'( X ) ) ] )
% 0.80/1.20 , clause( 369, [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T
% 0.80/1.20 , U, Z ), 'c_List_Oappend'( 'c_List_Olist__update'( X, T, U, Z ), Y, Z )
% 0.80/1.20 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 0.80/1.20 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ] )
% 0.80/1.20 , clause( 370, [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T
% 0.80/1.20 , U, Z ), 'c_List_Oappend'( 'c_List_Olist__update'( X, T, U, Z ), Y, Z )
% 0.80/1.20 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 0.80/1.20 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ] )
% 0.80/1.20 , clause( 371, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Orotate'( X, Y, Z )
% 0.80/1.20 , 'tc_List_Olist'( Z ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'(
% 0.80/1.20 Z ) ) ) ] )
% 0.80/1.20 , clause( 372, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 0.80/1.20 , clause( 373, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 0.80/1.20 , clause( 374, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.80/1.20 , clause( 375, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.80/1.20 , clause( 376, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.80/1.20 , clause( 377, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.80/1.20 ), =( Z, Y ) ] )
% 0.80/1.20 , clause( 378, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.80/1.20 ) ] )
% 0.80/1.20 , clause( 379, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 0.80/1.20 , clause( 380, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), =( Z, Y ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ] )
% 0.80/1.20 , clause( 381, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 0.80/1.20 , clause( 382, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.80/1.20 ), =( Z, Y ) ] )
% 0.80/1.20 , clause( 383, [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.80/1.20 'c_List_Oreplicate'( T, Y, Z ), Z ), 'c_List_Oappend'(
% 0.80/1.20 'c_List_Oreplicate'( T, Y, Z ), 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ]
% 0.80/1.20 )
% 0.80/1.20 , clause( 384, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 0.80/1.20 , clause( 385, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.80/1.20 ) ] )
% 0.80/1.20 , clause( 386, [ ~(
% 0.80/1.20 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.20 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.80/1.20 T, X ) ) ] )
% 0.80/1.20 , clause( 387, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.80/1.20 ] )
% 0.80/1.20 , clause( 388, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 0.80/1.20 , clause( 389, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Oreplicate'( X, Y,
% 0.80/1.20 Z ), 'tc_List_Olist'( Z ) ), X ) ] )
% 0.80/1.20 , clause( 390, [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_OCons'( Y, Z, T ), U
% 0.80/1.20 , T, W ), hAPP( hAPP( X, Y ), 'c_List_Ofoldr'( X, Z, U, T, W ) ) ) ] )
% 0.80/1.20 , clause( 391, [ =( 'c_Predicate_Oconversep'( 'c_Predicate_Oconversep'( X,
% 0.80/1.20 Y, Z ), Z, Y ), X ) ] )
% 0.80/1.20 , clause( 392, [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP(
% 0.80/1.20 hAPP( 'c_Type_Otype_OFun', Z ), T ) ) ), =( Y, T ) ] )
% 0.80/1.20 , clause( 393, [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP(
% 0.80/1.20 hAPP( 'c_Type_Otype_OFun', Z ), T ) ) ), =( X, Z ) ] )
% 0.80/1.20 , clause( 394, [ ~(
% 0.80/1.20 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.20 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.80/1.20 , clause( 395, [ ~(
% 0.80/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.20 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.80/1.20 , clause( 396, [ ~(
% 0.80/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.80/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 0.80/1.20 , clause( 397, [ ~(
% 0.80/1.20 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.20 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.80/1.20 , clause( 398, [ ~(
% 0.80/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.20 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.80/1.20 , clause( 399, [ ~(
% 0.80/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.80/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 0.80/1.20 , clause( 400, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Orev'( X, Y ),
% 0.80/1.20 'tc_List_Olist'( Y ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y
% 0.80/1.20 ) ) ) ] )
% 0.80/1.20 , clause( 401, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.80/1.20 Y, X ) ) ] )
% 0.80/1.20 , clause( 402, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.80/1.20 Y, X ) ) ] )
% 0.80/1.20 , clause( 403, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X
% 0.80/1.20 , Y ), T ) ) ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 0.80/1.20 , clause( 404, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.80/1.20 Y, X ) ) ] )
% 0.80/1.20 , clause( 405, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X
% 0.80/1.20 , Y ), T ) ) ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 0.80/1.20 , clause( 406, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.80/1.20 Y, X ) ) ] )
% 0.80/1.20 , clause( 407, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.80/1.20 , clause( 408, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 0.80/1.20 , clause( 409, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.80/1.20 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.80/1.20 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.80/1.20 , clause( 410, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.20 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.80/1.20 , clause( 411, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.20 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.80/1.20 , clause( 412, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.20 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.80/1.20 , clause( 413, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.20 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.80/1.20 , clause( 414, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.80/1.20 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.80/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.80/1.20 , clause( 415, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.20 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.80/1.20 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.80/1.20 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.80/1.20 , clause( 416, [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 'tc_nat' ), X, Y ), 'c_List_Olist_ONil'( Y ) ) ] )
% 0.80/1.20 , clause( 417, [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ),
% 0.80/1.20 'tc_List_Olist'( X ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.80/1.20 , clause( 418, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'(
% 0.80/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, X ) ) ] )
% 0.80/1.20 , clause( 419, [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Olist_ONil'(
% 0.80/1.20 Z ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.80/1.20 , clause( 420, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'( Y, Z
% 0.80/1.20 , X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.80/1.20 , clause( 421, [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y )
% 0.80/1.20 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_List_Olist_ONil'(
% 0.80/1.20 Y ) ) ] )
% 0.80/1.20 , clause( 422, [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.80/1.20 'c_List_Olist_OCons'( Y, T, Z ), Z ), 'c_List_Olist_OCons'( Y,
% 0.80/1.20 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ), T, Z ), Z ) ) ] )
% 0.80/1.20 , clause( 423, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.80/1.20 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ),
% 0.80/1.20 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ] )
% 0.80/1.20 , clause( 424, [ =( 'c_List_Ofilter'( X, 'c_List_Oreplicate'( Y, Z, T ), T
% 0.80/1.20 ), 'c_List_Olist_ONil'( T ) ), hBOOL( hAPP( X, Z ) ) ] )
% 0.80/1.20 , clause( 425, [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y )
% 0.80/1.20 , Z ), T ), ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y,
% 0.80/1.20 hAPP( hAPP( 'c_Type_Otype_OFun', U ), T ) ) ) ] )
% 0.80/1.20 , clause( 426, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 0.80/1.20 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ] )
% 0.80/1.20 , clause( 427, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.20 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.80/1.20 'tc_nat' ) ] )
