TSTP Solution File: LCL854-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL854-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 07:58:49 EDT 2022
% Result : Unsatisfiable 0.79s 1.20s
% Output : Refutation 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL854-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n015.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 : Sat Jul 2 18:26:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.79/1.19 *** allocated 10000 integers for termspace/termends
% 0.79/1.19 *** allocated 10000 integers for clauses
% 0.79/1.19 *** allocated 10000 integers for justifications
% 0.79/1.19 Bliksem 1.12
% 0.79/1.19
% 0.79/1.19
% 0.79/1.19 Automatic Strategy Selection
% 0.79/1.19
% 0.79/1.19 Clauses:
% 0.79/1.19 [
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.79/1.19 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.19 'c_Predicate_Oconversep'( X, Y, Y ), Y ), T ), Z ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.19 'c_Predicate_Oconversep'( X, Y, Y ), Y ), Z ), T ) ), ~( hBOOL( hAPP(
% 0.79/1.19 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), T ), Z ) ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.79/1.19 ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 0.79/1.19 ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.79/1.19 ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.79/1.19 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.79/1.19 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.79/1.19 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.79/1.19 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.79/1.19 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.79/1.19 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__types__1__1'(
% 0.79/1.19 Z, T, X, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ), T ) ), ~( 'c_Type_Otypings'( X, W, V0 ) ), ~(
% 0.79/1.19 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.79/1.19 , Z ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.79/1.19 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.79/1.19 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.19 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.79/1.19 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.79/1.19 , X ), X ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.79/1.19 , X ), X ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.79/1.19 Y ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.79/1.19 Y ) ],
% 0.79/1.19 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.79/1.19 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 0.79/1.19 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.79/1.19 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.79/1.19 Y ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.79/1.19 Y ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.79/1.19 Y ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.79/1.19 Y ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.79/1.19 Y ) ],
% 0.79/1.19 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.79/1.19 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 0.79/1.19 Y ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.79/1.19 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.79/1.19 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.79/1.19 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.79/1.19 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.79/1.19 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.79/1.19 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.19 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 0.79/1.19 ,
% 0.79/1.19 [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T ), Z ) ],
% 0.79/1.19 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeE__1__1'(
% 0.79/1.19 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.79/1.19 ,
% 0.79/1.19 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.79/1.19 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.79/1.19 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.19 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T ), U ) ),
% 0.79/1.19 ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.19 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T ), U ) ),
% 0.79/1.19 ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.19 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.19 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.79/1.19 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.19 X ), Y ), Z ) ), T ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.19 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.19 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.79/1.19 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.79/1.19 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.19 X ), Y ), Z ) ), T ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.79/1.19 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.79/1.19 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.79/1.19 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.79/1.19 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.19 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.79/1.19 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.79/1.19 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.79/1.19 ,
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.79/1.19 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.79/1.19 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.79/1.19 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.79/1.19 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.79/1.19 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.79/1.19 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.19 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.79/1.19 [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.79/1.19 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.79/1.19 ,
% 0.79/1.19 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.19 'c_Transitive__Closure_Ortranclp'( X, Z ), Y ), T ) ) ), ~(
