TSTP Solution File: LCL784-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL784-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 07:57:56 EDT 2022
% Result : Unsatisfiable 7.50s 7.90s
% Output : Refutation 7.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL784-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jul 3 02:35:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.78/1.18 *** allocated 10000 integers for termspace/termends
% 0.78/1.18 *** allocated 10000 integers for clauses
% 0.78/1.18 *** allocated 10000 integers for justifications
% 0.78/1.18 Bliksem 1.12
% 0.78/1.18
% 0.78/1.18
% 0.78/1.18 Automatic Strategy Selection
% 0.78/1.18
% 0.78/1.18 Clauses:
% 0.78/1.18 [
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.78/1.18 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.78/1.18 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3'( X ) )
% 0.78/1.18 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4'( X )
% 0.78/1.18 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1'( X ) )
% 0.78/1.18 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2'( X )
% 0.78/1.18 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ],
% 0.78/1.18 [ ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_Lambda_OdB_OAbs'(
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__Xlem__1__3'( X ) ),
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__Xlem__1__4'( X ),
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( X,
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__Xlem__1__1'( X ) ),
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__Xlem__1__2'( X ),
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( X, Y ) ) ],
% 0.78/1.18 [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.78/1.18 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X, Y, T ), Z,
% 0.78/1.18 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ), Z ) ) ],
% 0.78/1.18 [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.78/1.18 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X, Y, T ), Z,
% 0.78/1.18 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ), Z ) ) ],
% 0.78/1.18 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeE__1__1'(
% 0.78/1.18 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeD__1__1'(
% 0.78/1.18 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), =( Y, Z ), ~( 'c_ListOrder_Ostep1'(
% 0.78/1.18 X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( U )
% 0.78/1.18 , U ), U ), 'c_List_Oappend'( W, 'c_List_Olist_OCons'( Z,
% 0.78/1.18 'c_List_Olist_ONil'( U ), U ), U ), U ) ) ],
% 0.78/1.18 [ =( 'c_List_Ofoldr'( X, 'c_List_Oappend'( Y, Z, T ), U, T, W ),
% 0.78/1.18 'c_List_Ofoldr'( X, Y, 'c_List_Ofoldr'( X, Z, U, T, W ), T, W ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.78/1.18 , 'tc_Lambda_OdB' ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ), Z ) )
% 0.78/1.18 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 0.78/1.18 hAPP( 'c_Lambda_Obeta', Y ), T ) ) ) ],
% 0.78/1.18 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 0.78/1.18 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), Y, X ), Y ) ],
% 0.78/1.18 [ =( X, 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 0.78/1.18 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 0.78/1.18 [ =( 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ), X ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.78/1.18 X ) ) ), =( X, 'c_Lambda_OdB_OAbs'( 'v_sko__InductTermi__XIT__Xcases__3'(
% 0.78/1.18 X ) ) ), 'c_List_Olistsp'( 'c_InductTermi_OIT',
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB' ), ~( hBOOL(
% 0.78/1.18 hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.78/1.18 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), U )
% 0.78/1.18 , T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.78/1.18 ), Z ), U ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), Z )
% 0.78/1.18 ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), Z )
% 0.78/1.18 ) ],
% 0.78/1.18 [ 'c_Type_Otyping'( 'v_ea______', 'v_ua______', 'v_T____' ) ],
% 0.78/1.18 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( X, T, Z ) ) ),
% 0.78/1.18 =( Y, T ) ],
% 0.78/1.18 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, Y, Z ) ) ),
% 0.78/1.18 =( X, T ) ],
% 0.78/1.18 [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ],
% 0.78/1.18 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), 'c_ListOrder_Ostep1'( X,
% 0.78/1.18 'c_List_Olist_OCons'( Y, T, U ), 'c_List_Olist_OCons'( Z, T, U ), U ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U, 'c_List_Olist_OCons'(
% 0.78/1.18 Y, T, W ), 'c_List_Olist_OCons'( X, Z, W ), W ) ) ],
% 0.78/1.18 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OAbs'( T ), U ),
% 0.78/1.18 hAPP( Z, T ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.78/1.18 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.78/1.18 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.78/1.18 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.78/1.18 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.78/1.18 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X, 'c_List_Oappend'(
% 0.78/1.18 T, Y, Z ), Z ) ) ],
% 0.78/1.18 [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X, 'c_List_Oappend'(
% 0.78/1.18 Y, T, Z ), Z ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.78/1.18 , 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ), 'c_Lambda_OdB_OAbs'( Y )
% 0.78/1.18 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.78/1.18 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Y ) ) ) ],
% 0.78/1.18 [ 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( Y, Z, T ), 'c_List_Oappend'(
% 0.78/1.18 Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T ) ) ],
% 0.78/1.18 [ ~( 'c_ListOrder_Ostep1'( X, Y, Z, T ) ), 'c_ListOrder_Ostep1'( X,
% 0.78/1.18 'c_List_Oappend'( Y, U, T ), 'c_List_Oappend'( Z, U, T ), T ) ],
% 0.78/1.18 [ =( 'c_Lambda_Osubstn'( X, Y, Z ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.78/1.18 , X ), 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.78/1.18 ), Z ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.78/1.18 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.78/1.18 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, Z,
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ), ~( 'c_Type_Otypings'( X, Z, U )
% 0.78/1.18 ), ~( 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun', U, T
% 0.78/1.18 , 'tc_Type_Otype', 'tc_Type_Otype' ) ) ) ],
% 0.78/1.18 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.78/1.18 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.78/1.18 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.78/1.18 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.78/1.18 X ), Y ), Z ) ), T ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.78/1.18 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.78/1.18 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.78/1.18 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.78/1.18 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.78/1.18 X ), Y ), Z ) ), T ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.78/1.18 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.78/1.18 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.78/1.18 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.78/1.18 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.78/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.78/1.18 ), 'tc_nat' ) ) ],
% 0.78/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.78/1.18 ), 'tc_nat' ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.78/1.18 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T ), Z ) ],
% 0.78/1.18 [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 0.78/1.18 'c_List_Olist_ONil'( Z ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_ListOrder_Ostep1'( X, T, U, W ),
% 0.78/1.18 ~( 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y
% 0.78/1.18 , 'c_List_Olist_ONil'( W ), W ), W ), 'c_List_Oappend'( U,
% 0.78/1.18 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W ), W ), W ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.78/1.18 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.78/1.18 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.78/1.18 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ 'c_Type_Otypings'( X, 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.78/1.18 'c_Lambda_Osubst', Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.78/1.18 'tc_nat', 'tc_Lambda_OdB' ) ), Z, 'tc_Lambda_OdB', 'tc_nat',
% 0.78/1.18 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 0.78/1.18 'c_Type_Otypings'( 'c_Type_Oshift'( X, Z, W, 'tc_Type_Otype' ), T, U ) )
% 0.78/1.18 , ~( 'c_Type_Otyping'( X, Y, W ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.78/1.18 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 0.78/1.18 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.78/1.18 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 0.78/1.18 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.78/1.18 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.78/1.18 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.78/1.18 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.78/1.18 ), Z ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.78/1.18 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.78/1.18 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.78/1.18 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.78/1.18 ), Z ) ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.78/1.18 ) ) ) ],
% 0.78/1.18 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 0.78/1.18 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ =( 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U
% 0.78/1.18 ), 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ) ) ],
% 0.78/1.18 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 0.78/1.18 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.78/1.18 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.78/1.18 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.78/1.18 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.78/1.18 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.78/1.18 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.78/1.18 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.78/1.18 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.78/1.18 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.78/1.18 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 0.78/1.18 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.78/1.18 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ =( X, Y ), hBOOL( hAPP( hAPP( Z, Y ), X ) ), ~( 'c_ListOrder_Ostep1'(
% 0.78/1.18 Z, 'c_List_Olist_OCons'( Y, T, U ), 'c_List_Olist_OCons'( X, W, U ), U )
% 0.78/1.18 ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.78/1.18 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.78/1.18 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.78/1.18 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.78/1.18 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.78/1.18 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.78/1.18 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.78/1.18 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.78/1.18 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 0.78/1.18 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 0.78/1.18 ) ) ],
% 0.78/1.18 [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Type_Otyping'( X, T, Z ) ), ~(
% 0.78/1.18 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.78/1.18 'tc_Lambda_OdB' ), T ), Y ) ) ) ],
% 0.78/1.18 [ 'c_Type_Otypings'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ),
% 0.78/1.18 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Y, 'tc_Lambda_OdB', 'tc_nat'
% 0.78/1.18 , 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 0.78/1.18 'c_Type_Otypings'( X, T, U ) ) ],
% 0.78/1.18 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X ) ), Y ),
% 0.78/1.18 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.78/1.18 ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_Olift', X )
% 0.78/1.18 , Y ) ), hAPP( hAPP( 'c_Lambda_Olift', Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.78/1.18 'c_Lambda_Obeta', X ), Z ) ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ],
% 0.78/1.18 [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ],
% 0.78/1.18 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubstn'(
% 0.78/1.18 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'( X, Y,
% 0.78/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.78/1.18 [ =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Oappend'(
% 0.78/1.18 'c_List_Olist_ONil'( Z ), 'c_List_Olist_OCons'( X, Y, Z ), Z ) ) ],
% 0.78/1.18 [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 0.78/1.18 X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'( X, hAPP( hAPP(
% 0.78/1.18 hAPP( 'c_Lambda_Osubst', U ), Y ), T ), W ) ],
% 0.78/1.18 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, 'c_List_Olist_ONil'( Z
% 0.78/1.18 ), Z, X ) ) ],
% 0.78/1.18 [ =( X, Y ), 'c_ListOrder_Ostep1'( Z, X, Y, T ), ~( 'c_ListOrder_Ostep1'(
% 0.78/1.18 Z, 'c_List_Oappend'( X, 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( T )
% 0.78/1.18 , T ), T ), 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( W,
% 0.78/1.18 'c_List_Olist_ONil'( T ), T ), T ), T ) ) ],
% 0.78/1.18 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( 'c_List_Olist_ONil'( X
% 0.78/1.18 ), 'c_List_Olist_ONil'( X ), X ) ) ],
% 0.78/1.18 [ =( 'c_Transitive__Closure_Ortranclp'(
% 0.78/1.18 'c_Transitive__Closure_Ortranclp'( X, Y ), Y ),
% 0.78/1.18 'c_Transitive__Closure_Ortranclp'( X, Y ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.78/1.18 Y ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.78/1.18 Y ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.78/1.18 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.78/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.78/1.18 Y ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.78/1.18 Y ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.78/1.18 Y ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.78/1.18 Y ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.78/1.18 Y ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'( X ) ),
% 0.78/1.18 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X )
% 0.78/1.18 , Y ) ) ) ],
% 0.78/1.18 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_OrderedGroup_Omonoid__add'( Z,