% 0.80/1.20 , clause( 428, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.20 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.80/1.20 ) ) ] )
% 0.80/1.20 , clause( 429, [ 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.20 , Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ), ~( 'c_Type_Otypings'( X
% 0.80/1.20 , Z, U ) ), ~( 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 0.80/1.20 'c_Type_Otype_OFun', U, T, 'tc_Type_Otype', 'tc_Type_Otype' ) ) ) ] )
% 0.80/1.20 , clause( 430, [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y )
% 0.80/1.20 ), 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( T ) ) ) ), =(
% 0.80/1.20 'c_Map_Omap__upds'( U, 'c_List_Oappend'( X, W, Y ), Z, Y, T ),
% 0.80/1.20 'c_Map_Omap__upds'( U, X, Z, Y, T ) ) ] )
% 0.80/1.20 , clause( 431, [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y )
% 0.80/1.20 ), 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( T ) ) ) ), =(
% 0.80/1.20 'c_Map_Omap__upds'( U, X, 'c_List_Oappend'( Z, W, T ), Y, T ),
% 0.80/1.20 'c_Map_Omap__upds'( U, X, Z, Y, T ) ) ] )
% 0.80/1.20 , clause( 432, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.80/1.20 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.80/1.20 ) ) ] )
% 0.80/1.20 , clause( 433, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.80/1.20 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.80/1.20 ) ) ] )
% 0.80/1.20 , clause( 434, [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.80/1.20 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( Z ), Z ), Z ),
% 0.80/1.20 'c_List_Olist_OCons'( Y, 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ] )
% 0.80/1.20 , clause( 435, [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Osko__List__XCons__eq__filter__iff__1__3'( X, Z, T ) ) ), =(
% 0.80/1.20 'c_List_Olist_OCons'( Y, 'c_List_Ofilter'( X, U, T ), T ),
% 0.80/1.20 'c_List_Ofilter'( X, 'c_List_Oappend'( Z, 'c_List_Olist_OCons'( Y, U, T )
% 0.80/1.20 , T ), T ) ) ] )
% 0.80/1.20 , clause( 436, [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Osko__List__Xfilter__eq__Cons__iff__1__3'( X, Z, T ) ) ), =(
% 0.80/1.20 'c_List_Ofilter'( X, 'c_List_Oappend'( Z, 'c_List_Olist_OCons'( Y, U, T )
% 0.80/1.20 , T ), T ), 'c_List_Olist_OCons'( Y, 'c_List_Ofilter'( X, U, T ), T ) ) ]
% 0.80/1.20 )
% 0.80/1.20 , clause( 437, [ ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'(
% 0.80/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 'tc_nat' ) ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) )
% 0.80/1.20 , ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB' ) ),
% 0.80/1.20 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.20 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ] )
% 0.80/1.20 , clause( 438, [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X,
% 0.80/1.20 'c_List_Olist_OCons'( Y, Z, T ), T ), 'c_Nat_Osize__class_Osize'( X,
% 0.80/1.20 'tc_List_Olist'( T ) ), U, T ), 'c_List_Oappend'( X, 'c_List_Olist_OCons'(
% 0.80/1.20 U, Z, T ), T ) ) ] )
% 0.80/1.20 , clause( 439, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ),
% 0.80/1.20 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.80/1.20 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X, Y, T ), Z,
% 0.80/1.20 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), T,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.80/1.20 , clause( 440, [ =( X, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.80/1.20 'c_Type_Osko__Type__Xvar__app__types__1__1'( Y, X, Z, T ), Y,
% 0.80/1.20 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( Z,
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ), ~( 'c_Type_Otypings'( Z, W, V0
% 0.80/1.20 ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.80/1.20 , Y ) ) ] )
% 0.80/1.20 , clause( 441, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_OCons'( 'v_sko__List__Xconcat__Xinduct__1'( X ),
% 0.80/1.20 'v_sko__List__Xconcat__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X
% 0.80/1.20 , 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.20 , clause( 442, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_OCons'( 'v_sko__List__Xtake__Xinduct__1'( X ),
% 0.80/1.20 'v_sko__List__Xtake__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.20 , clause( 443, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_OCons'( 'v_sko__List__Xmap__Xinduct__1'( X ),
% 0.80/1.20 'v_sko__List__Xmap__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.20 , clause( 444, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_OCons'( 'v_sko__List__Xlist__Xinduct__1'( X ),
% 0.80/1.20 'v_sko__List__Xlist__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.20 , clause( 445, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_OCons'( 'v_sko__List__XdropWhile__Xinduct__1'( X ),
% 0.80/1.20 'v_sko__List__XdropWhile__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.80/1.20 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.20 , clause( 446, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_OCons'( 'v_sko__List__Xremove1__Xinduct__1'( X ),
% 0.80/1.20 'v_sko__List__Xremove1__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.80/1.20 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.20 , clause( 447, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Olist_OCons'( 'v_sko__List__Xdistinct__Xinduct__1'( X ),
% 0.80/1.20 'v_sko__List__Xdistinct__Xinduct__2'( X ), 't_a' ) ) ) ), ~( hBOOL( hAPP(
% 0.80/1.20 X, 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.20 , clause( 448, [ 'c_Type_Otypings'( X, Y,
% 0.80/1.20 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X, T, Y ) ), ~(
% 0.80/1.20 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', T, Y,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.80/1.20 , clause( 449, [ 'c_Type_Otypings'( X, Y,
% 0.80/1.20 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X, T, Y ) ), ~(
% 0.80/1.20 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', T, Y,
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.80/1.20 , clause( 450, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 0.80/1.20 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'(
% 0.80/1.20 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.80/1.20 , clause( 451, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.80/1.20 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.80/1.20 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.20 , clause( 452, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.80/1.20 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.80/1.20 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.20 , clause( 453, [ 'c_Type_Otypings'( X, Y,
% 0.80/1.20 'c_Type_Osko__Type__Xtypes__snocE__1__1'( Z, X, T, Y ) ), ~(
% 0.80/1.20 'c_Type_Otypings'( X, 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( T,
% 0.80/1.20 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ),
% 0.80/1.20 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.80/1.20 , clause( 454, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.80/1.20 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.80/1.20 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.80/1.20 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.20 , clause( 455, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.20 , clause( 456, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.20 , clause( 457, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.80/1.20 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.80/1.20 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.80/1.20 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.20 , clause( 458, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.80/1.20 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.20 , clause( 459, [ 'c_Type_Otyping'( X, Y,
% 0.80/1.20 'c_Type_Osko__Type__Xtypes__snocE__1__2'( Z, X, Y, T ) ), ~(
% 0.80/1.20 'c_Type_Otypings'( X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y,
% 0.80/1.20 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ),
% 0.80/1.20 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.80/1.20 , clause( 460, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__4'( X ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__5'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.80/1.20 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.20 , clause( 461, [ ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.20 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xlem__1__3'( X ) ),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xlem__1__4'( X ),
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xlem__1__1'( X ) ),
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__Xlem__1__2'( X ),