% 0.79/1.19 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.79/1.19 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( 'c_Wellfounded_Oaccp'( X, T, Z )
% 0.79/1.19 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Z ), Y )
% 0.79/1.19 , T ) ) ) ],
% 0.79/1.19 [ 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ), ~( hBOOL( hAPP(
% 0.79/1.19 'c_InductTermi_OIT', X ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', X ) ), ~( 'c_Wellfounded_Oaccp'(
% 0.79/1.19 'c_Predicate_Oconversep'( 'c_Lambda_Obeta', 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.79/1.19 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 0.79/1.19 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.79/1.19 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 0.79/1.19 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 0.79/1.19 ) ) ) ],
% 0.79/1.19 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.79/1.19 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.79/1.19 Y ) ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.79/1.19 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.79/1.19 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.79/1.19 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.79/1.19 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.79/1.19 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 0.79/1.19 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.19 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.79/1.19 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 0.79/1.19 ,
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.79/1.19 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.79/1.19 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 0.79/1.19 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.79/1.19 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.79/1.19 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.79/1.19 ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( 'c_List_Ofoldr'(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), 'c_List_Ofoldl'(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ],
% 0.79/1.19 [ ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_ONil'( Y ), Z, Y ) ) ],
% 0.79/1.19 [ ~( 'c_ListOrder_Ostep1'( X, Y, 'c_List_Olist_ONil'( Z ), Z ) ) ],
% 0.79/1.19 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.79/1.19 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.79/1.19 ,
% 0.79/1.19 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), Y ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.79/1.19 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.79/1.19 [ =( 'c_Predicate_Oconversep'( 'c_fequal'( X ), X, X ), 'c_fequal'( X )
% 0.79/1.19 ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 0.79/1.19 ,
% 0.79/1.19 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.19 'tc_nat' ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.79/1.19 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.19 X ), X ) ) ],
% 0.79/1.19 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.79/1.19 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.79/1.19 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.79/1.19 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.79/1.19 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.79/1.19 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.79/1.19 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.79/1.19 'c_lessequals'( Y, T, X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.79/1.19 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.79/1.19 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.79/1.19 'c_lessequals'( Z, T, X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.79/1.19 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.79/1.19 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.79/1.19 'c_lessequals'( Y, T, X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.79/1.19 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.79/1.19 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.79/1.19 'c_lessequals'( Z, T, X ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.79/1.19 'c_Lambda_OdB_OApp', X ), Y ), Z ) ],
% 0.79/1.19 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 0.79/1.19 ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.19 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.79/1.19 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.79/1.19 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeD__1__1'(
% 0.79/1.19 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.79/1.19 ,
% 0.79/1.19 [ =( 'c_Predicate_Oconversep'( 'c_Predicate_Oconversep'( X, Y, Z ), Z, Y
% 0.79/1.19 ), X ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.79/1.19 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.79/1.19 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.79/1.19 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.79/1.19 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.79/1.19 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.79/1.19 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.79/1.19 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.79/1.19 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.79/1.19 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.79/1.19 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.79/1.19 ,
% 0.79/1.19 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.79/1.19 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 0.79/1.19 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 0.79/1.19 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.79/1.19 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.79/1.19 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 0.79/1.19 [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.79/1.19 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.79/1.19 ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.79/1.19 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.79/1.19 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) )