% 0.78/1.18 X, T ) ) ],
% 0.78/1.18 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_OrderedGroup_Omonoid__add'( Y,
% 0.78/1.18 X, T ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X ) ) ), =( Z
% 0.78/1.18 , 'c_List_Olist_ONil'( T ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.78/1.18 , 'tc_Lambda_OdB' ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ), Z ) )
% 0.78/1.18 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', T ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 0.78/1.18 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.78/1.18 'tc_Lambda_OdB' ), X ), T ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.78/1.18 , 'tc_Lambda_OdB' ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ), Z ) )
% 0.78/1.18 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 0.78/1.18 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.78/1.18 'tc_Lambda_OdB' ), Y ), T ) ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.78/1.18 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.78/1.18 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.78/1.18 ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( 'c_List_Ofoldr'(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), 'c_List_Ofoldl'(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.78/1.18 ), ~( hBOOL( hAPP( hAPP( X, Z ), T ) ) ) ],
% 0.78/1.18 [ ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_ONil'( Y ), Z, Y ) ) ],
% 0.78/1.18 [ ~( 'c_ListOrder_Ostep1'( X, Y, 'c_List_Olist_ONil'( Z ), Z ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.78/1.18 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.78/1.18 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.78/1.18 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.78/1.18 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.78/1.18 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), hAPP( hAPP(
% 0.78/1.18 'c_Type_Otype_OFun', Z ), T ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( X
% 0.78/1.18 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_Type_Otype' ), Y, T ) )
% 0.78/1.18 ],
% 0.78/1.18 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ],
% 0.78/1.18 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.78/1.18 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.78/1.18 'tc_nat' ) ],
% 0.78/1.18 [ ~( =( 'v_T____', hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ) ) ), hBOOL(
% 0.78/1.18 hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', Z ), T )
% 0.78/1.18 , U ) ) ), ~( 'c_Type_Otyping'( W, T, X ) ), ~( hBOOL( hAPP(
% 0.78/1.18 'c_InductTermi_OIT', T ) ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( W, U
% 0.78/1.18 , X, 'tc_Type_Otype' ), Z, V0 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', Z
% 0.78/1.18 ) ) ) ],
% 0.78/1.18 [ ~( =( 'v_T____', hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ) ) ), hBOOL(
% 0.78/1.18 hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', Z ), T )
% 0.78/1.18 , U ) ) ), ~( 'c_Type_Otyping'( W, T, Y ) ), ~( hBOOL( hAPP(
% 0.78/1.18 'c_InductTermi_OIT', T ) ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( W, U
% 0.78/1.18 , Y, 'tc_Type_Otype' ), Z, V0 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', Z
% 0.78/1.18 ) ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Y
% 0.78/1.18 , 'c_List_Olist_ONil'( X ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Z
% 0.78/1.18 , 'c_List_Olist_ONil'( X ) ) ],
% 0.78/1.18 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.78/1.18 ) ],
% 0.78/1.18 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( X
% 0.78/1.18 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y
% 0.78/1.18 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.78/1.18 X ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.78/1.18 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.78/1.18 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.78/1.18 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.78/1.18 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.78/1.18 , X ) ) ],
% 0.78/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.78/1.18 , Y, X ) ) ],
% 0.78/1.18 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.78/1.18 , Y, X ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_Lambda_OdB_OAbs'( X ) ), Y ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X
% 0.78/1.18 ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.78/1.18 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_Olift', X ), Y ) ), hAPP( hAPP(
% 0.78/1.18 'c_Lambda_Olift', Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.78/1.18 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.78/1.18 ), Z ) ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), =( Z, Y ), ~( 'c_ListOrder_Ostep1'(
% 0.78/1.18 X, 'c_List_Olist_OCons'( U, Y, T ), 'c_List_Olist_OCons'( W, Z, T ), T )
% 0.78/1.18 ) ],
% 0.78/1.18 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.78/1.18 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_OrderedGroup_Osemigroup__add'( X, U )
% 0.78/1.18 ) ],
% 0.78/1.18 [ =( 'c_List_Omap'( X, 'c_List_Oappend'( Y, Z, T ), T, U ),
% 0.78/1.18 'c_List_Oappend'( 'c_List_Omap'( X, Y, T, U ), 'c_List_Omap'( X, Z, T, U
% 0.78/1.18 ), U ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.78/1.18 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.78/1.18 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.78/1.18 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.78/1.18 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.78/1.18 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.78/1.18 ), =( Z, Y ) ],
% 0.78/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.78/1.18 ) ],
% 0.78/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.78/1.18 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 0.78/1.18 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 0.78/1.18 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.78/1.18 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.78/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.78/1.18 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.78/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.78/1.18 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.78/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.78/1.18 ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.78/1.18 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.78/1.18 T, X ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T ),
% 0.78/1.18 ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y, hAPP( hAPP(
% 0.78/1.18 'c_Type_Otype_OFun', U ), T ) ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X
% 0.78/1.18 ), 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y,
% 0.78/1.18 'c_HOL_Ozero__class_Ozero'( X ), X, X ) ) ],
% 0.78/1.18 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U, 'c_List_Oappend'( X
% 0.78/1.18 , 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W ), W ),
% 0.78/1.18 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( T, 'c_List_Olist_ONil'( W ), W
% 0.78/1.18 ), W ), W ) ) ],
% 0.78/1.18 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.78/1.18 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_Olift', X ), Z ),
% 0.78/1.18 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Z, 'tc_Lambda_OdB', 'tc_nat'
% 0.78/1.18 , 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.78/1.18 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.78/1.18 [ 'c_List_Olistsp'( X, 'c_List_Oappend'( Y, Z, T ), T ), ~(
% 0.78/1.18 'c_List_Olistsp'( X, Z, T ) ), ~( 'c_List_Olistsp'( X, Y, T ) ) ],
% 0.78/1.18 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OAbs'( T ), U ),
% 0.78/1.18 hAPP( hAPP( Z, T ), 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, U ) ) ) ],
% 0.78/1.18 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 0.78/1.18 X ) ],
% 0.78/1.18 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.78/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ),
% 0.78/1.18 'c_OrderedGroup_Osemigroup__add'( 'c_HOL_Oplus__class_Oplus'( X ), X ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U ) ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ],
% 0.78/1.18 [ =( X, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.78/1.18 'c_Type_Osko__Type__Xvar__app__types__1__1'( Y, X, Z, T ), Y,
% 0.78/1.18 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( Z,
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ), ~( 'c_Type_Otypings'( Z, W, V0
% 0.78/1.18 ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.78/1.18 , Y ) ) ],
% 0.78/1.18 [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.78/1.18 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 0.78/1.18 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.78/1.18 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.78/1.18 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_OCons'( Y, Z, T ), U, T, W ),
% 0.78/1.18 hAPP( hAPP( X, Y ), 'c_List_Ofoldr'( X, Z, U, T, W ) ) ) ],
% 0.78/1.18 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.78/1.18 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.78/1.18 ],
% 0.78/1.18 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.78/1.18 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 0.78/1.18 ],
% 0.78/1.18 [ ~( =( 'c_List_Oappend'( X, Y, Z ), X ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.78/1.18 ) ) ],
% 0.78/1.18 [ ~( =( X, 'c_List_Oappend'( X, Y, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.78/1.18 ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Oappend'( X, Y, Z ), Y ) ), =( X, 'c_List_Olist_ONil'( Z
% 0.78/1.18 ) ) ],
% 0.78/1.18 [ ~( =( X, 'c_List_Oappend'( Y, X, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.78/1.18 ) ) ],
% 0.78/1.18 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP( hAPP(
% 0.78/1.18 'c_Type_Otype_OFun', Z ), T ) ) ), =( Y, T ) ],
% 0.78/1.18 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP( hAPP(
% 0.78/1.18 'c_Type_Otype_OFun', Z ), T ) ) ), =( X, Z ) ],
% 0.78/1.18 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y
% 0.78/1.18 , Z, X ), X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.78/1.18 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.78/1.18 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.78/1.18 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 0.78/1.18 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.78/1.18 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.78/1.18 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.78/1.18 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.78/1.18 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.78/1.18 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.78/1.18 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.78/1.18 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 0.78/1.18 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.78/1.18 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.78/1.18 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.78/1.18 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 0.78/1.18 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 0.78/1.18 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 0.78/1.18 ) ), =( X, T ) ],
% 0.78/1.18 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 0.78/1.18 ) ), =( Y, U ) ],
% 0.78/1.18 [ 'c_Type_Otyping'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', T
% 0.78/1.18 ), Y ) ) ), ~( 'c_Type_Otyping'( X, T, Z ) ) ],
% 0.78/1.18 [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), hBOOL( hAPP( hAPP( X, U ), W ) ),
% 0.78/1.18 ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( U, Y, T ),
% 0.78/1.18 'c_List_Olist_OCons'( W, Z, T ), T ) ) ],
% 0.78/1.18 [ 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 0.78/1.18 'c_List_Olist_OCons'( Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T
% 0.78/1.18 ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) ) ), =( Y
% 0.78/1.18 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.78/1.18 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.78/1.18 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( X, T
% 0.78/1.18 ) ],
% 0.78/1.18 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.78/1.18 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.78/1.18 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( Y, U
% 0.78/1.18 ) ],
% 0.78/1.18 [ 'c_Type_Otyping'( 'v_e____', 'v_u____', 'v_T____' ) ],
% 0.78/1.18 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_ONil'( X
% 0.78/1.18 ), X ), 'c_List_Olist_ONil'( X ) ) ],
% 0.78/1.18 [ 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'( 'c_COMBC'(
% 0.78/1.18 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_Lambda_OdB'
% 0.78/1.18 , 'tc_nat', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.78/1.18 'tc_Lambda_OdB' ), ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', X,
% 0.78/1.18 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.78/1.18 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.78/1.18 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.78/1.18 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 0.78/1.18 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.78/1.18 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.78/1.18 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.78/1.18 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 0.78/1.18 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ), hAPP(
% 0.78/1.18 hAPP( 'c_Lambda_Olift', T ), Y ), U ), ~( 'c_Type_Otyping'( X, T, U ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.78/1.18 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.78/1.18 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), U )
% 0.78/1.18 , T ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.78/1.18 ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.78/1.18 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ],
% 0.78/1.18 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.78/1.18 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.78/1.18 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.78/1.18 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.78/1.18 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.78/1.18 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( X, 'c_ListApplication_Osko__ListApplication__Xlem__1__3'(
% 0.78/1.18 X ) ) ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_Lambda_OdB_OVar'(
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__Xlem__1__1'( X ) ),