% 0.80/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( X, Y ) ) ] )
% 0.80/1.20 , clause( 462, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3'( X ) )
% 0.80/1.20 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4'( X )
% 0.80/1.20 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.20 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1'( X ) )
% 0.80/1.20 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2'( X )
% 0.80/1.20 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.80/1.20 , clause( 463, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.80/1.20 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP(
% 0.80/1.20 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.80/1.20 'tc_Lambda_OdB' ), X ), Z ) ) ) ] )
% 0.80/1.20 , clause( 464, [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U
% 0.80/1.20 ), 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U )
% 0.80/1.20 ) ] )
% 0.80/1.20 , clause( 465, [ =( 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z
% 0.80/1.20 , T, U ), U ), 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U )
% 0.80/1.20 ) ] )
% 0.80/1.20 , clause( 466, [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U
% 0.80/1.20 ), 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U )
% 0.80/1.20 ) ] )
% 0.80/1.20 , clause( 467, [ =( 'c_List_Olist_Olist__case'( X, Y, 'c_List_Olist_OCons'(
% 0.80/1.20 Z, T, U ), W, U ), hAPP( hAPP( Y, Z ), T ) ) ] )
% 0.80/1.20 , clause( 468, [ =( 'c_List_Oremove1'( X, 'c_List_Olist_OCons'( X, Y, Z ),
% 0.80/1.20 Z ), Y ) ] )
% 0.80/1.20 , clause( 469, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.80/1.20 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.80/1.20 , clause( 470, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) )
% 0.80/1.20 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.80/1.20 , clause( 471, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.80/1.20 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.80/1.20 , clause( 472, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.80/1.20 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ] )
% 0.80/1.20 , clause( 473, [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T
% 0.80/1.20 ), 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ] )
% 0.80/1.20 , clause( 474, [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T
% 0.80/1.20 ), 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ] )
% 0.80/1.20 , clause( 475, [ =( X, Y ), hBOOL( hAPP( hAPP( Z, Y ), X ) ), ~(
% 0.80/1.20 'c_ListOrder_Ostep1'( Z, 'c_List_Olist_OCons'( Y, T, U ),
% 0.80/1.20 'c_List_Olist_OCons'( X, W, U ), U ) ) ] )
% 0.80/1.20 , clause( 476, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( Y, X ), ~(
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Z, Y, X ), X ) )
% 0.80/1.20 ] )
% 0.80/1.20 , clause( 477, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.20 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) )
% 0.80/1.20 ) ] )
% 0.80/1.20 , clause( 478, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.80/1.20 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), ~( hBOOL( hAPP(
% 0.80/1.20 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.80/1.20 'tc_Lambda_OdB' ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.20 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.80/1.20 ), Z ) ) ) ] )
% 0.80/1.20 , clause( 479, [ =( 'c_List_Orev'( 'c_List_Oappend'( 'c_List_Orev'( X, Y )
% 0.80/1.20 , 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( Y ), Y ), Y ), Y ),
% 0.80/1.20 'c_List_Olist_OCons'( Z, X, Y ) ) ] )
% 0.80/1.20 , clause( 480, [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Type_Otyping'( X, T, Z
% 0.80/1.20 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), T ), Y ) ) ) ] )
% 0.80/1.20 , clause( 481, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X
% 0.80/1.20 ) ] )
% 0.80/1.20 , clause( 482, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Olift'( X,
% 0.80/1.20 Y ) ), 'c_Lambda_Olift'( Z, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.20 'c_Lambda_Obeta', X ), Z ) ) ) ] )
% 0.80/1.20 , clause( 483, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ] )
% 0.80/1.20 , clause( 484, [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ] )
% 0.80/1.20 , clause( 485, [ =( 'c_List_Olist__update'( 'c_List_Olist_OCons'( X, Y, Z )
% 0.80/1.20 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, Z ), 'c_List_Olist_OCons'( T
% 0.80/1.20 , Y, Z ) ) ] )
% 0.80/1.20 , clause( 486, [ =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Oappend'(
% 0.80/1.20 'c_List_Olist_ONil'( Z ), 'c_List_Olist_OCons'( X, Y, Z ), Z ) ) ] )
% 0.80/1.20 , clause( 487, [ =( 'c_List_Omap'( X, 'c_List_Olist__update'( Y, Z, T, U )
% 0.80/1.20 , U, W ), 'c_List_Olist__update'( 'c_List_Omap'( X, Y, U, W ), Z, hAPP( X
% 0.80/1.20 , T ), W ) ) ] )
% 0.80/1.20 , clause( 488, [ =( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y )
% 0.80/1.20 , 'c_List_Orev'( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.80/1.20 Y ) ) ] )
% 0.80/1.20 , clause( 489, [ =( X, Y ), 'c_ListOrder_Ostep1'( Z, X, Y, T ), ~(
% 0.80/1.20 'c_ListOrder_Ostep1'( Z, 'c_List_Oappend'( X, 'c_List_Olist_OCons'( U,
% 0.80/1.20 'c_List_Olist_ONil'( T ), T ), T ), 'c_List_Oappend'( Y,
% 0.80/1.20 'c_List_Olist_OCons'( W, 'c_List_Olist_ONil'( T ), T ), T ), T ) ) ] )
% 0.80/1.20 , clause( 490, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.20 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Y,
% 0.80/1.20 'c_List_Olist_ONil'( X ), X ), X ) ] )
% 0.80/1.20 , clause( 491, [ =( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.20 'c_Transitive__Closure_Ortranclp'( X, Y ), Y ),
% 0.80/1.20 'c_Transitive__Closure_Ortranclp'( X, Y ) ) ] )
% 0.80/1.20 , clause( 492, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 X ) ), Y ), Y ) ] )
% 0.80/1.20 , clause( 493, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.80/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.80/1.20 , Y ), Y ) ] )
% 0.80/1.20 , clause( 494, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.80/1.20 'class_Int_Onumber__ring'( X ) ), =( Y, hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 0.80/1.20 ] )
% 0.80/1.20 , clause( 495, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.80/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 0.80/1.20 ) ), Y ) ] )
% 0.80/1.20 , clause( 496, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.80/1.20 Y ) ] )
% 0.80/1.20 , clause( 497, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.80/1.20 Y ) ] )
% 0.80/1.20 , clause( 498, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.80/1.20 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 0.80/1.20 , clause( 499, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.20 X ) ), Y ), Y ) ] )
% 0.80/1.20 , clause( 500, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 X ) ), 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.20 'c_Lambda_Obeta', X ), Y ) ) ) ] )
% 0.80/1.20 , clause( 501, [ =( 'c_List_Orev'( 'c_List_Oappend'( X, Y, Z ), Z ),
% 0.80/1.20 'c_List_Oappend'( 'c_List_Orev'( Y, Z ), 'c_List_Orev'( X, Z ), Z ) ) ]
% 0.80/1.20 )
% 0.80/1.20 , clause( 502, [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~(
% 0.80/1.20 'c_OrderedGroup_Omonoid__add'( Z, X, T ) ) ] )
% 0.80/1.20 , clause( 503, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 0.80/1.20 'c_OrderedGroup_Omonoid__add'( Y, X, T ) ) ] )
% 0.80/1.20 , clause( 504, [ =( 'c_List_Ofilter'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.80/1.20 'c_List_Oappend'( 'c_List_Ofilter'( X, Y, T ), 'c_List_Ofilter'( X, Z, T
% 0.80/1.20 ), T ) ) ] )
% 0.80/1.20 , clause( 505, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.80/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.80/1.20 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.80/1.20 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.20 , clause( 506, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ),
% 0.80/1.20 'c_List_Olist_ONil'( X ), X ), 'c_List_Olist_ONil'( X ) ) ] )
% 0.80/1.20 , clause( 507, [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T
% 0.80/1.20 ) ) ), =( Y, 'c_List_Olist_ONil'( Z ) ) ] )
% 0.80/1.20 , clause( 508, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Orev'(
% 0.80/1.20 'c_List_Olist_ONil'( X ), X ) ) ] )
% 0.80/1.20 , clause( 509, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oremdups'(
% 0.80/1.20 'c_List_Olist_ONil'( X ), X ) ) ] )
% 0.80/1.20 , clause( 510, [ ~( =( X, 'c_List_Oappend'( Y, X, Z ) ) ), =( Y,
% 0.80/1.20 'c_List_Olist_ONil'( Z ) ) ] )
% 0.80/1.20 , clause( 511, [ ~( =( 'c_List_Oappend'( X, Y, Z ), Y ) ), =( X,