% 0.79/1.19 ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.79/1.19 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.79/1.19 'c_lessequals'( Z, Y, X ) ],
% 0.79/1.19 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) )
% 0.79/1.19 ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.79/1.19 ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.19 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.79/1.19 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), U )
% 0.79/1.19 , T ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ) ],
% 0.79/1.19 [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OAbs'( X ) ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Lambda_OdB_OdB__size'( X ) ),
% 0.79/1.19 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.79/1.19 [ =( 'c_Lambda_OdB_OdB__size'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y )
% 0.79/1.19 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Lambda_OdB_OdB__size'( X ) ),
% 0.79/1.19 'c_Lambda_OdB_OdB__size'( Y ) ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.19 'tc_nat' ) ) ) ) ],
% 0.79/1.19 [ =( 'c_Lambda_Osubst'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 0.79/1.19 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Z, T ) ),
% 0.79/1.19 'c_Lambda_Osubst'( Y, Z, T ) ) ) ],
% 0.79/1.19 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__typesE__1__1'(
% 0.79/1.19 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ), Z ) ) ],
% 0.79/1.19 [ =( 'c_Nat_Osize__class_Osize'( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y
% 0.79/1.19 ), 'tc_Type_Otype' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.79/1.19 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.19 'c_Nat_Osize__class_Osize'( X, 'tc_Type_Otype' ) ),
% 0.79/1.19 'c_Nat_Osize__class_Osize'( Y, 'tc_Type_Otype' ) ) ), 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.79/1.19 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.79/1.19 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.79/1.19 [ =( X, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.79/1.19 'c_Type_Osko__Type__Xvar__app__types__1__1'( Y, X, Z, T ), Y,
% 0.79/1.19 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( Z,
% 0.79/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ), ~( 'c_Type_Otypings'( Z, W, V0
% 0.79/1.19 ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.79/1.19 , Y ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.79/1.19 , 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~(
% 0.79/1.19 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.79/1.19 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.79/1.19 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.79/1.19 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.79/1.19 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.79/1.19 ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 0.79/1.19 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.19 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.79/1.19 [ =( 'c_Type_Otype_Otype__size'( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y
% 0.79/1.19 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Type_Otype_Otype__size'( X ) )
% 0.79/1.19 , 'c_Type_Otype_Otype__size'( Y ) ) ), 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.79/1.19 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 0.79/1.19 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 0.79/1.19 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X
% 0.79/1.19 ), 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), X, X ) ) ],
% 0.79/1.19 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.79/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Z, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ) ) ), ~( 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', Y, Z,
% 0.79/1.19 'tc_Lambda_OdB' ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.79/1.19 , 'tc_Lambda_OdB' ), 'c_Lambda_Olift'( X, Y ) ), 'c_Lambda_Olift'( Z, Y )
% 0.79/1.19 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.19 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.19 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.79/1.19 'tc_Lambda_OdB' ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Olift'( X, Y ) ) ), ~(
% 0.79/1.19 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.79/1.19 ), ~( hBOOL( hAPP( hAPP( X, Z ), T ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.79/1.19 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.79/1.19 , 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ), 'c_Lambda_Osubst'( X
% 0.79/1.19 , T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.19 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y ), T ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.79/1.19 , 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ), 'c_Lambda_Osubst'( T
% 0.79/1.19 , Y, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.19 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), T ) ) ) ],
% 0.79/1.19 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.79/1.19 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.79/1.19 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.79/1.19 [ =( 'c_Lambda_Olift'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z ),
% 0.79/1.19 hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Olift'( X, Z ) ),
% 0.79/1.19 'c_Lambda_Olift'( Y, Z ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.79/1.19 , 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ), 'c_Lambda_Osubst'( X
% 0.79/1.19 , T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', Y ), T ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.79/1.19 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.79/1.19 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X, Y, T ), Z,
% 0.79/1.19 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.79/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ), Z ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.79/1.19 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), U )
% 0.79/1.19 , T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.79/1.19 ), Z ), U ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), Z )