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__Xlem__1__2'( X ),
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( X, Y ) ) ],
% 0.78/1.18 [ =( 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, U, U ), hAPP( hAPP(
% 0.78/1.18 X, Y ), 'c_List_Ofoldl'( X, Z, T, U, U ) ) ), ~(
% 0.78/1.18 'c_OrderedGroup_Osemigroup__add'( X, U ) ) ],
% 0.78/1.18 [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.78/1.18 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.78/1.18 ) ) ],
% 0.78/1.18 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 0.78/1.18 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), T ), hAPP( hAPP(
% 0.78/1.18 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Z ), T ) )
% 0.78/1.18 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', Y ), Z ), T ) ) ) ],
% 0.78/1.18 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.78/1.18 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 0.78/1.18 Z ) ) ) ],
% 0.78/1.18 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__typesE__1__1'(
% 0.78/1.18 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ), Z ) ) ],
% 0.78/1.18 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.78/1.18 ) ],
% 0.78/1.18 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.78/1.18 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.78/1.18 ],
% 0.78/1.18 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 0.78/1.18 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 0.78/1.18 ],
% 0.78/1.18 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.78/1.18 Z ) ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.78/1.18 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.78/1.18 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.78/1.18 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.78/1.18 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.78/1.18 ), X ), Y ) ],
% 0.78/1.18 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP( hAPP(
% 0.78/1.18 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.78/1.18 Z, U ), W ) ) ) ],
% 0.78/1.18 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP( hAPP(
% 0.78/1.18 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.78/1.18 Z, U ), W ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.78/1.18 , X ), 'c_Lambda_OdB_OVar'( Y ) ), Z ) ) ), ~( hBOOL( hAPP(
% 0.78/1.18 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.78/1.18 ), Z ), 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.78/1.18 'tc_nat' ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.78/1.18 , 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~(
% 0.78/1.18 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.78/1.18 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.78/1.18 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.78/1.18 'c_Lambda_OdB_OApp', X ), Y ), Z ) ],
% 0.78/1.18 [ ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.78/1.18 ) ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.78/1.18 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.78/1.18 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.78/1.18 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.78/1.18 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.78/1.18 , 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ),
% 0.78/1.18 ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y, 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.78/1.18 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 0.78/1.18 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.78/1.18 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 0.78/1.18 [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ), X ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Z, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ) ), ~( 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', Y, Z,
% 0.78/1.18 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3'( X ) )
% 0.78/1.18 ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_Lambda_OdB_OVar'(
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1'( X ) )
% 0.78/1.18 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2'( X )
% 0.78/1.18 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) )
% 0.78/1.18 ) ],
% 0.78/1.18 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OVar'( X )
% 0.78/1.18 , Y ) ],
% 0.78/1.18 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.78/1.18 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OVar'( T ), U ),
% 0.78/1.18 hAPP( X, T ) ) ],
% 0.78/1.18 [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.78/1.18 Z ) ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.78/1.18 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 0.78/1.18 ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), Y ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.78/1.18 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.78/1.18 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 0.78/1.18 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB'
% 0.78/1.18 , 'tc_Lambda_OdB' ) ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.78/1.18 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.78/1.18 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 0.78/1.18 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ =( 'v_n____', 'v_i____' ) ],
% 0.78/1.18 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X ) ) ) ],
% 0.78/1.18 [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y )
% 0.78/1.18 , Z ) ) ],
% 0.78/1.18 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.78/1.18 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.78/1.18 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.78/1.18 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.78/1.18 X ) ) ), =( X, 'c_Lambda_OdB_OAbs'( 'v_sko__InductTermi__XIT__Xcases__3'(
% 0.78/1.18 X ) ) ), =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.78/1.18 , Y ) ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.78/1.18 'c_Lambda_Olift', X ), Z ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ) )
% 0.78/1.18 ],
% 0.78/1.18 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), T )
% 0.78/1.18 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP(
% 0.78/1.18 'c_Lambda_Osubst', X ), Z ), T ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 0.78/1.18 'c_Lambda_Osubst', Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 0.78/1.18 'tc_nat', 'tc_Lambda_OdB' ) ), T, 'tc_Lambda_OdB', 'tc_nat',
% 0.78/1.18 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB'
% 0.78/1.18 , 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_ea______', 'v_ia______',
% 0.78/1.18 'v_T____', 'tc_Type_Otype' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_Lambda_OdB_OVar'( 'v_n____' ), 'v_rs____', 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ), 'v_T_Ha______' ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( hAPP(
% 0.78/1.18 'c_Lambda_Osubst', X ), Y ), Z ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 0.78/1.18 T ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), T ) ) ) ]
% 0.78/1.18 ,
% 0.78/1.18 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.78/1.18 ), Z ), 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'(
% 0.78/1.18 Z, X, 'tc_nat' ) ],
% 0.78/1.18 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), 'c_List_Ofoldr'(
% 0.78/1.18 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X,
% 0.78/1.18 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), T,
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_ua______' ) ) ],
% 0.78/1.18 [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____', 'v_T____',
% 0.78/1.18 'tc_Type_Otype' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_Lambda_OdB_OVar'( 'v_n____' ), 'v_rs____', 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ), 'v_T_H____' ) ],
% 0.78/1.18 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ),
% 0.78/1.18 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( hAPP(
% 0.78/1.18 'c_Lambda_Obeta', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_Lambda_OdB_OVar'( Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ) )
% 0.78/1.18 ) ],
% 0.78/1.18 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, hAPP( hAPP( 'c_Lambda_OdB_OApp'
% 0.78/1.18 , T ), U ), W ), hAPP( hAPP( Y, T ), U ) ) ],
% 0.78/1.18 [ =( hAPP( hAPP( X, Y ), 'c_List_Ofoldl'( X, Z, T, U, U ) ),
% 0.78/1.18 'c_List_Ofoldl'( X, Y, T, U, U ) ), ~( 'c_OrderedGroup_Omonoid__add'( Z,
% 0.78/1.18 X, U ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__5'(
% 0.78/1.18 X ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 0.78/1.18 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OVar'( T ), U ),
% 0.78/1.18 hAPP( X, T ) ) ],
% 0.78/1.18 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( hAPP( hAPP( hAPP(
% 0.78/1.18 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y ) ],
% 0.78/1.18 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_OCons'( Z, T, U ), W, U ),
% 0.78/1.18 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, W, U ) ) ],
% 0.78/1.18 [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', Z, T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X,
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z,
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1'( X
% 0.78/1.18 , Y, Z, T ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), =( T,
% 0.78/1.18 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y ) ) ],
% 0.78/1.18 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 0.78/1.18 , Y ) ],
% 0.78/1.18 [ =( 'v_rs____', 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.78/1.18 T ), U ), W ), hAPP( hAPP( hAPP( hAPP( Y, T ), U ),
% 0.78/1.18 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, W ) ), 'c_Lambda_OdB_OdB__rec'( X, Y
% 0.78/1.18 , Z, U, W ) ) ) ],
% 0.78/1.18 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2'( X ),
% 0.78/1.18 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1'( X ),
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.78/1.18 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.78/1.18 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__types__1__1'(
% 0.78/1.18 Z, T, X, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.78/1.18 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ), T ) ), ~( 'c_Type_Otypings'( X, W, V0 ) ), ~(
% 0.78/1.18 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.78/1.18 , Z ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X ) ) ), ~(
% 0.78/1.18 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.78/1.18 X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP(
% 0.78/1.18 hAPP( 'c_Lambda_Obeta', Y ), Z ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.78/1.18 X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP(
% 0.78/1.18 hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ],
% 0.78/1.18 [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T
% 0.78/1.18 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y, T ) ),
% 0.78/1.18 'c_Lambda_Oliftn'( X, Z, T ) ) ) ],
% 0.78/1.18 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( 'c_Lambda_Olift',
% 0.78/1.18 X ), Y ) ), Z ), Y ), X ) ],
% 0.78/1.18 [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.78/1.18 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.78/1.18 ), 'c_Lambda_OdB_OAbs'( X ) ) ],
% 0.78/1.18 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.78/1.18 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.78/1.18 , 'c_Lambda_OdB_OVar'( Y ) ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.78/1.18 ) ) ) ],
% 0.78/1.18 [ 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', X,
% 0.78/1.18 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, X, Z ),
% 0.78/1.18 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.78/1.18 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), X,
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ) ) ) ],
% 0.78/1.18 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y )
% 0.78/1.18 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.78/1.18 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.78/1.18 [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 0.78/1.18 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X, Z, T ) ),
% 0.78/1.18 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ],
% 0.78/1.18 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Oappend'( Z, T, U ), W, U ),
% 0.78/1.18 'c_List_Ofoldl'( X, 'c_List_Ofoldl'( X, Y, Z, W, U ), T, W, U ) ) ],
% 0.78/1.18 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OVar'(
% 0.78/1.18 Z ) ) ) ],
% 0.78/1.18 [ =( 'v_rs____', 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.78/1.18 [ =( 'v_n____', 'v_i____' ) ],
% 0.78/1.18 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ],
% 0.78/1.18 [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 0.78/1.18 'c_Lambda_Osubst', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.78/1.18 'c_Lambda_OdB_OVar'( 'v_n____' ), 'v_rs____', 'tc_Lambda_OdB',
% 0.78/1.18 'tc_Lambda_OdB' ) ), 'v_u____' ), 'v_i____' ) ) ) ) ],
% 0.78/1.18 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.78/1.18 'class_Orderings_Opreorder'( Y ) ) ],
% 0.78/1.18 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.78/1.18 'class_Orderings_Oorder'( Y ) ) ],
% 0.78/1.18 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.78/1.18 ],
% 0.78/1.18 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.78/1.18 ) ],
% 0.78/1.18 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.78/1.18 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.78/1.18 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.78/1.18 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.78/1.18 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.78/1.18 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.78/1.18 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.78/1.18 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 0.78/1.18 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.78/1.18 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.78/1.18 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.78/1.18 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.78/1.18 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 0.78/1.18 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 0.78/1.18 [ 'c_fequal'( X, X, Y ) ],
% 0.78/1.18 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 0.78/1.18 ] .
% 0.78/1.18
% 0.78/1.18
% 0.78/1.18 percentage equality = 0.367521, percentage horn = 0.894737
% 0.78/1.18 This is a problem with some equality
% 0.78/1.18