% 0.80/1.20 'c_List_Olist_ONil'( Z ) ) ] )
% 0.80/1.20 , clause( 512, [ ~( =( X, 'c_List_Oappend'( X, Y, Z ) ) ), =( Y,
% 0.80/1.20 'c_List_Olist_ONil'( Z ) ) ] )
% 0.80/1.20 , clause( 513, [ ~( =( 'c_List_Oappend'( X, Y, Z ), X ) ), =( Y,
% 0.80/1.20 'c_List_Olist_ONil'( Z ) ) ] )
% 0.80/1.20 , clause( 514, [ ~( =( 'c_List_Oremdups'( X, Y ), 'c_List_Olist_ONil'( Y )
% 0.80/1.20 ) ), =( X, 'c_List_Olist_ONil'( Y ) ) ] )
% 0.80/1.20 , clause( 515, [ ~( =( 'c_List_Orotate'( X, Y, Z ), 'c_List_Olist_ONil'( Z
% 0.80/1.20 ) ) ), =( Y, 'c_List_Olist_ONil'( Z ) ) ] )
% 0.80/1.20 , clause( 516, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Orev'( Y, X ) ) )
% 0.80/1.20 , =( Y, 'c_List_Olist_ONil'( X ) ) ] )
% 0.80/1.20 , clause( 517, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y, Z
% 0.80/1.20 , X ) ) ) ] )
% 0.80/1.20 , clause( 518, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z
% 0.80/1.20 ) ) ), =( Y, 'c_List_Olist_ONil'( Z ) ) ] )
% 0.80/1.20 , clause( 519, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z
% 0.80/1.20 ) ) ), =( X, 'c_List_Olist_ONil'( Z ) ) ] )
% 0.80/1.20 , clause( 520, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X
% 0.80/1.20 ) ) ), =( Z, 'c_List_Olist_ONil'( X ) ) ] )
% 0.80/1.20 , clause( 521, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X
% 0.80/1.20 ) ) ), =( Y, 'c_List_Olist_ONil'( X ) ) ] )
% 0.80/1.20 , clause( 522, [ ~( 'c_ListOrder_Ostep1'( X, Y, 'c_List_Olist_ONil'( Z ), Z
% 0.80/1.20 ) ) ] )
% 0.80/1.20 , clause( 523, [ ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_ONil'( Y ), Z, Y
% 0.80/1.20 ) ) ] )
% 0.80/1.20 , clause( 524, [ =( 'c_List_Oremdups'( 'c_List_Olist_ONil'( X ), X ),
% 0.80/1.20 'c_List_Olist_ONil'( X ) ) ] )
% 0.80/1.20 , clause( 525, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X
% 0.80/1.20 ) ) ), =( Z, 'c_List_Olist_ONil'( T ) ) ] )
% 0.80/1.20 , clause( 526, [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) )
% 0.80/1.20 ] )
% 0.80/1.20 , clause( 527, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), Y, X ), Y )
% 0.80/1.20 ] )
% 0.80/1.20 , clause( 528, [ =( X, 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ) )
% 0.80/1.20 ] )
% 0.80/1.20 , clause( 529, [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) )
% 0.80/1.20 ] )
% 0.80/1.20 , clause( 530, [ =( 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ), X )
% 0.80/1.20 ] )
% 0.80/1.20 , clause( 531, [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ] )
% 0.80/1.20 , clause( 532, [ ~( hBOOL( hAPP( X, 'c_List_Olist_Olist__case'( Y, Z,
% 0.80/1.21 'c_List_Olist_ONil'( 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X, Y ) )
% 0.80/1.21 ] )
% 0.80/1.21 , clause( 533, [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 0.80/1.21 'c_List_Olist_ONil'( Z ) ) ] )
% 0.80/1.21 , clause( 534, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.80/1.21 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP(
% 0.80/1.21 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.80/1.21 'tc_Lambda_OdB' ), Y ), Z ) ) ) ] )
% 0.80/1.21 , clause( 535, [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z
% 0.80/1.21 ), 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.80/1.21 , clause( 536, [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z
% 0.80/1.21 ), 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.80/1.21 , clause( 537, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.21 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( Y, Z, X ), X ),
% 0.80/1.21 ~( 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_OCons'( T,
% 0.80/1.21 'c_List_Olist_OCons'( Y, Z, X ), X ), X ) ) ] )
% 0.80/1.21 , clause( 538, [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_OCons'( Z, T, Y
% 0.80/1.21 ) ) ), =( X, 'c_List_Oappend'( 'c_List_Orev'( T, Y ),
% 0.80/1.21 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( Y ), Y ), Y ) ) ] )
% 0.80/1.21 , clause( 539, [ =( 'c_List_Orev'( 'c_List_Olist_OCons'( X,
% 0.80/1.21 'c_List_Olist_ONil'( Y ), Y ), Y ), 'c_List_Olist_OCons'( X,
% 0.80/1.21 'c_List_Olist_ONil'( Y ), Y ) ) ] )
% 0.80/1.21 , clause( 540, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_ListOrder_Ostep1'( X
% 0.80/1.21 , T, U, W ), ~( 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( T,
% 0.80/1.21 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( W ), W ), W ),
% 0.80/1.21 'c_List_Oappend'( U, 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W
% 0.80/1.21 ), W ), W ) ) ] )
% 0.80/1.21 , clause( 541, [ =( 'c_List_Orev'( 'c_List_Olist_OCons'( X, Y, Z ), Z ),
% 0.80/1.21 'c_List_Oappend'( 'c_List_Orev'( Y, Z ), 'c_List_Olist_OCons'( X,
% 0.80/1.21 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ] )
% 0.80/1.21 , clause( 542, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Ofilter'( T
% 0.80/1.21 , U, Z ) ) ), hBOOL( hAPP( T, X ) ) ] )
% 0.80/1.21 , clause( 543, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ] )
% 0.80/1.21 , clause( 544, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.80/1.21 , clause( 545, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.80/1.21 , clause( 546, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 X ), Y ), T ) ), Z ) ) ] )
% 0.80/1.21 , clause( 547, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 X ), Y ), Z ) ), T ) ) ] )
% 0.80/1.21 , clause( 548, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.80/1.21 , clause( 549, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.80/1.21 , clause( 550, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.80/1.21 , clause( 551, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.80/1.21 , clause( 552, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 X ), Y ), Z ) ), T ) ) ] )
% 0.80/1.21 , clause( 553, [ =( 'c_List_Oremdups'( 'c_List_Ofilter'( X, Y, Z ), Z ),
% 0.80/1.21 'c_List_Ofilter'( X, 'c_List_Oremdups'( Y, Z ), Z ) ) ] )
% 0.80/1.21 , clause( 554, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.21 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.80/1.21 , clause( 555, [ =( 'c_List_Ofilter'( X, 'c_List_Olist_OCons'( Y, Z, T ), T
% 0.80/1.21 ), 'c_List_Olist_OCons'( Y, 'c_List_Ofilter'( X, Z, T ), T ) ), ~( hBOOL(
% 0.80/1.21 hAPP( X, Y ) ) ) ] )
% 0.80/1.21 , clause( 556, [ ~( =( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y
% 0.80/1.21 ), 'c_List_Orev'( Z, Y ) ) ), =( Z, 'c_List_Olist_OCons'( X,
% 0.80/1.21 'c_List_Olist_ONil'( Y ), Y ) ) ] )
% 0.80/1.21 , clause( 557, [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 0.80/1.21 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 0.80/1.21 ] )
% 0.80/1.21 , clause( 558, [ ~( 'c_ListOrder_Ostep1'( X, Y, Z, T ) ),
% 0.80/1.21 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( Y, U, T ), 'c_List_Oappend'( Z
% 0.80/1.21 , U, T ), T ) ] )
% 0.80/1.21 , clause( 559, [ 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( Y, Z, T ),
% 0.80/1.21 'c_List_Oappend'( Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T ) )
% 0.80/1.21 ] )
% 0.80/1.21 , clause( 560, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ),
% 0.80/1.21 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.80/1.21 ), Y ) ) ) ] )
% 0.80/1.21 , clause( 561, [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X,
% 0.80/1.21 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.80/1.21 , clause( 562, [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X,
% 0.80/1.21 'c_List_Oappend'( T, Y, Z ), Z ) ) ] )
% 0.80/1.21 , clause( 563, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OAbs'(
% 0.80/1.21 T ), U ), hAPP( Z, T ) ) ] )
% 0.80/1.21 , clause( 564, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Osubst'( X
% 0.80/1.21 , Y, Z ) ), 'c_Lambda_Osubst'( T, Y, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Lambda_Obeta', X ), T ) ) ) ] )
% 0.80/1.21 , clause( 565, [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U,
% 0.80/1.21 'c_List_Olist_OCons'( Y, T, W ), 'c_List_Olist_OCons'( X, Z, W ), W ) ) ]
% 0.80/1.21 )
% 0.80/1.21 , clause( 566, [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ),
% 0.80/1.21 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( Y, T, U ),
% 0.80/1.21 'c_List_Olist_OCons'( Z, T, U ), U ) ] )
% 0.80/1.21 , clause( 567, [ =( 'c_List_Orev'( 'c_List_Omap'( X, Y, Z, T ), T ),
% 0.80/1.21 'c_List_Omap'( X, 'c_List_Orev'( Y, Z ), Z, T ) ) ] )
% 0.80/1.21 , clause( 568, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, Y
% 0.80/1.21 , Z ) ) ), =( X, T ) ] )
% 0.80/1.21 , clause( 569, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( X, T
% 0.80/1.21 , Z ) ) ), =( Y, T ) ] )