% 0.79/1.19 ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), Z )
% 0.79/1.19 ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.79/1.19 'c_Lambda_Osubst'( T, Y, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta'
% 0.79/1.19 , X ), T ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.79/1.19 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.79/1.19 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.79/1.19 [ ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.79/1.19 , 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z,
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ), ~(
% 0.79/1.19 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB' ) ),
% 0.79/1.19 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.79/1.19 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, Z,
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ), ~( 'c_Type_Otypings'( X, Z, U )
% 0.79/1.19 ), ~( 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun', U, T
% 0.79/1.19 , 'tc_Type_Otype', 'tc_Type_Otype' ) ) ) ],
% 0.79/1.19 [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.19 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.79/1.19 [ =( 'c_Nat_Osize__class_Osize'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y
% 0.79/1.19 ), 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.79/1.19 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.19 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ),
% 0.79/1.19 'c_Nat_Osize__class_Osize'( Y, 'tc_Lambda_OdB' ) ) ), 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.79/1.19 [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.19 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.79/1.19 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP( hAPP(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 0.79/1.19 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.79/1.19 ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.79/1.19 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.79/1.19 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.79/1.19 [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OAbs'( X ),
% 0.79/1.19 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.19 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ), 'c_Suc'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.79/1.19 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X ) ],
% 0.79/1.19 [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.79/1.19 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.79/1.19 ), 'c_Lambda_OdB_OAbs'( X ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Olift'( X, Y ) ),
% 0.79/1.19 'c_Lambda_Olift'( Z, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X )
% 0.79/1.19 , Z ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.19 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.79/1.19 'tc_Lambda_OdB' ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.79/1.19 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X, Y, T ), Z,
% 0.79/1.19 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.79/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ), Z ) ) ],
% 0.79/1.19 [ 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', X,
% 0.79/1.19 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, X, Z ),
% 0.79/1.19 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.79/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), X,
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.79/1.19 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.79/1.19 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 0.79/1.19 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.79/1.19 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.79/1.19 [ =( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.19 'c_Transitive__Closure_Ortranclp'( X, Y ), Y ),
% 0.79/1.19 'c_Transitive__Closure_Ortranclp'( X, Y ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OVar'(
% 0.79/1.19 Z ) ) ) ],
% 0.79/1.19 [ =( 'c_Type_Otype_Otype__case'( X, Y, 'c_Type_Otype_OAtom'( Z ), T ),
% 0.79/1.19 hAPP( X, Z ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'( X ) ),
% 0.79/1.19 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X )
% 0.79/1.19 , Y ) ) ) ],
% 0.79/1.19 [ =( X, 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'(
% 0.79/1.19 Y, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'(
% 0.79/1.19 Y ) ), X ) ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y )
% 0.79/1.19 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.79/1.19 [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 0.79/1.19 X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'( X,
% 0.79/1.19 'c_Lambda_Osubst'( U, Y, T ), W ) ],
% 0.79/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.79/1.19 , 'c_Lambda_OdB_OVar'( Y ) ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.79/1.19 ) ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Type_Otyping'( X, T, Z ) ), ~(
% 0.79/1.19 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.79/1.19 'tc_Lambda_OdB' ), T ), Y ) ) ) ],
% 0.79/1.19 [ =( 'c_Type_Otype_Otype__size'( 'c_Type_Otype_OAtom'( X ) ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.79/1.19 X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP(
% 0.79/1.19 hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.79/1.19 X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP(
% 0.79/1.19 hAPP( 'c_Lambda_Obeta', Y ), Z ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.79/1.19 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.79/1.19 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.19 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.79/1.19 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.19 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X ) ) ), ~(
% 0.79/1.19 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.79/1.19 [ ~( hBOOL( hAPP( X, 'c_Type_Otype_Otype__case'( Y, Z,
% 0.79/1.19 'c_Type_Otype_OAtom'( T ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, T ) )
% 0.79/1.19 ) ],
% 0.79/1.19 [ ~( hBOOL( hAPP( X, 'c_Type_Otype_Otype__case'( Y, Z,