% 0.78/1.18
% 0.78/1.18
% 0.78/1.18 Options Used:
% 0.78/1.18
% 0.78/1.18 useres = 1
% 0.78/1.18 useparamod = 1
% 0.78/1.18 useeqrefl = 1
% 0.78/1.18 useeqfact = 1
% 0.78/1.18 usefactor = 1
% 0.78/1.18 usesimpsplitting = 0
% 0.78/1.18 usesimpdemod = 5
% 0.78/1.18 usesimpres = 3
% 0.78/1.18
% 0.78/1.18 resimpinuse = 1000
% 0.78/1.18 resimpclauses = 20000
% 0.78/1.18 substype = eqrewr
% 0.78/1.18 backwardsubs = 1
% 0.78/1.18 selectoldest = 5
% 0.78/1.18
% 0.78/1.18 litorderings [0] = split
% 0.78/1.18 litorderings [1] = extend the termordering, first sorting on arguments
% 0.78/1.18
% 0.78/1.18 termordering = kbo
% 0.78/1.18
% 0.78/1.18 litapriori = 0
% 0.78/1.18 termapriori = 1
% 0.78/1.18 litaposteriori = 0
% 0.78/1.18 termaposteriori = 0
% 0.78/1.18 demodaposteriori = 0
% 0.78/1.18 ordereqreflfact = 0
% 0.78/1.18
% 0.78/1.18 litselect = negord
% 0.78/1.18
% 0.78/1.18 maxweight = 15
% 0.78/1.18 maxdepth = 30000
% 0.78/1.18 maxlength = 115
% 0.78/1.18 maxnrvars = 195
% 0.78/1.18 excuselevel = 1
% 0.78/1.18 increasemaxweight = 1
% 0.78/1.18
% 0.78/1.18 maxselected = 10000000
% 0.78/1.18 maxnrclauses = 10000000
% 0.78/1.18
% 0.78/1.18 showgenerated = 0
% 0.78/1.18 showkept = 0
% 0.78/1.18 showselected = 0
% 0.78/1.18 showdeleted = 0
% 0.78/1.18 showresimp = 1
% 0.78/1.18 showstatus = 2000
% 0.78/1.18
% 0.78/1.18 prologoutput = 1
% 0.78/1.18 nrgoals = 5000000
% 0.78/1.18 totalproof = 1
% 0.78/1.18
% 0.78/1.18 Symbols occurring in the translation:
% 0.78/1.18
% 0.78/1.18 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.78/1.18 . [1, 2] (w:1, o:150, a:1, s:1, b:0),
% 0.78/1.18 ! [4, 1] (w:0, o:104, a:1, s:1, b:0),
% 0.78/1.18 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.18 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.18 'class_Ring__and__Field_Oidom' [40, 1] (w:1, o:109, a:1, s:1, b:0),
% 0.78/1.18 'class_Int_Onumber__ring' [41, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.57/1.93 'c_HOL_Oplus__class_Oplus' [43, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.57/1.93 hAPP [44, 2] (w:1, o:175, a:1, s:1, b:0),
% 1.57/1.93 'c_HOL_Ozero__class_Ozero' [46, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.57/1.93 hBOOL [49, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.57/1.93 'c_Lambda_OdB_OApp' [50, 0] (w:1, o:18, a:1, s:1, b:0),
% 1.57/1.93 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3' [51, 1
% 1.57/1.93 ] (w:1, o:115, a:1, s:1, b:0),
% 1.57/1.93 'c_Lambda_OdB_OAbs' [52, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.57/1.93 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4' [53, 1
% 1.57/1.93 ] (w:1, o:117, a:1, s:1, b:0),
% 1.57/1.93 'tc_Lambda_OdB' [54, 0] (w:1, o:19, a:1, s:1, b:0),
% 1.57/1.93 'c_List_Ofoldl' [55, 5] (w:1, o:198, a:1, s:1, b:0),
% 1.57/1.93 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1' [56, 1
% 1.57/1.93 ] (w:1, o:118, a:1, s:1, b:0),
% 1.57/1.93 'c_Lambda_OdB_OVar' [57, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.57/1.93 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2' [58, 1
% 1.57/1.93 ] (w:1, o:114, a:1, s:1, b:0),
% 1.57/1.93 'c_ListApplication_Osko__ListApplication__Xlem__1__3' [59, 1] (w:1
% 1.57/1.93 , o:121, a:1, s:1, b:0),
% 1.57/1.93 'c_ListApplication_Osko__ListApplication__Xlem__1__4' [60, 1] (w:1
% 1.57/1.93 , o:122, a:1, s:1, b:0),
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% 1.57/1.93 , o:123, a:1, s:1, b:0),
% 1.57/1.93 'c_ListApplication_Osko__ListApplication__Xlem__1__2' [62, 1] (w:1
% 1.57/1.93 , o:120, a:1, s:1, b:0),
% 1.57/1.93 'c_Type_Otype_OFun' [64, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.57/1.93 'c_Type_Osko__Type__Xlist__app__typeD__1__1' [67, 4] (w:1, o:190, a:1
% 1.57/1.93 , s:1, b:0),
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% 1.57/1.93 'c_List_Ofoldr' [69, 5] (w:1, o:199, a:1, s:1, b:0),
% 1.57/1.93 'c_Type_Otyping' [70, 3] (w:1, o:179, a:1, s:1, b:0),
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% 1.57/1.93 , s:1, b:0),
% 1.57/1.93 'c_Type_Otypings' [72, 3] (w:1, o:180, a:1, s:1, b:0),
% 1.57/1.93 'c_List_Olist_ONil' [76, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.57/1.93 'c_List_Olist_OCons' [77, 3] (w:1, o:181, a:1, s:1, b:0),
% 1.57/1.93 'c_List_Oappend' [78, 3] (w:1, o:182, a:1, s:1, b:0),
% 1.57/1.93 'c_ListOrder_Ostep1' [80, 4] (w:1, o:192, a:1, s:1, b:0),
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% 1.57/1.93 , s:1, b:0),
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% 1.57/1.93 , b:0),
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% 1.57/1.93 'c_Transitive__Closure_Ortranclp' [88, 2] (w:1, o:176, a:1, s:1, b:0)
% 1.57/1.93 ,
% 1.57/1.93 'c_Lambda_Osubst' [89, 0] (w:1, o:49, a:1, s:1, b:0),
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% 1.57/1.93 , b:0),
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% 1.57/1.93 , b:0),
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% 1.57/1.93 , b:0),
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% 1.57/1.93 'v_ea______' [98, 0] (w:1, o:53, a:1, s:1, b:0),
% 1.57/1.93 'v_ua______' [99, 0] (w:1, o:54, a:1, s:1, b:0),
% 1.57/1.93 'v_T____' [100, 0] (w:1, o:55, a:1, s:1, b:0),
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% 1.57/1.93 , b:0),
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% 1.57/1.93 , b:0),
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% 1.57/1.93 , a:1, s:1, b:0),
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% 1.57/1.93 'c_HOL_Oord__class_Oless' [121, 3] (w:1, o:186, a:1, s:1, b:0),
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% 1.57/1.93 , b:0),
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% 1.57/1.93 , s:1, b:0),
% 1.57/1.93 'c_COMBC' [130, 5] (w:1, o:201, a:1, s:1, b:0),
% 1.57/1.93 'c_List_Omap' [132, 4] (w:1, o:193, a:1, s:1, b:0),
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% 7.50/7.90 , b:0),
% 7.50/7.90 'tc_fun' [134, 2] (w:1, o:177, a:1, s:1, b:0),
% 7.50/7.90 'c_Type_Oshift' [135, 4] (w:1, o:194, a:1, s:1, b:0),
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% 7.50/7.90 138, a:1, s:1, b:0),
% 7.50/7.90 'class_OrderedGroup_Omonoid__add' [138, 1] (w:1, o:139, a:1, s:1, b:0
% 7.50/7.90 ),
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% 7.50/7.90 1, s:1, b:0),
% 7.50/7.90 'c_Lambda_Olift' [147, 0] (w:1, o:84, a:1, s:1, b:0),
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% 7.50/7.90 1, b:0),
% 7.50/7.90 'class_Orderings_Olinorder' [158, 1] (w:1, o:143, a:1, s:1, b:0),
% 7.50/7.90 'c_OrderedGroup_Osemigroup__add' [159, 2] (w:1, o:178, a:1, s:1, b:0)
% 7.50/7.90 ,
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% 7.50/7.90 (w:1, o:144, a:1, s:1, b:0),
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% 7.50/7.90 , b:0),
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% 7.50/7.90 , s:1, b:0),
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% 7.50/7.90 , s:1, b:0),
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% 7.50/7.90 1, o:188, a:1, s:1, b:0),
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% 7.50/7.90 194, 4] (w:1, o:197, a:1, s:1, b:0),
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% 7.50/7.90 ] (w:1, o:149, a:1, s:1, b:0),
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% 7.50/7.90 ] (w:1, o:148, a:1, s:1, b:0),
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% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Starting Search:
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 6072
% 7.50/7.90 Kept: 2310
% 7.50/7.90 Inuse: 106
% 7.50/7.90 Deleted: 0
% 7.50/7.90 Deletedinuse: 0
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 16403
% 7.50/7.90 Kept: 4385
% 7.50/7.90 Inuse: 217
% 7.50/7.90 Deleted: 1
% 7.50/7.90 Deletedinuse: 0
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 27151
% 7.50/7.90 Kept: 6493
% 7.50/7.90 Inuse: 278
% 7.50/7.90 Deleted: 3
% 7.50/7.90 Deletedinuse: 0
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 38876
% 7.50/7.90 Kept: 8906
% 7.50/7.90 Inuse: 293
% 7.50/7.90 Deleted: 3
% 7.50/7.90 Deletedinuse: 0
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 51463
% 7.50/7.90 Kept: 11630
% 7.50/7.90 Inuse: 347
% 7.50/7.90 Deleted: 4
% 7.50/7.90 Deletedinuse: 0
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 59956
% 7.50/7.90 Kept: 14265
% 7.50/7.90 Inuse: 388
% 7.50/7.90 Deleted: 4
% 7.50/7.90 Deletedinuse: 0
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 64918
% 7.50/7.90 Kept: 16357
% 7.50/7.90 Inuse: 402
% 7.50/7.90 Deleted: 4
% 7.50/7.90 Deletedinuse: 0
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 72077
% 7.50/7.90 Kept: 18688
% 7.50/7.90 Inuse: 420
% 7.50/7.90 Deleted: 17
% 7.50/7.90 Deletedinuse: 1
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying clauses:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 78872
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% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 87540
% 7.50/7.90 Kept: 23193
% 7.50/7.90 Inuse: 470
% 7.50/7.90 Deleted: 107
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% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 96770
% 7.50/7.90 Kept: 26035
% 7.50/7.90 Inuse: 490
% 7.50/7.90 Deleted: 107
% 7.50/7.90 Deletedinuse: 1
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 105652
% 7.50/7.90 Kept: 28348
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% 7.50/7.90 Deleted: 107
% 7.50/7.90 Deletedinuse: 1
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
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% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 118552
% 7.50/7.90 Kept: 30366
% 7.50/7.90 Inuse: 530
% 7.50/7.90 Deleted: 107
% 7.50/7.90 Deletedinuse: 1
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 131126
% 7.50/7.90 Kept: 32774
% 7.50/7.90 Inuse: 555
% 7.50/7.90 Deleted: 107
% 7.50/7.90 Deletedinuse: 1
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 149901
% 7.50/7.90 Kept: 35392
% 7.50/7.90 Inuse: 560
% 7.50/7.90 Deleted: 107
% 7.50/7.90 Deletedinuse: 1
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
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% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 157226
% 7.50/7.90 Kept: 38124
% 7.50/7.90 Inuse: 570
% 7.50/7.90 Deleted: 107
% 7.50/7.90 Deletedinuse: 1
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 168665
% 7.50/7.90 Kept: 41559
% 7.50/7.90 Inuse: 604
% 7.50/7.90 Deleted: 108
% 7.50/7.90 Deletedinuse: 1
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying clauses:
% 7.50/7.90 Done
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% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 179763
% 7.50/7.90 Kept: 44247
% 7.50/7.90 Inuse: 614
% 7.50/7.90 Deleted: 270
% 7.50/7.90 Deletedinuse: 1
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 190936
% 7.50/7.90 Kept: 46781
% 7.50/7.90 Inuse: 617
% 7.50/7.90 Deleted: 273
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
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% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
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% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 196445
% 7.50/7.90 Kept: 48861
% 7.50/7.90 Inuse: 624
% 7.50/7.90 Deleted: 301
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 208639
% 7.50/7.90 Kept: 51005
% 7.50/7.90 Inuse: 628
% 7.50/7.90 Deleted: 312
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
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% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 222017
% 7.50/7.90 Kept: 53118
% 7.50/7.90 Inuse: 634
% 7.50/7.90 Deleted: 326
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
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% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 228418
% 7.50/7.90 Kept: 55279
% 7.50/7.90 Inuse: 644
% 7.50/7.90 Deleted: 366
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 242809
% 7.50/7.90 Kept: 57439
% 7.50/7.90 Inuse: 647
% 7.50/7.90 Deleted: 378
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 257411
% 7.50/7.90 Kept: 60532
% 7.50/7.90 Inuse: 667
% 7.50/7.90 Deleted: 383
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying clauses:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 274094
% 7.50/7.90 Kept: 62766
% 7.50/7.90 Inuse: 675
% 7.50/7.90 Deleted: 2091
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 293099
% 7.50/7.90 Kept: 65488
% 7.50/7.90 Inuse: 690
% 7.50/7.90 Deleted: 2091
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 307832
% 7.50/7.90 Kept: 67750
% 7.50/7.90 Inuse: 705
% 7.50/7.90 Deleted: 2091
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 318839
% 7.50/7.90 Kept: 69756
% 7.50/7.90 Inuse: 724
% 7.50/7.90 Deleted: 2091
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 334030
% 7.50/7.90 Kept: 73076
% 7.50/7.90 Inuse: 745
% 7.50/7.90 Deleted: 2091
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 346698
% 7.50/7.90 Kept: 75532
% 7.50/7.90 Inuse: 765
% 7.50/7.90 Deleted: 2091
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 361801
% 7.50/7.90 Kept: 78703
% 7.50/7.90 Inuse: 779
% 7.50/7.90 Deleted: 2092
% 7.50/7.90 Deletedinuse: 2
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 Intermediate Status:
% 7.50/7.90 Generated: 372870
% 7.50/7.90 Kept: 80765
% 7.50/7.90 Inuse: 793
% 7.50/7.90 Deleted: 2094
% 7.50/7.90 Deletedinuse: 3
% 7.50/7.90
% 7.50/7.90 Resimplifying inuse:
% 7.50/7.90 Done
% 7.50/7.90
% 7.50/7.90 Resimplifying clauses:
% 7.50/7.90
% 7.50/7.90 Bliksems!, er is een bewijs:
% 7.50/7.90 % SZS status Unsatisfiable
% 7.50/7.90 % SZS output start Refutation
% 7.50/7.90
% 7.50/7.90 clause( 178, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'(
% 7.50/7.90 X ) ), Y ), X ), Y ) ] )
% 7.50/7.90 .
% 7.50/7.90 clause( 201, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ),
% 7.50/7.90 Y ) ] )
% 7.50/7.90 .
% 7.50/7.90 clause( 204, [ =( 'v_i____', 'v_n____' ) ] )
% 7.50/7.90 .
% 7.50/7.90 clause( 225, [ =( 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'v_rs____' ) ] )
% 7.50/7.90 .
% 7.50/7.90 clause( 234, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ] )
% 7.50/7.90 .
% 7.50/7.90 clause( 243, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( 'v_n____' ), 'v_rs____', 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), 'v_u____' ), 'v_n____' ) ) ) ) ] )
% 7.50/7.90 .
% 7.50/7.90 clause( 70485, [ =( 'c_List_Ofoldl'( X, Y, 'v_rs____', Z, 'tc_Lambda_OdB' )
% 7.50/7.90 , Y ) ] )
% 7.50/7.90 .
% 7.50/7.90 clause( 81628, [] )
% 7.50/7.90 .
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 % SZS output end Refutation
% 7.50/7.90 found a proof!