% 0.80/1.21 , clause( 570, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.80/1.21 ), Z ), Z ) ) ] )
% 0.80/1.21 , clause( 571, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.80/1.21 ), Z ), Z ) ) ] )
% 0.80/1.21 , clause( 572, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.80/1.21 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 X, Y ), U ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ] )
% 0.80/1.21 , clause( 573, [ ~( =( 'c_List_Ofilter'( X, Y, Z ), 'c_List_Olist_OCons'( T
% 0.80/1.21 , U, Z ) ) ), hBOOL( hAPP( X, T ) ) ] )
% 0.80/1.21 , clause( 574, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.21 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.80/1.21 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.80/1.21 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.80/1.21 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.21 , clause( 575, [ =( 'c_List_Orotate'( X, 'c_List_Omap'( Y, Z, T, U ), U ),
% 0.80/1.21 'c_List_Omap'( Y, 'c_List_Orotate'( X, Z, T ), T, U ) ) ] )
% 0.80/1.21 , clause( 576, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.80/1.21 'c_Lambda_Osubst'( X, T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta'
% 0.80/1.21 , Y ), T ) ) ) ] )
% 0.80/1.21 , clause( 577, [ =( X, 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ) ) ] )
% 0.80/1.21 , clause( 578, [ =( 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ), X ) ] )
% 0.80/1.21 , clause( 579, [ =( 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ), X ) ] )
% 0.80/1.21 , clause( 580, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.80/1.21 , clause( 581, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.80/1.21 , clause( 582, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.80/1.21 , clause( 583, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), =( Y, Z ), ~(
% 0.80/1.21 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y,
% 0.80/1.21 'c_List_Olist_ONil'( U ), U ), U ), 'c_List_Oappend'( W,
% 0.80/1.21 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( U ), U ), U ), U ) ) ] )
% 0.80/1.21 , clause( 584, [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_OCons'( Z,
% 0.80/1.21 'c_List_Olist_ONil'( Y ), Y ) ) ), =( X, 'c_List_Olist_OCons'( Z,
% 0.80/1.21 'c_List_Olist_ONil'( Y ), Y ) ) ] )
% 0.80/1.21 , clause( 585, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.80/1.21 'class_Int_Onumber__ring'( X ) ), ~( =( Y, hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), =( Z,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.80/1.21 , clause( 586, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.80/1.21 'c_Lambda_Osubst'( T, Y, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.80/1.21 ), T ) ) ) ] )
% 0.80/1.21 , clause( 587, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.80/1.21 'c_Lambda_Osubst'( X, T, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.80/1.21 ), T ) ) ) ] )
% 0.80/1.21 , clause( 588, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.21 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.80/1.21 ) ) ] )
% 0.80/1.21 , clause( 589, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.80/1.21 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( X, Z ), T ) ) ) ] )
% 0.80/1.21 , clause( 590, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.80/1.21 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.80/1.21 )
% 0.80/1.21 , clause( 591, [ 'c_List_Olistrelp'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 0.80/1.21 'c_List_Olist_OCons'( U, W, T ), T ), ~( 'c_List_Olistrelp'( X, Z, W, T )
% 0.80/1.21 ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ) ] )
% 0.80/1.21 , clause( 592, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.80/1.21 ), =( X, Y ) ] )
% 0.80/1.21 , clause( 593, [ =( 'c_List_Oremove1'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 0.80/1.21 T ), 'c_List_Olist_OCons'( Y, 'c_List_Oremove1'( X, Z, T ), T ) ), =( X,
% 0.80/1.21 Y ) ] )
% 0.80/1.21 , clause( 594, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.21 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), hBOOL( hAPP(
% 0.80/1.21 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ),
% 0.80/1.21 'c_List_Olistsp'( 'c_InductTermi_OIT',
% 0.80/1.21 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB' ), ~( hBOOL(
% 0.80/1.21 hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.21 , clause( 595, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.80/1.21 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ) ), 'c_Lambda_Osubst'(
% 0.80/1.21 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.80/1.21 , clause( 596, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Olift'( X, Y ) ),
% 0.80/1.21 'c_Lambda_Olift'( Z, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.80/1.21 ), Z ) ) ) ] )
% 0.80/1.21 , clause( 597, [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), =( Z, Y ), ~(
% 0.80/1.21 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( U, Y, T ),
% 0.80/1.21 'c_List_Olist_OCons'( W, Z, T ), T ) ) ] )
% 0.80/1.21 , clause( 598, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 0.80/1.21 hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ) ), ~(
% 0.80/1.21 'c_OrderedGroup_Osemigroup__add'( X, U ) ) ] )
% 0.80/1.21 , clause( 599, [ =( 'c_List_Omap'( X, 'c_List_Oappend'( Y, Z, T ), T, U ),
% 0.80/1.21 'c_List_Oappend'( 'c_List_Omap'( X, Y, T, U ), 'c_List_Omap'( X, Z, T, U
% 0.80/1.21 ), U ) ) ] )
% 0.80/1.21 , clause( 600, [ =( 'c_List_Oremove1'( X, 'c_List_Ofilter'( Y, Z, T ), T )
% 0.80/1.21 , 'c_List_Ofilter'( Y, Z, T ) ), hBOOL( hAPP( Y, X ) ) ] )
% 0.80/1.21 , clause( 601, [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Orev'( Z, Y ) ) ),
% 0.80/1.21 =( X, Z ) ] )
% 0.80/1.21 , clause( 602, [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U,
% 0.80/1.21 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W
% 0.80/1.21 ), W ), 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( T,
% 0.80/1.21 'c_List_Olist_ONil'( W ), W ), W ), W ) ) ] )
% 0.80/1.21 , clause( 603, [ 'c_List_Olistsp'( X, 'c_List_Oappend'( Y, Z, T ), T ), ~(
% 0.80/1.21 'c_List_Olistsp'( X, Z, T ) ), ~( 'c_List_Olistsp'( X, Y, T ) ) ] )
% 0.80/1.21 , clause( 604, [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OAbs'(
% 0.80/1.21 T ), U ), hAPP( hAPP( Z, T ), 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, U ) )
% 0.80/1.21 ) ] )
% 0.80/1.21 , clause( 605, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.21 ), X, Y ), X ) ] )
% 0.80/1.21 , clause( 606, [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ),
% 0.80/1.21 'c_OrderedGroup_Osemigroup__add'( 'c_HOL_Oplus__class_Oplus'( X ), X ) ]
% 0.80/1.21 )
% 0.80/1.21 , clause( 607, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ) ), 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ) ) ) ] )
% 0.80/1.21 , clause( 608, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.80/1.21 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.80/1.21 ] )
% 0.80/1.21 , clause( 609, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.80/1.21 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.80/1.21 ] )
% 0.80/1.21 , clause( 610, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ),
% 0.80/1.21 'c_List_Olist_OCons'( Y, Z, X ), X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ]
% 0.80/1.21 )
% 0.80/1.21 , clause( 611, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 0.80/1.21 'c_List_Olist_OCons'( T, U, Z ) ) ), =( X, T ) ] )
% 0.80/1.21 , clause( 612, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 0.80/1.21 'c_List_Olist_OCons'( T, U, Z ) ) ), =( Y, U ) ] )
% 0.80/1.21 , clause( 613, [ 'c_Type_Otyping'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Lambda_Obeta', T ), Y ) ) ), ~( 'c_Type_Otyping'( X, T, Z ) ) ] )
% 0.80/1.21 , clause( 614, [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), hBOOL( hAPP( hAPP( X,
% 0.80/1.21 U ), W ) ), ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( U, Y, T ),
% 0.80/1.21 'c_List_Olist_OCons'( W, Z, T ), T ) ) ] )
% 0.80/1.21 , clause( 615, [ 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 0.80/1.21 'c_List_Olist_OCons'( Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T
% 0.80/1.21 ) ) ] )
% 0.80/1.21 , clause( 616, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.21 'c_List_Olinorder__class_Osorted'( Y, X ), ~(
% 0.80/1.21 'c_List_Olinorder__class_Osorted'( 'c_List_Oappend'( Y, Z, X ), X ) ) ]
% 0.80/1.21 )
% 0.80/1.21 , clause( 617, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.21 'c_List_Olinorder__class_Osorted'( Y, X ), ~(
% 0.80/1.21 'c_List_Olinorder__class_Osorted'( 'c_List_Oappend'( Z, Y, X ), X ) ) ]
% 0.80/1.21 )