% 0.79/1.19 'c_Type_Otype_OAtom'( T ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, T ) )
% 0.79/1.19 ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.79/1.19 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.79/1.19 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.19 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.79/1.19 ), Z ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.79/1.19 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.79/1.19 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.19 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.79/1.19 ), Z ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.19 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 0.79/1.19 , Y ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.79/1.19 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.19 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.79/1.19 'c_Type_Osko__Type__Xtype__induct__1__1'( X ) ) ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.79/1.19 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.79/1.19 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.79/1.19 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.19 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( X, Y, 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z,
% 0.79/1.19 X, T, Y ) ), ~( 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', T )
% 0.79/1.19 , Y ), Z ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.19 'tc_nat' ), 'c_Type_Osko__Type__Xtyping__elims__3__1'( Y, X, Z ),
% 0.79/1.19 'tc_Type_Otype' ), Z, 'c_Type_Osko__Type__Xtyping__elims__3__2'( Y, X, Z
% 0.79/1.19 ) ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Z ), Y ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_ta____' ) ) ],
% 0.79/1.19 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ),
% 0.79/1.19 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.19 'c_Lambda_Obeta', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.19 'c_Lambda_OdB_OVar'( Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ) )
% 0.79/1.19 ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.79/1.19 , 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ), 'c_Lambda_OdB_OAbs'( Y )
% 0.79/1.19 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.19 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Y ) ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), 'c_List_Ofoldr'(
% 0.79/1.19 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X,
% 0.79/1.19 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.79/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), T,
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ],
% 0.79/1.19 [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OVar'( X ) ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.19 'tc_nat' ), 'c_Type_Osko__Type__Xabs__typeE__1__1'( X, Y ),
% 0.79/1.19 'tc_Type_Otype' ), Y, 'c_Type_Osko__Type__Xabs__typeE__1__2'( X, Y ) ),
% 0.79/1.19 ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ) ) ],
% 0.79/1.19 [ ~( =( 'c_Type_Otype_OAtom'( X ), 'c_Type_Otype_OAtom'( Y ) ) ), =( X,
% 0.79/1.19 Y ) ],
% 0.79/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X ) ) ) ],
% 0.79/1.19 [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 0.79/1.19 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 0.79/1.19 'c_Suc'( Y ), Z, T ) ) ],
% 0.79/1.19 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.79/1.19 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.79/1.19 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.79/1.19 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.79/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ) ) ) ) ],
% 0.79/1.19 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ],
% 0.79/1.19 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.79/1.19 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.79/1.19 ) ],
% 0.79/1.19 [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.79/1.19 Z ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.19 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OVar'( X )
% 0.79/1.19 , Y ) ],
% 0.79/1.19 [ =( 'c_Type_Otype_Otype__rec'( X, Y, 'c_Type_Otype_OAtom'( Z ), T ),
% 0.79/1.19 hAPP( X, Z ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.79/1.19 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) )
% 0.79/1.19 ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.79/1.19 'c_Lambda_OdB_OAbs'( X ) ), Y ) ), 'c_Lambda_Osubst'( X, Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.79/1.19 [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ), X ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.79/1.19 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.79/1.19 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 0.79/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.79/1.19 , 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ),
% 0.79/1.19 ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y, 'tc_Lambda_OdB' ) ) ],
% 0.79/1.19 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.79/1.19 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.79/1.19 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.79/1.19 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.79/1.19 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.79/1.19 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 0.79/1.19 [ ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.79/1.19 ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ),
% 0.79/1.19 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'( X, Y ) ) ), ~( hBOOL( hAPP(
% 0.79/1.19 hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'( X ) ), Y ) ) ) ],
% 0.79/1.19 [ =( 'c_Nat_Osize__class_Osize'( 'c_Type_Otype_OAtom'( X ),
% 0.79/1.19 'tc_Type_Otype' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.79/1.19 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.79/1.19 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.79/1.19 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.79/1.19 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.79/1.19 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.79/1.19 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.79/1.19 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( X,