% 7.50/7.90
% 7.50/7.90 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 7.50/7.90
% 7.50/7.90 initialclauses(
% 7.50/7.90 [ clause( 81630, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 7.50/7.90 'class_Int_Onumber__ring'( X ) ), ~( =( Y, hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), =( Z,
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 7.50/7.90 , clause( 81631, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3'( X ) )
% 7.50/7.90 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4'( X )
% 7.50/7.90 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( X,
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1'( X ) )
% 7.50/7.90 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2'( X )
% 7.50/7.90 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ] )
% 7.50/7.90 , clause( 81632, [ ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 7.50/7.90 , 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__Xlem__1__3'( X ) ),
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__Xlem__1__4'( X ),
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( X,
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__Xlem__1__1'( X ) ),
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__Xlem__1__2'( X ),
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( X, Y ) ) ] )
% 7.50/7.90 , clause( 81633, [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 7.50/7.90 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X,
% 7.50/7.90 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ), Z ) ) ] )
% 7.50/7.90 , clause( 81634, [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 7.50/7.90 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X,
% 7.50/7.90 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ), Z ) ) ] )
% 7.50/7.90 , clause( 81635, [ 'c_Type_Otypings'( X, Y,
% 7.50/7.90 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X, T, Y ) ), ~(
% 7.50/7.90 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', T, Y,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 7.50/7.90 , clause( 81636, [ 'c_Type_Otypings'( X, Y,
% 7.50/7.90 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X, T, Y ) ), ~(
% 7.50/7.90 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', T, Y,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 7.50/7.90 , clause( 81637, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), =( Y, Z ), ~(
% 7.50/7.90 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( T, 'c_List_Olist_OCons'( Y,
% 7.50/7.90 'c_List_Olist_ONil'( U ), U ), U ), 'c_List_Oappend'( W,
% 7.50/7.90 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( U ), U ), U ), U ) ) ] )
% 7.50/7.90 , clause( 81638, [ =( 'c_List_Ofoldr'( X, 'c_List_Oappend'( Y, Z, T ), U, T
% 7.50/7.90 , W ), 'c_List_Ofoldr'( X, Y, 'c_List_Ofoldr'( X, Z, U, T, W ), T, W ) )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81639, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 7.50/7.90 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 7.50/7.90 , clause( 81640, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 7.50/7.90 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 7.50/7.90 , clause( 81641, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 7.50/7.90 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 7.50/7.90 , clause( 81642, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 7.50/7.90 , X ), Y ), Z ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), T ), Z ) ) )
% 7.50/7.90 , ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', Y ), T ) ) ) ] )
% 7.50/7.90 , clause( 81643, [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y )
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81644, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), Y, X ), Y
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81645, [ =( X, 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y )
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81646, [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y )
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81647, [ =( 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ), X
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81648, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 7.50/7.90 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 7.50/7.90 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81649, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 7.50/7.90 , Y ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 7.50/7.90 'c_Transitive__Closure_Ortranclp'( X, Y ), U ), T ) ) ), ~( hBOOL( hAPP(
% 7.50/7.90 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ] )
% 7.50/7.90 , clause( 81650, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 7.50/7.90 , Y ), Z ), Z ) ) ] )
% 7.50/7.90 , clause( 81651, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 7.50/7.90 , Y ), Z ), Z ) ) ] )
% 7.50/7.90 , clause( 81652, [ 'c_Type_Otyping'( 'v_ea______', 'v_ua______', 'v_T____'
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81653, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( X,
% 7.50/7.90 T, Z ) ) ), =( Y, T ) ] )
% 7.50/7.90 , clause( 81654, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T,
% 7.50/7.90 Y, Z ) ) ), =( X, T ) ] )
% 7.50/7.90 , clause( 81655, [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ] )
% 7.50/7.90 , clause( 81656, [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ),
% 7.50/7.90 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( Y, T, U ),
% 7.50/7.90 'c_List_Olist_OCons'( Z, T, U ), U ) ] )
% 7.50/7.90 , clause( 81657, [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U,
% 7.50/7.90 'c_List_Olist_OCons'( Y, T, W ), 'c_List_Olist_OCons'( X, Z, W ), W ) ) ]
% 7.50/7.90 )
% 7.50/7.90 , clause( 81658, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z,
% 7.50/7.90 'c_Lambda_OdB_OAbs'( T ), U ), hAPP( Z, T ) ) ] )
% 7.50/7.90 , clause( 81659, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 7.50/7.90 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 7.50/7.90 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 7.50/7.90 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 7.50/7.90 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81660, [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X,
% 7.50/7.90 'c_List_Oappend'( T, Y, Z ), Z ) ) ] )
% 7.50/7.90 , clause( 81661, [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X,
% 7.50/7.90 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 7.50/7.90 , clause( 81662, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ),
% 7.50/7.90 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 7.50/7.90 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 7.50/7.90 ), Y ) ) ) ] )
% 7.50/7.90 , clause( 81663, [ 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( Y, Z, T ),
% 7.50/7.90 'c_List_Oappend'( Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U, T ) )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81664, [ ~( 'c_ListOrder_Ostep1'( X, Y, Z, T ) ),
% 7.50/7.90 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( Y, U, T ), 'c_List_Oappend'( Z
% 7.50/7.90 , U, T ), T ) ] )
% 7.50/7.90 , clause( 81665, [ =( 'c_Lambda_Osubstn'( X, Y, Z ), hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', X ), 'c_Lambda_Oliftn'( Z, Y,
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), Z ) ) ] )
% 7.50/7.90 , clause( 81666, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 7.50/7.90 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 7.50/7.90 , clause( 81667, [ 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ), ~(
% 7.50/7.90 'c_Type_Otypings'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y,
% 7.50/7.90 'c_List_Ofoldr'( 'c_Type_Otype_OFun', U, T, 'tc_Type_Otype',
% 7.50/7.90 'tc_Type_Otype' ) ) ) ] )
% 7.50/7.90 , clause( 81668, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 7.50/7.90 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 7.50/7.90 , clause( 81669, [ ~( 'class_Orderings_Oorder'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 7.50/7.90 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 7.50/7.90 , clause( 81670, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 7.50/7.90 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 7.50/7.90 X ), Y ), Z ) ), T ) ) ] )
% 7.50/7.90 , clause( 81671, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 7.50/7.90 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 7.50/7.90 , clause( 81672, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 7.50/7.90 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 7.50/7.90 , clause( 81673, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 7.50/7.90 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 7.50/7.90 , clause( 81674, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 7.50/7.90 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 7.50/7.90 , clause( 81675, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 7.50/7.90 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 7.50/7.90 X ), Y ), Z ) ), T ) ) ] )
% 7.50/7.90 , clause( 81676, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 7.50/7.90 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 7.50/7.90 X ), Y ), T ) ), Z ) ) ] )
% 7.50/7.90 , clause( 81677, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 7.50/7.90 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 7.50/7.90 , clause( 81678, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 7.50/7.90 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 7.50/7.90 , clause( 81679, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 7.50/7.90 , clause( 81680, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 7.50/7.90 , clause( 81681, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 7.50/7.90 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ] )
% 7.50/7.90 , clause( 81682, [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X
% 7.50/7.90 , W ), Y ) ) ] )
% 7.50/7.90 , clause( 81683, [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T
% 7.50/7.90 ), Z ) ] )
% 7.50/7.90 , clause( 81684, [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 7.50/7.90 'c_List_Olist_ONil'( Z ) ) ] )
% 7.50/7.90 , clause( 81685, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_ListOrder_Ostep1'(
% 7.50/7.90 X, T, U, W ), ~( 'c_ListOrder_Ostep1'( X, 'c_List_Oappend'( T,
% 7.50/7.90 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( W ), W ), W ),
% 7.50/7.90 'c_List_Oappend'( U, 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W
% 7.50/7.90 ), W ), W ) ) ] )
% 7.50/7.90 , clause( 81686, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 7.50/7.90 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 7.50/7.90 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81687, [ 'c_Type_Otypings'( X, 'c_List_Omap'( 'c_COMBC'(
% 7.50/7.90 'c_COMBC'( 'c_Lambda_Osubst', Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB',
% 7.50/7.90 'tc_fun'( 'tc_nat', 'tc_Lambda_OdB' ) ), Z, 'tc_Lambda_OdB', 'tc_nat',
% 7.50/7.90 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 7.50/7.90 'c_Type_Otypings'( 'c_Type_Oshift'( X, Z, W, 'tc_Type_Otype' ), T, U ) )
% 7.50/7.90 , ~( 'c_Type_Otyping'( X, Y, W ) ) ] )
% 7.50/7.90 , clause( 81688, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 7.50/7.90 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 7.50/7.90 X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 7.50/7.90 , clause( 81689, [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T
% 7.50/7.90 , Z ), 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 7.50/7.90 , clause( 81690, [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T
% 7.50/7.90 , Z ), 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 7.50/7.90 , clause( 81691, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 7.50/7.90 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP(
% 7.50/7.90 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 7.50/7.90 'tc_Lambda_OdB' ), Y ), Z ) ) ) ] )
% 7.50/7.90 , clause( 81692, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 7.50/7.90 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP(
% 7.50/7.90 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 7.50/7.90 'tc_Lambda_OdB' ), X ), Z ) ) ) ] )
% 7.50/7.90 , clause( 81693, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 7.50/7.90 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP(
% 7.50/7.90 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 7.50/7.90 ) ) ) ] )
% 7.50/7.90 , clause( 81694, [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T
% 7.50/7.90 , U ), 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U
% 7.50/7.90 ) ) ] )
% 7.50/7.90 , clause( 81695, [ =( 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X
% 7.50/7.90 , Z, T, U ), U ), 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U
% 7.50/7.90 ) ) ] )
% 7.50/7.90 , clause( 81696, [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T
% 7.50/7.90 , U ), 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U
% 7.50/7.90 ) ) ] )
% 7.50/7.90 , clause( 81697, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 7.50/7.90 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 7.50/7.90 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81698, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 7.50/7.90 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 7.50/7.90 , clause( 81699, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 7.50/7.90 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 7.50/7.90 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 7.50/7.90 , clause( 81700, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 7.50/7.90 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 7.50/7.90 , clause( 81701, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 7.50/7.90 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ] )
% 7.50/7.90 , clause( 81702, [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T )
% 7.50/7.90 , T ), 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ] )
% 7.50/7.90 , clause( 81703, [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T )
% 7.50/7.90 , T ), 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ] )
% 7.50/7.90 , clause( 81704, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 7.50/7.90 'c_List_Olist_ONil'( Z ) ) ) ] )
% 7.50/7.90 , clause( 81705, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 7.50/7.90 'c_List_Olist_ONil'( Z ) ) ) ] )
% 7.50/7.90 , clause( 81706, [ =( X, Y ), hBOOL( hAPP( hAPP( Z, Y ), X ) ), ~(
% 7.50/7.90 'c_ListOrder_Ostep1'( Z, 'c_List_Olist_OCons'( Y, T, U ),
% 7.50/7.90 'c_List_Olist_OCons'( X, W, U ), U ) ) ] )
% 7.50/7.90 , clause( 81707, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 7.50/7.90 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 7.50/7.90 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) )
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81708, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 7.50/7.90 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), ~( hBOOL( hAPP(
% 7.50/7.90 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 7.50/7.90 'tc_Lambda_OdB' ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 7.50/7.90 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 7.50/7.90 ), Z ) ) ) ] )
% 7.50/7.90 , clause( 81709, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 7.50/7.90 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 7.50/7.90 ) ) ] )
% 7.50/7.90 , clause( 81710, [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Type_Otyping'( X, T,
% 7.50/7.90 Z ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), T ), Y ) ) ) ] )
% 7.50/7.90 , clause( 81711, [ 'c_Type_Otypings'( 'c_Type_Oshift'( X, Y, Z,