% 0.80/1.21 , clause( 618, [ =( 'c_List_Olist__update'( 'c_List_Olist__update'( X, Y, Z
% 0.80/1.21 , T ), U, W, T ), 'c_List_Olist__update'( 'c_List_Olist__update'( X, U, W
% 0.80/1.21 , T ), Y, Z, T ) ), =( Y, U ) ] )
% 0.80/1.21 , clause( 619, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.21 'c_List_Olinorder__class_Osorted'( 'c_List_Oremdups'( Y, X ), X ), ~(
% 0.80/1.21 'c_List_Olinorder__class_Osorted'( Y, X ) ) ] )
% 0.80/1.21 , clause( 620, [ =( 'c_List_Ofilter'( X, 'c_List_Olist_OCons'( Y, Z, T ), T
% 0.80/1.21 ), 'c_List_Ofilter'( X, Z, T ) ), hBOOL( hAPP( X, Y ) ) ] )
% 0.80/1.21 , clause( 621, [ =( 'c_List_Orev'( 'c_List_Ofilter'( X, Y, Z ), Z ),
% 0.80/1.21 'c_List_Ofilter'( X, 'c_List_Orev'( Y, Z ), Z ) ) ] )
% 0.80/1.21 , clause( 622, [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.80/1.21 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.80/1.21 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( X, T
% 0.80/1.21 ) ] )
% 0.80/1.21 , clause( 623, [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.80/1.21 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.80/1.21 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( Y, U
% 0.80/1.21 ) ] )
% 0.80/1.21 , clause( 624, [ ~( hBOOL( hAPP( X, 'c_List_Olist_Olist__case'( Y, Z,
% 0.80/1.21 'c_List_Olist_OCons'( T, U, 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X
% 0.80/1.21 , hAPP( hAPP( Z, T ), U ) ) ) ] )
% 0.80/1.21 , clause( 625, [ ~( hBOOL( hAPP( X, 'c_List_Olist_Olist__case'( Y, Z,
% 0.80/1.21 'c_List_Olist_OCons'( T, U, 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X
% 0.80/1.21 , hAPP( hAPP( Z, T ), U ) ) ) ] )
% 0.80/1.21 , clause( 626, [ =( 'c_List_Olist__update'( 'c_List_Olist__update'( X, Y, Z
% 0.80/1.21 , T ), Y, U, T ), 'c_List_Olist__update'( X, Y, U, T ) ) ] )
% 0.80/1.21 , clause( 627, [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.80/1.21 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.80/1.21 , clause( 628, [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.80/1.21 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ] )
% 0.80/1.21 , clause( 629, [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.80/1.21 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 0.80/1.21 , clause( 630, [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.80/1.21 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ] )
% 0.80/1.21 , clause( 631, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.21 'c_List_Olinorder__class_Osorted'( 'c_List_Oremove1'( Y, Z, X ), X ), ~(
% 0.80/1.21 'c_List_Olinorder__class_Osorted'( Z, X ) ) ] )
% 0.80/1.21 , clause( 632, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.80/1.21 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 X, Y ), U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ) ] )
% 0.80/1.21 , clause( 633, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.80/1.21 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP(
% 0.80/1.21 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ] )
% 0.80/1.21 , clause( 634, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.21 'v_sko__List__XdropWhile__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.21 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.21 , clause( 635, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.21 'v_sko__List__Xtake__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.21 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.21 , clause( 636, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.80/1.21 'c_List_Olinorder__class_Osorted'( 'c_List_Olist_ONil'( X ), X ) ] )
% 0.80/1.21 , clause( 637, [ =( 'c_List_Ofiltermap'( X, 'c_List_Olist_ONil'( Y ), Y, Z
% 0.80/1.21 ), 'c_List_Olist_ONil'( Z ) ) ] )
% 0.80/1.21 , clause( 638, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oremdups'( Y, X )
% 0.80/1.21 ) ), =( Y, 'c_List_Olist_ONil'( X ) ) ] )
% 0.80/1.21 , clause( 639, [ =( 'c_List_Ofilter'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.80/1.21 'c_List_Olist_ONil'( Y ) ) ] )
% 0.80/1.21 , clause( 640, [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z
% 0.80/1.21 , X ), 'c_List_Olist_ONil'( X ) ) ] )
% 0.80/1.21 , clause( 641, [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z
% 0.80/1.21 , X ), 'c_List_Olist_ONil'( X ) ) ] )
% 0.80/1.21 , clause( 642, [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z
% 0.80/1.21 , X ), 'c_List_Olist_ONil'( X ) ) ] )
% 0.80/1.21 , clause( 643, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.21 'v_sko__List__Xconcat__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.21 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.21 , clause( 644, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'(
% 0.80/1.21 Z ) ) ) ] )
% 0.80/1.21 , clause( 645, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'(
% 0.80/1.21 Z ) ) ) ] )
% 0.80/1.21 , clause( 646, [ =( 'c_List_Oremove1'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.80/1.21 'c_List_Olist_ONil'( Y ) ) ] )
% 0.80/1.21 , clause( 647, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.21 'v_sko__List__Xdistinct__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.21 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.21 , clause( 648, [ =( 'c_Map_Omap__upds'( X, Y, 'c_List_Olist_ONil'( Z ), T,
% 0.80/1.21 Z ), X ) ] )
% 0.80/1.21 , clause( 649, [ =( 'c_Map_Omap__upds'( X, 'c_List_Olist_ONil'( Y ), Z, Y,
% 0.80/1.21 T ), X ) ] )
% 0.80/1.21 , clause( 650, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.21 'v_sko__List__Xremove1__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.21 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.21 , clause( 651, [ =( 'c_List_Olist_Olist__case'( X, Y, 'c_List_Olist_ONil'(
% 0.80/1.21 Z ), T, Z ), X ) ] )
% 0.80/1.21 , clause( 652, [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_ONil'( Y ) ) )
% 0.80/1.21 , =( X, 'c_List_Olist_ONil'( Y ) ) ] )
% 0.80/1.21 , clause( 653, [ =( 'c_List_Orotate'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.80/1.21 'c_List_Olist_ONil'( Y ) ) ] )
% 0.80/1.21 , clause( 654, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.21 'v_sko__List__Xlist__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.21 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.21 , clause( 655, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y,
% 0.80/1.21 'c_List_Olist_ONil'( Z ), Z, X ) ) ] )
% 0.80/1.21 , clause( 656, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'(
% 0.80/1.21 'c_List_Olist_ONil'( X ), 'c_List_Olist_ONil'( X ), X ) ) ] )
% 0.80/1.21 , clause( 657, [ 'c_List_Olistrelp'( X, 'c_List_Olist_ONil'( Y ),
% 0.80/1.21 'c_List_Olist_ONil'( Y ), Y ) ] )
% 0.80/1.21 , clause( 658, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.21 'v_sko__List__Xmap__Xinduct__2'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.80/1.21 'c_List_Olist_ONil'( 't_a' ) ) ) ) ] )
% 0.80/1.21 , clause( 659, [ =( 'c_List_Orev'( 'c_List_Olist_ONil'( X ), X ),
% 0.80/1.21 'c_List_Olist_ONil'( X ) ) ] )
% 0.80/1.21 , clause( 660, [ ~( =( 'c_List_Olist__update'( X, Y, Z, T ),
% 0.80/1.21 'c_List_Olist_ONil'( T ) ) ), =( X, 'c_List_Olist_ONil'( T ) ) ] )
% 0.80/1.21 , clause( 661, [ =( 'c_Lambda_Osubst'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.80/1.21 , Y ), Z, T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Z,
% 0.80/1.21 T ) ), 'c_Lambda_Osubst'( Y, Z, T ) ) ) ] )
% 0.80/1.21 , clause( 662, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.80/1.21 'c_Lambda_OdB_OAbs'( Z ) ) ) ] )
% 0.80/1.21 , clause( 663, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP(
% 0.80/1.21 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 0.80/1.21 , clause( 664, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP(
% 0.80/1.21 hAPP( 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP(
% 0.80/1.21 hAPP( Z, U ), W ) ) ) ] )
% 0.80/1.21 , clause( 665, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP(
% 0.80/1.21 hAPP( 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP(
% 0.80/1.21 hAPP( Z, U ), W ) ) ) ] )
% 0.80/1.21 , clause( 666, [ =( 'c_Lambda_Olift'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.80/1.21 , Y ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Olift'( X, Z ) ),
% 0.80/1.21 'c_Lambda_Olift'( Y, Z ) ) ) ] )
% 0.80/1.21 , clause( 667, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, hAPP( hAPP(
% 0.80/1.21 'c_Lambda_OdB_OApp', T ), U ), W ), hAPP( hAPP( Y, T ), U ) ) ] )
% 0.80/1.21 , clause( 668, [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, hAPP( hAPP(
% 0.80/1.21 'c_Lambda_OdB_OApp', T ), U ), W ), hAPP( hAPP( hAPP( hAPP( Y, T ), U ),
% 0.80/1.21 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, W ) ), 'c_Lambda_OdB_OdB__rec'( X, Y
% 0.80/1.21 , Z, U, W ) ) ) ] )
% 0.80/1.21 , clause( 669, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.80/1.21 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z
% 0.80/1.21 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', Y ), Z ) ) ) ] )
% 0.80/1.21 , clause( 670, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.80/1.21 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y
% 0.80/1.21 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ] )
% 0.80/1.21 , clause( 671, [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.80/1.21 Y ), Z ), T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y,
% 0.80/1.21 T ) ), 'c_Lambda_Oliftn'( X, Z, T ) ) ) ] )
% 0.80/1.21 , clause( 672, [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 0.80/1.21 ), Y ), Z, T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X,
% 0.80/1.21 Z, T ) ), 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ] )
% 0.80/1.21 , clause( 673, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.21 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~(
% 0.80/1.21 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.80/1.21 'tc_Lambda_OdB' ), X ), Z ) ) ) ] )
% 0.80/1.21 , clause( 674, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Z, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ) ) ), ~( 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', Y, Z,
% 0.80/1.21 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 675, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2'( X ),
% 0.80/1.21 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1'( X ),
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 676, [ =( 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, U, U )
% 0.80/1.21 , hAPP( hAPP( X, Y ), 'c_List_Ofoldl'( X, Z, T, U, U ) ) ), ~(
% 0.80/1.21 'c_OrderedGroup_Osemigroup__add'( X, U ) ) ] )
% 0.80/1.21 , clause( 677, [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =(
% 0.80/1.21 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), T, X, X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ] )
% 0.80/1.21 , clause( 678, [ =( hAPP( hAPP( X, Y ), 'c_List_Ofoldl'( X, Z, T, U, U ) )
% 0.80/1.21 , 'c_List_Ofoldl'( X, Y, T, U, U ) ), ~( 'c_OrderedGroup_Omonoid__add'( Z
% 0.80/1.21 , X, U ) ) ] )
% 0.80/1.21 , clause( 679, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_OCons'( Z, T, U )
% 0.80/1.21 , W, U ), 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, W, U ) ) ] )
% 0.80/1.21 , clause( 680, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Oappend'( Z, T, U ), W,
% 0.80/1.21 U ), 'c_List_Ofoldl'( X, 'c_List_Ofoldl'( X, Y, Z, W, U ), T, W, U ) ) ]
% 0.80/1.21 )
% 0.80/1.21 , clause( 681, [ hBOOL( hAPP( X,
% 0.80/1.21 'c_ListApplication_Osko__ListApplication__Xlem__1__3'( X ) ) ), ~( hBOOL(
% 0.80/1.21 hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.21 'c_ListApplication_Osko__ListApplication__Xlem__1__1'( X ) ),
% 0.80/1.21 'c_ListApplication_Osko__ListApplication__Xlem__1__2'( X ),
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( X, Y ) ) ] )
% 0.80/1.21 , clause( 682, [ 'c_Type_Otypings'( X, Y,
% 0.80/1.21 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X, T, Y ) ), ~(
% 0.80/1.21 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.80/1.21 )
% 0.80/1.21 , clause( 683, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.80/1.21 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3'( X ) )
% 0.80/1.21 ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OVar'(
% 0.80/1.21 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1'( X ) )
% 0.80/1.21 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2'( X )
% 0.80/1.21 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.80/1.21 , clause( 684, [ 'c_Type_Otypings'( X, Y,
% 0.80/1.21 'c_Type_Osko__Type__Xvar__app__types__1__1'( Z, T, X, Y ) ), ~(
% 0.80/1.21 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ) ),
% 0.80/1.21 ~( 'c_Type_Otypings'( X, W, V0 ) ), ~( 'c_Type_Otyping'( X,
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.80/1.21 , clause( 685, [ 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', X,
% 0.80/1.21 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, X, Z ),
% 0.80/1.21 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), X,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ) ) ) ] )
% 0.80/1.21 , clause( 686, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.21 X ) ), Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.80/1.21 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.80/1.21 , clause( 687, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.21 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), hBOOL( hAPP(
% 0.80/1.21 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X
% 0.80/1.21 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.80/1.21 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.80/1.21 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.21 , clause( 688, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) )
% 0.80/1.21 ) ] )
% 0.80/1.21 , clause( 689, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.80/1.21 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.80/1.21 ] )
% 0.80/1.21 , clause( 690, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.80/1.21 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.80/1.21 ] )
% 0.80/1.21 , clause( 691, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y
% 0.80/1.21 ) ] )
% 0.80/1.21 , clause( 692, [ ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.80/1.21 'c_Lambda_OdB_OVar'( X ) ), Y ) ) ) ] )
% 0.80/1.21 , clause( 693, [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OVar'(
% 0.80/1.21 T ), U ), hAPP( X, T ) ) ] )
% 0.80/1.21 , clause( 694, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.80/1.21 ) ] )
% 0.80/1.21 , clause( 695, [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X,
% 0.80/1.21 'c_Lambda_OdB_OVar'( Y ), Z ) ) ] )
% 0.80/1.21 , clause( 696, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OVar'(
% 0.80/1.21 T ), U ), hAPP( X, T ) ) ] )
% 0.80/1.21 , clause( 697, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y
% 0.80/1.21 ) ) ] )
% 0.80/1.21 , clause( 698, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, T, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ) ) ), =( T, 'c_List_Oappend'(
% 0.80/1.21 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1'( X
% 0.80/1.21 , Y, Z, T ), 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'(
% 0.80/1.21 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ), =( T,
% 0.80/1.21 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 699, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Olift'( X, Y )
% 0.80/1.21 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.21 , clause( 700, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X )
% 0.80/1.21 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.80/1.21 , clause( 701, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OVar'( Y ),
% 0.80/1.21 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Lambda_Obeta', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OVar'( Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ) )
% 0.80/1.21 ) ] )
% 0.80/1.21 , clause( 702, [ =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.80/1.21 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ),
% 0.80/1.21 'tc_Lambda_OdB' ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ), =( hAPP(
% 0.80/1.21 hAPP( 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, X,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Y ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', Z, 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.80/1.21 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ),
% 0.80/1.21 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 703, [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, 'c_List_Oappend'( Y,
% 0.80/1.21 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.80/1.21 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.80/1.21 ) ] )
% 0.80/1.21 , clause( 704, [ ~( =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.80/1.21 'c_Lambda_OdB_OApp', X ), Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) )
% 0.80/1.21 , =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.80/1.21 'c_List_Oappend'( Z, 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'(
% 0.80/1.21 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), 'tc_Lambda_OdB'
% 0.80/1.21 , 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 705, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.80/1.21 'c_Lambda_OdB_OAbs'( Z ) ) ] )