% 7.50/7.90 'tc_Type_Otype' ), 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Y,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ), U ), ~( 'c_Type_Otypings'( X, T, U ) ) ] )
% 7.50/7.90 , clause( 81712, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OVar'( X
% 7.50/7.90 ) ), Y ), 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y
% 7.50/7.90 , 'tc_nat' ) ) ] )
% 7.50/7.90 , clause( 81713, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Olift', X ), Y ) ), hAPP( hAPP( 'c_Lambda_Olift', Z ), Y ) ) )
% 7.50/7.90 , ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ] )
% 7.50/7.90 , clause( 81714, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ] )
% 7.50/7.90 , clause( 81715, [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ] )
% 7.50/7.90 , clause( 81716, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81717, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 7.50/7.90 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'(
% 7.50/7.90 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 7.50/7.90 , clause( 81718, [ =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Oappend'(
% 7.50/7.90 'c_List_Olist_ONil'( Z ), 'c_List_Olist_OCons'( X, Y, Z ), Z ) ) ] )
% 7.50/7.90 , clause( 81719, [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'(
% 7.50/7.90 'c_Type_Oshift'( X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'(
% 7.50/7.90 X, hAPP( hAPP( hAPP( 'c_Lambda_Osubst', U ), Y ), T ), W ) ] )
% 7.50/7.90 , clause( 81720, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y,
% 7.50/7.90 'c_List_Olist_ONil'( Z ), Z, X ) ) ] )
% 7.50/7.90 , clause( 81721, [ =( X, Y ), 'c_ListOrder_Ostep1'( Z, X, Y, T ), ~(
% 7.50/7.90 'c_ListOrder_Ostep1'( Z, 'c_List_Oappend'( X, 'c_List_Olist_OCons'( U,
% 7.50/7.90 'c_List_Olist_ONil'( T ), T ), T ), 'c_List_Oappend'( Y,
% 7.50/7.90 'c_List_Olist_OCons'( W, 'c_List_Olist_ONil'( T ), T ), T ), T ) ) ] )
% 7.50/7.90 , clause( 81722, [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'(
% 7.50/7.90 'c_List_Olist_ONil'( X ), 'c_List_Olist_ONil'( X ), X ) ) ] )
% 7.50/7.90 , clause( 81723, [ =( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Transitive__Closure_Ortranclp'( X, Y ), Y ),
% 7.50/7.90 'c_Transitive__Closure_Ortranclp'( X, Y ) ) ] )
% 7.50/7.90 , clause( 81724, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 7.50/7.90 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y ) ] )
% 7.50/7.90 , clause( 81725, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 7.50/7.90 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 7.50/7.90 X ) ), Y ), Y ) ] )
% 7.50/7.90 , clause( 81726, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 7.50/7.90 'class_Int_Onumber__ring'( X ) ), =( Y, hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81727, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 7.50/7.90 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 7.50/7.90 , clause( 81728, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 7.50/7.90 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 7.50/7.90 , Y ), Y ) ] )
% 7.50/7.90 , clause( 81729, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 7.50/7.90 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 7.50/7.90 ) ), Y ) ] )
% 7.50/7.90 , clause( 81730, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 7.50/7.90 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 7.50/7.90 , clause( 81731, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 7.50/7.90 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y ) ] )
% 7.50/7.90 , clause( 81732, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 X ) ), 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Obeta', X ), Y ) ) ) ] )
% 7.50/7.90 , clause( 81733, [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~(
% 7.50/7.90 'c_OrderedGroup_Omonoid__add'( Z, X, T ) ) ] )
% 7.50/7.90 , clause( 81734, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 7.50/7.90 'c_OrderedGroup_Omonoid__add'( Y, X, T ) ) ] )
% 7.50/7.90 , clause( 81735, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 7.50/7.90 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 7.50/7.90 , clause( 81736, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 7.50/7.90 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 7.50/7.90 , clause( 81737, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T,
% 7.50/7.90 X ) ) ), =( Z, 'c_List_Olist_ONil'( T ) ) ] )
% 7.50/7.90 , clause( 81738, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 7.50/7.90 , X ), Y ), Z ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', T ), Y ), Z ) ) )
% 7.50/7.90 , ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), T ) ) ) ] )
% 7.50/7.90 , clause( 81739, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 7.50/7.90 , X ), Y ), Z ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), T ), Z ) ) )
% 7.50/7.90 , ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y ), T ) ) ) ] )
% 7.50/7.90 , clause( 81740, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 7.50/7.90 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 7.50/7.90 ) ) ] )
% 7.50/7.90 , clause( 81741, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 7.50/7.90 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ),
% 7.50/7.90 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ] )
% 7.50/7.90 , clause( 81742, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 7.50/7.90 , Y ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( X, Z ), T ) ) ) ] )
% 7.50/7.90 , clause( 81743, [ ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_ONil'( Y ), Z
% 7.50/7.90 , Y ) ) ] )
% 7.50/7.90 , clause( 81744, [ ~( 'c_ListOrder_Ostep1'( X, Y, 'c_List_Olist_ONil'( Z )
% 7.50/7.90 , Z ) ) ] )
% 7.50/7.90 , clause( 81745, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 7.50/7.90 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 7.50/7.90 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 7.50/7.90 , clause( 81746, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 7.50/7.90 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 7.50/7.90 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 7.50/7.90 , clause( 81747, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 7.50/7.90 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 7.50/7.90 , clause( 81748, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 7.50/7.90 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 7.50/7.90 , clause( 81749, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 7.50/7.90 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 7.50/7.90 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 7.50/7.90 )
% 7.50/7.90 , clause( 81750, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), hAPP(
% 7.50/7.90 hAPP( 'c_Type_Otype_OFun', Z ), T ) ), ~( 'c_Type_Otyping'(
% 7.50/7.90 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 7.50/7.90 'tc_Type_Otype' ), Y, T ) ) ] )
% 7.50/7.90 , clause( 81751, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ] )
% 7.50/7.90 , clause( 81752, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z )
% 7.50/7.90 , 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X
% 7.50/7.90 , 'tc_nat' ) ] )
% 7.50/7.90 , clause( 81753, [ ~( =( 'v_T____', hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y
% 7.50/7.90 ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', Z ), T ), U ) ) ), ~( 'c_Type_Otyping'( W, T, X ) ),
% 7.50/7.90 ~( hBOOL( hAPP( 'c_InductTermi_OIT', T ) ) ), ~( 'c_Type_Otyping'(
% 7.50/7.90 'c_Type_Oshift'( W, U, X, 'tc_Type_Otype' ), Z, V0 ) ), ~( hBOOL( hAPP(
% 7.50/7.90 'c_InductTermi_OIT', Z ) ) ) ] )
% 7.50/7.90 , clause( 81754, [ ~( =( 'v_T____', hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y
% 7.50/7.90 ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', Z ), T ), U ) ) ), ~( 'c_Type_Otyping'( W, T, Y ) ),
% 7.50/7.90 ~( hBOOL( hAPP( 'c_InductTermi_OIT', T ) ) ), ~( 'c_Type_Otyping'(
% 7.50/7.90 'c_Type_Oshift'( W, U, Y, 'tc_Type_Otype' ), Z, V0 ) ), ~( hBOOL( hAPP(
% 7.50/7.90 'c_InductTermi_OIT', Z ) ) ) ] )
% 7.50/7.90 , clause( 81755, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z,
% 7.50/7.90 X ) ) ), =( Y, 'c_List_Olist_ONil'( X ) ) ] )
% 7.50/7.90 , clause( 81756, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z,
% 7.50/7.90 X ) ) ), =( Z, 'c_List_Olist_ONil'( X ) ) ] )
% 7.50/7.90 , clause( 81757, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 7.50/7.90 ) ), =( X, Y ) ] )
% 7.50/7.90 , clause( 81758, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'(
% 7.50/7.90 Z ) ) ), =( X, 'c_List_Olist_ONil'( Z ) ) ] )
% 7.50/7.90 , clause( 81759, [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'(
% 7.50/7.90 Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z ) ) ] )
% 7.50/7.90 , clause( 81760, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), hBOOL( hAPP(
% 7.50/7.90 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ),
% 7.50/7.90 'c_List_Olistsp'( 'c_InductTermi_OIT',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB' ), ~( hBOOL(
% 7.50/7.90 hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81761, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 7.50/7.90 , clause( 81762, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 7.50/7.90 , clause( 81763, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 7.50/7.90 , clause( 81764, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 7.50/7.90 , clause( 81765, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 7.50/7.90 , clause( 81766, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ) ), hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81767, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 7.50/7.90 ) ), hAPP( hAPP( 'c_Lambda_Olift', Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 7.50/7.90 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 7.50/7.90 ), Z ) ) ) ] )
% 7.50/7.90 , clause( 81768, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 7.50/7.90 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 7.50/7.90 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 7.50/7.90 , clause( 81769, [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), =( Z, Y ), ~(
% 7.50/7.90 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( U, Y, T ),
% 7.50/7.90 'c_List_Olist_OCons'( W, Z, T ), T ) ) ] )
% 7.50/7.90 , clause( 81770, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 7.50/7.90 hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ) ), ~(
% 7.50/7.90 'c_OrderedGroup_Osemigroup__add'( X, U ) ) ] )
% 7.50/7.90 , clause( 81771, [ =( 'c_List_Omap'( X, 'c_List_Oappend'( Y, Z, T ), T, U )
% 7.50/7.90 , 'c_List_Oappend'( 'c_List_Omap'( X, Y, T, U ), 'c_List_Omap'( X, Z, T,
% 7.50/7.90 U ), U ) ) ] )
% 7.50/7.90 , clause( 81772, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 7.50/7.90 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 7.50/7.90 , 'tc_Lambda_OdB' ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 7.50/7.90 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 7.50/7.90 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81773, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 7.50/7.90 ), =( Z, Y ) ] )
% 7.50/7.90 , clause( 81774, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81775, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 7.50/7.90 , clause( 81776, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), =( Z, Y ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ] )
% 7.50/7.90 , clause( 81777, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 7.50/7.90 , clause( 81778, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 7.50/7.90 ), =( Z, Y ) ] )
% 7.50/7.90 , clause( 81779, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 7.50/7.90 , clause( 81780, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81781, [ ~(
% 7.50/7.90 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 7.50/7.90 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 7.50/7.90 T, X ) ) ] )
% 7.50/7.90 , clause( 81782, [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y
% 7.50/7.90 , Z, X ) ) ) ] )
% 7.50/7.90 , clause( 81783, [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y
% 7.50/7.90 ), Z ), T ), ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y
% 7.50/7.90 , hAPP( hAPP( 'c_Type_Otype_OFun', U ), T ) ) ) ] )
% 7.50/7.90 , clause( 81784, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 7.50/7.90 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ),
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ), 'c_List_Ofoldr'(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 7.50/7.90 ) ) ] )
% 7.50/7.90 , clause( 81785, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81786, [ =( X, Y ), =( Z, T ), ~( 'c_ListOrder_Ostep1'( U,
% 7.50/7.90 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( W ), W
% 7.50/7.90 ), W ), 'c_List_Oappend'( Y, 'c_List_Olist_OCons'( T,
% 7.50/7.90 'c_List_Olist_ONil'( W ), W ), W ), W ) ) ] )
% 7.50/7.90 , clause( 81787, [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ),
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_Olift', X ),
% 7.50/7.90 Z ), 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Z, 'tc_Lambda_OdB',
% 7.50/7.90 'tc_nat', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81788, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 7.50/7.90 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81789, [ 'c_List_Olistsp'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 7.50/7.90 ~( 'c_List_Olistsp'( X, Z, T ) ), ~( 'c_List_Olistsp'( X, Y, T ) ) ] )
% 7.50/7.90 , clause( 81790, [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 T ), U ), hAPP( hAPP( Z, T ), 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, U ) )
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81791, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'(
% 7.50/7.90 'tc_nat' ), X, Y ), X ) ] )
% 7.50/7.90 , clause( 81792, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 7.50/7.90 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 7.50/7.90 , clause( 81793, [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ),
% 7.50/7.90 'c_OrderedGroup_Osemigroup__add'( 'c_HOL_Oplus__class_Oplus'( X ), X ) ]
% 7.50/7.90 )
% 7.50/7.90 , clause( 81794, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U
% 7.50/7.90 ) ), ~( 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ] )
% 7.50/7.90 , clause( 81795, [ =( X, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 7.50/7.90 'c_Type_Osko__Type__Xvar__app__types__1__1'( Y, X, Z, T ), Y,
% 7.50/7.90 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( Z,
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ), ~( 'c_Type_Otypings'( Z, W, V0
% 7.50/7.90 ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 7.50/7.90 , Y ) ) ] )
% 7.50/7.90 , clause( 81796, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 7.50/7.90 'tc_nat' ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 7.50/7.90 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 7.50/7.90 , clause( 81797, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 7.50/7.90 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 7.50/7.90 , clause( 81798, [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_OCons'( Y, Z, T ),
% 7.50/7.90 U, T, W ), hAPP( hAPP( X, Y ), 'c_List_Ofoldr'( X, Z, U, T, W ) ) ) ] )
% 7.50/7.90 , clause( 81799, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 7.50/7.90 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81800, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 7.50/7.90 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81801, [ ~( =( 'c_List_Oappend'( X, Y, Z ), X ) ), =( Y,
% 7.50/7.90 'c_List_Olist_ONil'( Z ) ) ] )
% 7.50/7.90 , clause( 81802, [ ~( =( X, 'c_List_Oappend'( X, Y, Z ) ) ), =( Y,
% 7.50/7.90 'c_List_Olist_ONil'( Z ) ) ] )