% 0.80/1.21 , clause( 706, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.80/1.21 , clause( 707, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 0.80/1.21 , clause( 708, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) )
% 0.80/1.21 ) ] )
% 0.80/1.21 , clause( 709, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 0.80/1.21 'c_Lambda_OdB_OAbs'( X ), Y ) ] )
% 0.80/1.21 , clause( 710, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( X,
% 0.80/1.21 'c_Lambda_OdB_OVar'( Y ), Z ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.80/1.21 ) ) ) ] )
% 0.80/1.21 , clause( 711, [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ), X ) ) ] )
% 0.80/1.21 , clause( 712, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.80/1.21 , clause( 713, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.21 X ) ), Y ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z
% 0.80/1.21 ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.80/1.21 , clause( 714, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 0.80/1.21 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 715, [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'(
% 0.80/1.21 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 716, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, T, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ) ) ), =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z,
% 0.80/1.21 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1'( X
% 0.80/1.21 , Y, Z, T ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), =( T,
% 0.80/1.21 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 717, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.80/1.21 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 718, [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ) ] )
% 0.80/1.21 , clause( 719, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ) ) ), ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y,
% 0.80/1.21 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 720, [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 0.80/1.21 ), Y ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 721, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) )
% 0.80/1.21 ), =( X, Y ) ] )
% 0.80/1.21 , clause( 722, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.80/1.21 , clause( 723, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 0.80/1.21 , clause( 724, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'(
% 0.80/1.21 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_Lambda_OdB_OApp', X ), Y ), Z ) ] )
% 0.80/1.21 , clause( 725, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.80/1.21 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ] )
% 0.80/1.21 , clause( 726, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.80/1.21 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ] )
% 0.80/1.21 , clause( 727, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 0.80/1.21 'c_Lambda_OdB_OVar'( X ), Y ) ] )
% 0.80/1.21 , clause( 728, [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP(
% 0.80/1.21 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 0.80/1.21 , clause( 729, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z )
% 0.80/1.21 , Y ) ] )
% 0.80/1.21 , clause( 730, [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'(
% 0.80/1.21 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 731, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.21 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.80/1.21 , clause( 732, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 0.80/1.21 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.80/1.21 , clause( 733, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.80/1.21 'c_Lambda_OdB_OVar'( Z ) ) ) ] )
% 0.80/1.21 , clause( 734, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( 'v_n' ), 'c_List_Olist_ONil'(
% 0.80/1.21 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.80/1.21 , clause( 735, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'(
% 0.80/1.21 'v_n' ) ) ) ) ] )
% 0.80/1.21 , clause( 736, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.80/1.21 'class_Orderings_Opreorder'( Y ) ) ] )
% 0.80/1.21 , clause( 737, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.80/1.21 'class_Orderings_Oorder'( Y ) ) ] )
% 0.80/1.21 , clause( 738, [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.80/1.21 'tc_nat' ) ] )
% 0.80/1.21 , clause( 739, [
% 0.80/1.21 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 0.80/1.21 )
% 0.80/1.21 , clause( 740, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.80/1.21 'tc_nat' ) ] )
% 0.80/1.21 , clause( 741, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat'
% 0.80/1.21 ) ] )
% 0.80/1.21 , clause( 742, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ]
% 0.80/1.21 )
% 0.80/1.21 , clause( 743, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 0.80/1.21 )
% 0.80/1.21 , clause( 744, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ]
% 0.80/1.21 )
% 0.80/1.21 , clause( 745, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ] )
% 0.80/1.21 , clause( 746, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 0.80/1.21 , clause( 747, [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ] )
% 0.80/1.21 , clause( 748, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 0.80/1.21 , clause( 749, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 0.80/1.21 , clause( 750, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 0.80/1.21 , clause( 751, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 0.80/1.21 , clause( 752, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 0.80/1.21 , clause( 753, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 0.80/1.21 , clause( 754, [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ] )
% 0.80/1.21 , clause( 755, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y )
% 0.80/1.21 ) ) ] )
% 0.80/1.21 ] ).
% 0.80/1.21
% 0.80/1.21
% 0.80/1.21
% 0.80/1.21 subsumption(
% 0.80/1.21 clause( 328, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ),
% 0.80/1.21 Y ) ] )
% 0.80/1.21 , clause( 729, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z )
% 0.80/1.21 , Y ) ] )
% 0.80/1.21 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.80/1.21 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.80/1.21
% 0.80/1.21
% 0.80/1.21 paramod(
% 0.80/1.21 clause( 1991, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'(
% 0.80/1.21 'v_n' ) ) ) ] )
% 0.80/1.21 , clause( 328, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z )
% 0.80/1.22 , Y ) ] )
% 0.80/1.22 , 0, clause( 734, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.80/1.22 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( 'v_n' ), 'c_List_Olist_ONil'(
% 0.80/1.22 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.80/1.22 , 0, 3, substitution( 0, [ :=( X, 'c_Lambda_OdB_OApp' ), :=( Y,
% 0.80/1.22 'c_Lambda_OdB_OVar'( 'v_n' ) ), :=( Z, 'tc_Lambda_OdB' ), :=( T,
% 0.80/1.22 'tc_Lambda_OdB' )] ), substitution( 1, [] )).
% 0.80/1.22
% 0.80/1.22
% 0.80/1.22 subsumption(
% 0.80/1.22 clause( 331, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( 'v_n'
% 0.80/1.22 ) ) ) ] )
% 0.80/1.22 , clause( 1991, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'(
% 0.80/1.22 'v_n' ) ) ) ] )
% 0.80/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.80/1.22
% 0.80/1.22
% 0.80/1.22 resolution(
% 0.80/1.22 clause( 2399, [] )
% 0.80/1.22 , clause( 735, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'(
% 0.80/1.22 'v_n' ) ) ) ) ] )
% 0.80/1.22 , 0, clause( 331, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'(
% 0.80/1.22 'v_n' ) ) ) ] )
% 0.80/1.22 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.80/1.22
% 0.80/1.22
% 0.80/1.22 subsumption(
% 0.80/1.22 clause( 332, [] )
% 0.80/1.22 , clause( 2399, [] )
% 0.80/1.22 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.80/1.22
% 0.80/1.22
% 0.80/1.22 end.
% 0.80/1.22
% 0.80/1.22 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.80/1.22
% 0.80/1.22 Memory use:
% 0.80/1.22
% 0.80/1.22 space for terms: 21786
% 0.80/1.22 space for clauses: 34295
% 0.80/1.22
% 0.80/1.22
% 0.80/1.22 clauses generated: 402
% 0.80/1.22 clauses kept: 333
% 0.80/1.22 clauses selected: 0
% 0.80/1.22 clauses deleted: 0
% 0.80/1.22 clauses inuse deleted: 0
% 0.80/1.22
% 0.80/1.22 subsentry: 9311
% 0.80/1.22 literals s-matched: 3773
% 0.80/1.22 literals matched: 3737
% 0.80/1.22 full subsumption: 501
% 0.80/1.22
% 0.80/1.22 checksum: -947553787
% 0.80/1.22
% 0.80/1.22
% 0.80/1.22 Bliksem ended
%------------------------------------------------------------------------------