% 7.50/7.90 , clause( 81803, [ ~( =( 'c_List_Oappend'( X, Y, Z ), Y ) ), =( X,
% 7.50/7.90 'c_List_Olist_ONil'( Z ) ) ] )
% 7.50/7.90 , clause( 81804, [ ~( =( X, 'c_List_Oappend'( Y, X, Z ) ) ), =( Y,
% 7.50/7.90 'c_List_Olist_ONil'( Z ) ) ] )
% 7.50/7.90 , clause( 81805, [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP(
% 7.50/7.90 hAPP( 'c_Type_Otype_OFun', Z ), T ) ) ), =( Y, T ) ] )
% 7.50/7.90 , clause( 81806, [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP(
% 7.50/7.90 hAPP( 'c_Type_Otype_OFun', Z ), T ) ) ), =( X, Z ) ] )
% 7.50/7.90 , clause( 81807, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ),
% 7.50/7.90 'c_List_Olist_OCons'( Y, Z, X ), X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ]
% 7.50/7.90 )
% 7.50/7.90 , clause( 81808, [ ~(
% 7.50/7.90 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 7.50/7.90 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 7.50/7.90 , clause( 81809, [ ~(
% 7.50/7.90 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 7.50/7.90 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 7.50/7.90 , clause( 81810, [ ~(
% 7.50/7.90 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 7.50/7.90 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 7.50/7.90 , clause( 81811, [ ~(
% 7.50/7.90 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 7.50/7.90 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 7.50/7.90 , clause( 81812, [ ~(
% 7.50/7.90 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 7.50/7.90 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 7.50/7.90 , clause( 81813, [ ~(
% 7.50/7.90 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 7.50/7.90 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 7.50/7.90 , clause( 81814, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__4'( X ) ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__5'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), 'c_List_Olistsp'(
% 7.50/7.90 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__1'( X ),
% 7.50/7.90 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81815, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 7.50/7.90 'c_List_Olist_OCons'( T, U, Z ) ) ), =( X, T ) ] )
% 7.50/7.90 , clause( 81816, [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ),
% 7.50/7.90 'c_List_Olist_OCons'( T, U, Z ) ) ), =( Y, U ) ] )
% 7.50/7.90 , clause( 81817, [ 'c_Type_Otyping'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Obeta', T ), Y ) ) ), ~( 'c_Type_Otyping'( X, T, Z ) ) ] )
% 7.50/7.90 , clause( 81818, [ 'c_ListOrder_Ostep1'( X, Y, Z, T ), hBOOL( hAPP( hAPP( X
% 7.50/7.90 , U ), W ) ), ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( U, Y, T )
% 7.50/7.90 , 'c_List_Olist_OCons'( W, Z, T ), T ) ) ] )
% 7.50/7.90 , clause( 81819, [ 'c_ListOrder_Ostep1'( X, 'c_List_Olist_OCons'( Y, Z, T )
% 7.50/7.90 , 'c_List_Olist_OCons'( Y, U, T ), T ), ~( 'c_ListOrder_Ostep1'( X, Z, U
% 7.50/7.90 , T ) ) ] )
% 7.50/7.90 , clause( 81820, [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'(
% 7.50/7.90 T ) ) ), =( Y, 'c_List_Olist_ONil'( Z ) ) ] )
% 7.50/7.90 , clause( 81821, [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 7.50/7.90 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 7.50/7.90 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( X, T
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81822, [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 7.50/7.90 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 7.50/7.90 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( Y, U
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81823, [ 'c_Type_Otyping'( 'v_e____', 'v_u____', 'v_T____' ) ] )
% 7.50/7.90 , clause( 81824, [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ),
% 7.50/7.90 'c_List_Olist_ONil'( X ), X ), 'c_List_Olist_ONil'( X ) ) ] )
% 7.50/7.90 , clause( 81825, [ 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'(
% 7.50/7.90 'c_COMBC'( 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 7.50/7.90 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ), ~( 'c_List_Olistsp'(
% 7.50/7.90 'c_InductTermi_OIT', X, 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81826, [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z )
% 7.50/7.90 , 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 7.50/7.90 , clause( 81827, [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T )
% 7.50/7.90 , 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ] )
% 7.50/7.90 , clause( 81828, [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z )
% 7.50/7.90 , 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ] )
% 7.50/7.90 , clause( 81829, [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T )
% 7.50/7.90 , 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ] )
% 7.50/7.90 , clause( 81830, [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z,
% 7.50/7.90 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_Olift', T ), Y ), U ), ~(
% 7.50/7.90 'c_Type_Otyping'( X, T, U ) ) ] )
% 7.50/7.90 , clause( 81831, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 7.50/7.90 Y, X ) ) ] )
% 7.50/7.90 , clause( 81832, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 7.50/7.90 , Y ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 7.50/7.90 'c_Transitive__Closure_Ortranclp'( X, Y ), U ), T ) ) ), ~( hBOOL( hAPP(
% 7.50/7.90 hAPP( X, Z ), U ) ) ) ] )
% 7.50/7.90 , clause( 81833, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 7.50/7.90 , Y ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP(
% 7.50/7.90 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ] )
% 7.50/7.90 , clause( 81834, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 7.50/7.90 Y, X ) ) ] )
% 7.50/7.90 , clause( 81835, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 7.50/7.90 Y, X ) ) ] )
% 7.50/7.90 , clause( 81836, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 7.50/7.90 Y, X ) ) ] )
% 7.50/7.90 , clause( 81837, [ hBOOL( hAPP( X,
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__Xlem__1__3'( X ) ) ), ~( hBOOL(
% 7.50/7.90 hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__Xlem__1__1'( X ) ),
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__Xlem__1__2'( X ),
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( X, Y ) ) ] )
% 7.50/7.90 , clause( 81838, [ =( 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, U, U
% 7.50/7.90 ), hAPP( hAPP( X, Y ), 'c_List_Ofoldl'( X, Z, T, U, U ) ) ), ~(
% 7.50/7.90 'c_OrderedGroup_Osemigroup__add'( X, U ) ) ] )
% 7.50/7.90 , clause( 81839, [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 7.50/7.90 ), Y ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81840, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), T ), hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Z ), T ) )
% 7.50/7.90 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', Y ), Z ), T ) ) ) ] )
% 7.50/7.90 , clause( 81841, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y )
% 7.50/7.90 ) ) ] )
% 7.50/7.90 , clause( 81842, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 7.50/7.90 'c_Lambda_OdB_OAbs'( Z ) ) ) ] )
% 7.50/7.90 , clause( 81843, [ 'c_Type_Otypings'( X, Y,
% 7.50/7.90 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X, T, Y ) ), ~(
% 7.50/7.90 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 7.50/7.90 )
% 7.50/7.90 , clause( 81844, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y )
% 7.50/7.90 ) ), =( X, Y ) ] )
% 7.50/7.90 , clause( 81845, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 7.50/7.90 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81846, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 7.50/7.90 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81847, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 7.50/7.90 , clause( 81848, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 7.50/7.90 , clause( 81849, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 7.50/7.90 , clause( 81850, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 7.50/7.90 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y ) ] )
% 7.50/7.90 , clause( 81851, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 7.50/7.90 hAPP( hAPP( 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X
% 7.50/7.90 , hAPP( hAPP( Z, U ), W ) ) ) ] )
% 7.50/7.90 , clause( 81852, [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 7.50/7.90 hAPP( hAPP( 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X
% 7.50/7.90 , hAPP( hAPP( Z, U ), W ) ) ) ] )
% 7.50/7.90 , clause( 81853, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', X ), 'c_Lambda_OdB_OVar'( Y ) ), Z ) ) ), ~( hBOOL(
% 7.50/7.90 hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81854, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 7.50/7.90 'c_Lambda_OdB_OVar'( X ) ), Y ), Z ), 'c_Lambda_OdB_OVar'( X ) ), ~(
% 7.50/7.90 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 7.50/7.90 , clause( 81855, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 7.50/7.90 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 7.50/7.90 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~(
% 7.50/7.90 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 7.50/7.90 'tc_Lambda_OdB' ), X ), Z ) ) ) ] )
% 7.50/7.90 , clause( 81856, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'(
% 7.50/7.90 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', X ), Y ), Z ) ] )
% 7.50/7.90 , clause( 81857, [ ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 7.50/7.90 'c_Lambda_OdB_OVar'( X ) ), Y ) ) ) ] )
% 7.50/7.90 , clause( 81858, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 7.50/7.90 'c_Lambda_OdB_OAbs'( Z ) ) ] )
% 7.50/7.90 , clause( 81859, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 7.50/7.90 , clause( 81860, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 7.50/7.90 , clause( 81861, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ) ), ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y,
% 7.50/7.90 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81862, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 7.50/7.90 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ] )
% 7.50/7.90 , clause( 81863, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 7.50/7.90 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ] )
% 7.50/7.90 , clause( 81864, [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ), X ) ) ] )
% 7.50/7.90 , clause( 81865, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Z, 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ) ), ~( 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', Y, Z,
% 7.50/7.90 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81866, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3'( X ) )
% 7.50/7.90 ), ~( hBOOL( hAPP( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'(
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1'( X ) )
% 7.50/7.90 , 'c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2'( X )
% 7.50/7.90 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ] )
% 7.50/7.90 , clause( 81867, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) )
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81868, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 7.50/7.90 'c_Lambda_OdB_OVar'( X ), Y ) ] )
% 7.50/7.90 , clause( 81869, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 7.50/7.90 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81870, [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OVar'(
% 7.50/7.90 T ), U ), hAPP( X, T ) ) ] )
% 7.50/7.90 , clause( 81871, [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 7.50/7.90 , clause( 81872, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 7.50/7.90 , clause( 81873, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Olift', X ), Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X )
% 7.50/7.90 ) ) ] )
% 7.50/7.90 , clause( 81874, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z
% 7.50/7.90 ), Y ) ] )
% 7.50/7.90 , clause( 81875, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 X ) ), Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 7.50/7.90 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 7.50/7.90 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB'
% 7.50/7.90 , 'tc_Lambda_OdB' ) ) ) ) ] )
% 7.50/7.90 , clause( 81876, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__4'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__5'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 7.50/7.90 'tc_nat' ) ), 'v_sko__InductTermi__XIT__Xcases__6'( X ), 'tc_Lambda_OdB'
% 7.50/7.90 , 'tc_Lambda_OdB' ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81877, [ =( 'v_n____', 'v_i____' ) ] )
% 7.50/7.90 , clause( 81878, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 7.50/7.90 ) ) ] )
% 7.50/7.90 , clause( 81879, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X
% 7.50/7.90 ) ) ) ] )
% 7.50/7.90 , clause( 81880, [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X,
% 7.50/7.90 'c_Lambda_OdB_OVar'( Y ), Z ) ) ] )
% 7.50/7.90 , clause( 81881, [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =(
% 7.50/7.90 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), T, X, X ), hAPP( hAPP(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 7.50/7.90 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ] )
% 7.50/7.90 , clause( 81882, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), =( X, 'c_Lambda_OdB_OAbs'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X, 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81883, [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 7.50/7.90 hAPP( hAPP( 'c_Lambda_Olift', X ), Z ) ), hAPP( hAPP( 'c_Lambda_Olift', Y
% 7.50/7.90 ), Z ) ) ) ] )
% 7.50/7.90 , clause( 81884, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), T )
% 7.50/7.90 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', X ), Z ), T ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 7.50/7.90 'c_Lambda_Osubst', Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 7.50/7.90 'tc_nat', 'tc_Lambda_OdB' ) ), T, 'tc_Lambda_OdB', 'tc_nat',
% 7.50/7.90 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB'
% 7.50/7.90 , 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81885, [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_ea______',
% 7.50/7.90 'v_ia______', 'v_T____', 'tc_Type_Otype' ), 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( 'v_n____' ), 'v_rs____',
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'v_T_Ha______' ) ] )
% 7.50/7.90 , clause( 81886, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', X ), Y ), Z ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 7.50/7.90 T ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), T ) ) ) ]
% 7.50/7.90 )
% 7.50/7.90 , clause( 81887, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 7.50/7.90 'c_Lambda_OdB_OVar'( X ) ), Y ), Z ), 'c_Lambda_OdB_OVar'( X ) ), =( X, Z
% 7.50/7.90 ), 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ] )
% 7.50/7.90 , clause( 81888, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ),
% 7.50/7.90 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 7.50/7.90 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X, Y, T ), Z,
% 7.50/7.90 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), T,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 7.50/7.90 , clause( 81889, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_ua______' ) ) ] )
% 7.50/7.90 , clause( 81890, [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____'
% 7.50/7.90 , 'v_T____', 'tc_Type_Otype' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( 'v_n____' ), 'v_rs____', 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ), 'v_T_H____' ) ] )
% 7.50/7.90 , clause( 81891, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( Y ),
% 7.50/7.90 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Obeta', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ) )
% 7.50/7.90 ) ] )
% 7.50/7.90 , clause( 81892, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', T ), U ), W ), hAPP( hAPP( Y, T ), U ) ) ] )
% 7.50/7.90 , clause( 81893, [ =( hAPP( hAPP( X, Y ), 'c_List_Ofoldl'( X, Z, T, U, U )
% 7.50/7.90 ), 'c_List_Ofoldl'( X, Y, T, U, U ) ), ~( 'c_OrderedGroup_Omonoid__add'(
% 7.50/7.90 Z, X, U ) ) ] )
% 7.50/7.90 , clause( 81894, [ hBOOL( hAPP( 'c_InductTermi_OIT',
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__5'( X ) ) ), hBOOL( hAPP(
% 7.50/7.90 'c_InductTermi_OIT', 'v_sko__InductTermi__XIT__Xcases__3'( X ) ) ), =( X
% 7.50/7.90 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__2'( X ) ),
% 7.50/7.90 'v_sko__InductTermi__XIT__Xcases__1'( X ), 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81895, [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'(
% 7.50/7.90 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81896, [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z,
% 7.50/7.90 'c_Lambda_OdB_OVar'( T ), U ), hAPP( X, T ) ) ] )
% 7.50/7.90 , clause( 81897, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( hAPP(
% 7.50/7.90 hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81898, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_OCons'( Z, T, U
% 7.50/7.90 ), W, U ), 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, W, U ) ) ] )
% 7.50/7.90 , clause( 81899, [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'(
% 7.50/7.90 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81900, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, T, 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ) ), =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z,
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1'( X
% 7.50/7.90 , Y, Z, T ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), =( T,
% 7.50/7.90 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81901, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X,
% 7.50/7.90 Y ) ) ] )
% 7.50/7.90 , clause( 81902, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 7.50/7.90 'c_Lambda_OdB_OAbs'( X ), Y ) ] )
% 7.50/7.90 , clause( 81903, [ =( 'v_rs____', 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81904, [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', T ), U ), W ), hAPP( hAPP( hAPP( hAPP( Y, T ), U ),
% 7.50/7.90 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, W ) ), 'c_Lambda_OdB_OdB__rec'( X, Y
% 7.50/7.90 , Z, U, W ) ) ) ] )
% 7.50/7.90 , clause( 81905, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2'( X ),
% 7.50/7.90 'c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1'( X ),
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81906, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 7.50/7.90 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81907, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 7.50/7.90 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 7.50/7.90 , clause( 81908, [ 'c_Type_Otypings'( X, Y,
% 7.50/7.90 'c_Type_Osko__Type__Xvar__app__types__1__1'( Z, T, X, Y ) ), ~(
% 7.50/7.90 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ) ),
% 7.50/7.90 ~( 'c_Type_Otypings'( X, W, V0 ) ), ~( 'c_Type_Otyping'( X,
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 7.50/7.90 , clause( 81909, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X
% 7.50/7.90 ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81910, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z
% 7.50/7.90 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', Y ), Z ) ) ) ] )
% 7.50/7.90 , clause( 81911, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y
% 7.50/7.90 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ] )
% 7.50/7.90 , clause( 81912, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ] )
% 7.50/7.90 , clause( 81913, [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp'
% 7.50/7.90 , Y ), Z ), T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y
% 7.50/7.90 , T ) ), 'c_Lambda_Oliftn'( X, Z, T ) ) ) ] )
% 7.50/7.90 , clause( 81914, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Olift', X ), Y ) ), Z ), Y ), X ) ] )
% 7.50/7.90 , clause( 81915, [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ) ] )
% 7.50/7.90 , clause( 81916, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 7.50/7.90 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 7.50/7.90 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 81917, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 7.50/7.90 'c_Lambda_OdB_OApp', X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ), ~( hBOOL( hAPP(
% 7.50/7.90 'c_InductTermi_OIT', X ) ) ) ] )
% 7.50/7.90 , clause( 81918, [ 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', X,
% 7.50/7.90 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, X, Z ),
% 7.50/7.90 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 7.50/7.90 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), X,
% 7.50/7.90 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ) ) ) ] )
% 7.50/7.90 , clause( 81919, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OAbs'( X ) ), Y ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 7.50/7.90 , clause( 81920, [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 7.50/7.90 X ), Y ), Z, T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X
% 7.50/7.90 , Z, T ) ), 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ] )
% 7.50/7.90 , clause( 81921, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Oappend'( Z, T, U ), W
% 7.50/7.90 , U ), 'c_List_Ofoldl'( X, 'c_List_Ofoldl'( X, Y, Z, W, U ), T, W, U ) )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81922, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 7.50/7.90 'c_Lambda_OdB_OVar'( Z ) ) ) ] )
% 7.50/7.90 , clause( 81923, [ =( 'v_rs____', 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81924, [ =( 'v_n____', 'v_i____' ) ] )
% 7.50/7.90 , clause( 81925, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ] )
% 7.50/7.90 , clause( 81926, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( 'v_n____' ), 'v_rs____', 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), 'v_u____' ), 'v_i____' ) ) ) ) ] )
% 7.50/7.90 , clause( 81927, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 7.50/7.90 'class_Orderings_Opreorder'( Y ) ) ] )
% 7.50/7.90 , clause( 81928, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 7.50/7.90 'class_Orderings_Oorder'( Y ) ) ] )
% 7.50/7.90 , clause( 81929, [
% 7.50/7.90 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 7.50/7.90 )
% 7.50/7.90 , clause( 81930, [
% 7.50/7.90 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 7.50/7.90 )
% 7.50/7.90 , clause( 81931, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 7.50/7.90 'tc_nat' ) ] )
% 7.50/7.90 , clause( 81932, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 7.50/7.90 'tc_nat' ) ] )
% 7.50/7.90 , clause( 81933, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81934, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 7.50/7.90 )
% 7.50/7.90 , clause( 81935, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 7.50/7.90 ] )
% 7.50/7.90 , clause( 81936, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 7.50/7.90 )
% 7.50/7.90 , clause( 81937, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 7.50/7.90 , clause( 81938, [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ] )
% 7.50/7.90 , clause( 81939, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 7.50/7.90 , clause( 81940, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 7.50/7.90 , clause( 81941, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 7.50/7.90 , clause( 81942, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 7.50/7.90 , clause( 81943, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 7.50/7.90 , clause( 81944, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 7.50/7.90 , clause( 81945, [ 'c_fequal'( X, X, Y ) ] )
% 7.50/7.90 , clause( 81946, [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ] )
% 7.50/7.90 ] ).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 subsumption(
% 7.50/7.90 clause( 178, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'(
% 7.50/7.90 X ) ), Y ), X ), Y ) ] )
% 7.50/7.90 , clause( 81850, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 7.50/7.90 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y ) ] )
% 7.50/7.90 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 7.50/7.90 )] ) ).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 subsumption(
% 7.50/7.90 clause( 201, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ),
% 7.50/7.90 Y ) ] )
% 7.50/7.90 , clause( 81874, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z
% 7.50/7.90 ), Y ) ] )
% 7.50/7.90 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 7.50/7.90 permutation( 0, [ ==>( 0, 0 )] ) ).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 eqswap(
% 7.50/7.90 clause( 82588, [ =( 'v_i____', 'v_n____' ) ] )
% 7.50/7.90 , clause( 81877, [ =( 'v_n____', 'v_i____' ) ] )
% 7.50/7.90 , 0, substitution( 0, [] )).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 subsumption(
% 7.50/7.90 clause( 204, [ =( 'v_i____', 'v_n____' ) ] )
% 7.50/7.90 , clause( 82588, [ =( 'v_i____', 'v_n____' ) ] )
% 7.50/7.90 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 eqswap(
% 7.50/7.90 clause( 82842, [ =( 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'v_rs____' ) ]
% 7.50/7.90 )
% 7.50/7.90 , clause( 81903, [ =( 'v_rs____', 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) )
% 7.50/7.90 ] )
% 7.50/7.90 , 0, substitution( 0, [] )).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 subsumption(
% 7.50/7.90 clause( 225, [ =( 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'v_rs____' ) ] )
% 7.50/7.90 , clause( 82842, [ =( 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'v_rs____' )
% 7.50/7.90 ] )
% 7.50/7.90 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 subsumption(
% 7.50/7.90 clause( 234, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ] )
% 7.50/7.90 , clause( 81912, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ] )
% 7.50/7.90 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 paramod(
% 7.50/7.90 clause( 83677, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( 'v_n____' ), 'v_rs____', 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), 'v_u____' ), 'v_n____' ) ) ) ) ] )
% 7.50/7.90 , clause( 204, [ =( 'v_i____', 'v_n____' ) ] )
% 7.50/7.90 , 0, clause( 81926, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( 'v_n____' ), 'v_rs____', 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), 'v_u____' ), 'v_i____' ) ) ) ) ] )
% 7.50/7.90 , 0, 16, substitution( 0, [] ), substitution( 1, [] )).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 subsumption(
% 7.50/7.90 clause( 243, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( 'v_n____' ), 'v_rs____', 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), 'v_u____' ), 'v_n____' ) ) ) ) ] )
% 7.50/7.90 , clause( 83677, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 7.50/7.90 'c_Lambda_Osubst', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.90 'c_Lambda_OdB_OVar'( 'v_n____' ), 'v_rs____', 'tc_Lambda_OdB',
% 7.50/7.90 'tc_Lambda_OdB' ) ), 'v_u____' ), 'v_n____' ) ) ) ) ] )
% 7.50/7.90 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 eqswap(
% 7.50/7.90 clause( 83679, [ =( Y, 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T,
% 7.50/7.90 Z ) ) ] )
% 7.50/7.90 , clause( 201, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z )
% 7.50/7.90 , Y ) ] )
% 7.50/7.90 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 7.50/7.90 ).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 paramod(
% 7.50/7.90 clause( 83680, [ =( X, 'c_List_Ofoldl'( Y, X, 'v_rs____', Z,
% 7.50/7.90 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , clause( 225, [ =( 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'v_rs____' ) ]
% 7.50/7.90 )
% 7.50/7.90 , 0, clause( 83679, [ =( Y, 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z )
% 7.50/7.90 , T, Z ) ) ] )
% 7.50/7.90 , 0, 5, substitution( 0, [] ), substitution( 1, [ :=( X, Y ), :=( Y, X ),
% 7.50/7.90 :=( Z, 'tc_Lambda_OdB' ), :=( T, Z )] )).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 eqswap(
% 7.50/7.90 clause( 83681, [ =( 'c_List_Ofoldl'( Y, X, 'v_rs____', Z, 'tc_Lambda_OdB' )
% 7.50/7.90 , X ) ] )
% 7.50/7.90 , clause( 83680, [ =( X, 'c_List_Ofoldl'( Y, X, 'v_rs____', Z,
% 7.50/7.90 'tc_Lambda_OdB' ) ) ] )
% 7.50/7.90 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 subsumption(
% 7.50/7.90 clause( 70485, [ =( 'c_List_Ofoldl'( X, Y, 'v_rs____', Z, 'tc_Lambda_OdB' )
% 7.50/7.90 , Y ) ] )
% 7.50/7.90 , clause( 83681, [ =( 'c_List_Ofoldl'( Y, X, 'v_rs____', Z, 'tc_Lambda_OdB'
% 7.50/7.90 ), X ) ] )
% 7.50/7.90 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 7.50/7.90 permutation( 0, [ ==>( 0, 0 )] ) ).
% 7.50/7.90
% 7.50/7.90
% 7.50/7.90 paramod(
% 7.50/7.90 clause( 83684, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 7.50/7.91 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( 'v_n____' ) ), 'v_u____' ),
% 7.50/7.91 'v_n____' ) ) ) ) ] )
% 7.50/7.91 , clause( 70485, [ =( 'c_List_Ofoldl'( X, Y, 'v_rs____', Z, 'tc_Lambda_OdB'
% 7.50/7.91 ), Y ) ] )
% 7.50/7.91 , 0, clause( 243, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 7.50/7.91 'c_Lambda_Osubst', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 7.50/7.91 'c_Lambda_OdB_OVar'( 'v_n____' ), 'v_rs____', 'tc_Lambda_OdB',
% 7.50/7.91 'tc_Lambda_OdB' ) ), 'v_u____' ), 'v_n____' ) ) ) ) ] )
% 7.50/7.91 , 0, 8, substitution( 0, [ :=( X, 'c_Lambda_OdB_OApp' ), :=( Y,
% 7.50/7.91 'c_Lambda_OdB_OVar'( 'v_n____' ) ), :=( Z, 'tc_Lambda_OdB' )] ),
% 7.50/7.91 substitution( 1, [] )).
% 7.50/7.91
% 7.50/7.91
% 7.50/7.91 paramod(
% 7.50/7.91 clause( 83685, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ) ] )
% 7.50/7.91 , clause( 178, [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 7.50/7.91 'c_Lambda_OdB_OVar'( X ) ), Y ), X ), Y ) ] )
% 7.50/7.91 , 0, clause( 83684, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( hAPP(
% 7.50/7.91 'c_Lambda_Osubst', 'c_Lambda_OdB_OVar'( 'v_n____' ) ), 'v_u____' ),
% 7.50/7.91 'v_n____' ) ) ) ) ] )
% 7.50/7.91 , 0, 4, substitution( 0, [ :=( X, 'v_n____' ), :=( Y, 'v_u____' )] ),
% 7.50/7.91 substitution( 1, [] )).
% 7.50/7.91
% 7.50/7.91
% 7.50/7.91 resolution(
% 7.50/7.91 clause( 83686, [] )
% 7.50/7.91 , clause( 83685, [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ) ]
% 7.50/7.91 )
% 7.50/7.91 , 0, clause( 234, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ] )
% 7.50/7.91 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 7.50/7.91
% 7.50/7.91
% 7.50/7.91 subsumption(
% 7.50/7.91 clause( 81628, [] )
% 7.50/7.91 , clause( 83686, [] )
% 7.50/7.91 , substitution( 0, [] ), permutation( 0, [] ) ).
% 7.50/7.91
% 7.50/7.91
% 7.50/7.91 end.
% 7.50/7.91
% 7.50/7.91 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 7.50/7.91
% 7.50/7.91 Memory use:
% 7.50/7.91
% 7.50/7.91 space for terms: 2490007
% 7.50/7.91 space for clauses: 3715982
% 7.50/7.91
% 7.50/7.91
% 7.50/7.91 clauses generated: 378654
% 7.50/7.91 clauses kept: 81629
% 7.50/7.91 clauses selected: 806
% 7.50/7.91 clauses deleted: 2265
% 7.50/7.91 clauses inuse deleted: 3
% 7.50/7.91
% 7.50/7.91 subsentry: 1413810
% 7.50/7.91 literals s-matched: 907393
% 7.50/7.91 literals matched: 841616
% 7.50/7.91 full subsumption: 455060
% 7.50/7.91
% 7.50/7.91 checksum: 1331226315
% 7.50/7.91
% 7.50/7.91
% 7.50/7.91 Bliksem ended
%------------------------------------------------------------------------------