% 0.79/1.19 'c_Lambda_OdB_OVar'( Y ), Z ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.79/1.19 ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.79/1.19 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.79/1.19 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.79/1.19 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.79/1.19 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.79/1.19 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.79/1.19 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.79/1.19 Z ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.79/1.19 ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 0.79/1.19 Z ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.79/1.19 [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OVar'( X ),
% 0.79/1.19 'tc_Lambda_OdB' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( X, Y, Z ) ) ),
% 0.79/1.19 ~( 'c_Type_Otyping'( T, Y, U ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', Y
% 0.79/1.19 ) ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( T, Z, U, 'tc_Type_Otype' )
% 0.79/1.19 , X, W ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ),
% 0.79/1.19 'c_Lambda_Olift'( T, Y ), U ), ~( 'c_Type_Otyping'( X, T, U ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), 'c_Type_Otype_OAtom'(
% 0.79/1.19 Z ) ) ) ],
% 0.79/1.19 [ =( X, hAPP( hAPP( 'c_Type_Otype_OFun',
% 0.79/1.19 'c_Type_Osko__Type__Xtyping__elims__3__1'( X, Y, Z ) ),
% 0.79/1.19 'c_Type_Osko__Type__Xtyping__elims__3__2'( X, Y, Z ) ) ), ~(
% 0.79/1.19 'c_Type_Otyping'( Y, 'c_Lambda_OdB_OAbs'( Z ), X ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', T
% 0.79/1.19 ), Y ) ) ), ~( 'c_Type_Otyping'( X, T, Z ) ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP( hAPP(
% 0.79/1.19 'c_Type_Otype_OFun', Z ), T ) ) ), =( X, Z ) ],
% 0.79/1.19 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP( hAPP(
% 0.79/1.19 'c_Type_Otype_OFun', Z ), T ) ) ), =( Y, T ) ],
% 0.79/1.19 [ ~( =( 'c_Type_Osko__Type__Xtype__induct__1__1'( X ), hAPP( hAPP(
% 0.79/1.19 'c_Type_Otype_OFun', Y ), Z ) ) ), hBOOL( hAPP( X, T ) ), hBOOL( hAPP( X
% 0.79/1.19 , Z ) ) ],
% 0.79/1.19 [ ~( =( 'c_Type_Osko__Type__Xtype__induct__1__1'( X ), hAPP( hAPP(
% 0.79/1.19 'c_Type_Otype_OFun', Y ), Z ) ) ), hBOOL( hAPP( X, T ) ), hBOOL( hAPP( X
% 0.79/1.19 , Y ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T ),
% 0.79/1.19 ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y, hAPP( hAPP(
% 0.79/1.19 'c_Type_Otype_OFun', U ), T ) ) ) ],
% 0.79/1.19 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_s____' ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), hAPP( hAPP(
% 0.79/1.19 'c_Type_Otype_OFun', Z ), T ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( X
% 0.79/1.19 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_Type_Otype' ), Y, T ) )
% 0.79/1.19 ],
% 0.79/1.19 [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y )
% 0.79/1.19 , Z ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( 'v_ea____', 'v_ta____', 'v_Ta____' ) ],
% 0.79/1.19 [ =( 'c_Type_Otype_Otype__rec'( X, Y, hAPP( hAPP( 'c_Type_Otype_OFun', Z
% 0.79/1.19 ), T ), U ), hAPP( hAPP( hAPP( hAPP( Y, Z ), T ),
% 0.79/1.19 'c_Type_Otype_Otype__rec'( X, Y, Z, U ) ), 'c_Type_Otype_Otype__rec'( X,
% 0.79/1.19 Y, T, U ) ) ) ],
% 0.79/1.19 [ =( 'c_Type_Otype_Otype__case'( X, Y, hAPP( hAPP( 'c_Type_Otype_OFun',
% 0.79/1.19 Z ), T ), U ), hAPP( hAPP( Y, Z ), T ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( 'v_ea____', 'v_s____', hAPP( hAPP(
% 0.79/1.19 'c_Type_Otype_OFun', 'v_Ta____' ), 'v_U____' ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y ) ) ],
% 0.79/1.19 [ ~( hBOOL( hAPP( X, 'c_Type_Otype_Otype__case'( Y, Z, hAPP( hAPP(
% 0.79/1.19 'c_Type_Otype_OFun', T ), U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.79/1.19 Z, T ), U ) ) ) ],
% 0.79/1.19 [ ~( hBOOL( hAPP( X, 'c_Type_Otype_Otype__case'( Y, Z, hAPP( hAPP(
% 0.79/1.19 'c_Type_Otype_OFun', T ), U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.79/1.19 Z, T ), U ) ) ) ],
% 0.79/1.19 [ ~( =( 'c_Type_Otype_OAtom'( X ), hAPP( hAPP( 'c_Type_Otype_OFun', Y )
% 0.79/1.19 , Z ) ) ) ],
% 0.79/1.19 [ 'c_Type_Otyping'( X, Y, hAPP( hAPP( 'c_Type_Otype_OFun',
% 0.79/1.19 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, Y, T ) ), Z ) ), ~(
% 0.79/1.19 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), T ), Z ) ) ]
% 0.79/1.19 ,
% 0.79/1.19 [ ~( 'c_Type_Otyping'( 'v_ea____', 'v_s____', hAPP( hAPP(
% 0.79/1.19 'c_Type_Otype_OFun', 'v_Ta____' ), 'v_U____' ) ) ) ],
% 0.79/1.19 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.79/1.19 'class_Orderings_Opreorder'( Y ) ) ],
% 0.79/1.19 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.79/1.19 'class_Orderings_Oorder'( Y ) ) ],
% 0.79/1.19 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.79/1.19 ) ],
% 0.79/1.19 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 0.79/1.19 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 0.79/1.19 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 0.79/1.19 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 0.79/1.19 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 0.79/1.19 ] .
% 0.79/1.19
% 0.79/1.19
% 0.79/1.19 percentage equality = 0.361854, percentage horn = 0.952381
% 0.79/1.19 This is a problem with some equality
% 0.79/1.19
% 0.79/1.19
% 0.79/1.19
% 0.79/1.19 Options Used:
% 0.79/1.19
% 0.79/1.19 useres = 1
% 0.79/1.19 useparamod = 1
% 0.79/1.19 useeqrefl = 1
% 0.79/1.19 useeqfact = 1
% 0.79/1.19 usefactor = 1
% 0.79/1.19 usesimpsplitting = 0
% 0.79/1.19 usesimpdemod = 5
% 0.79/1.19 usesimpres = 3
% 0.79/1.19
% 0.79/1.19 resimpinuse = 1000
% 0.79/1.19 resimpclauses = 20000
% 0.79/1.19 substype = eqrewr
% 0.79/1.19 backwardsubs = 1
% 0.79/1.19 selectoldest = 5
% 0.79/1.19
% 0.79/1.19 litorderings [0] = split
% 0.79/1.19 litorderings [1] = extend the termordering, first sorting on arguments
% 0.79/1.19
% 0.79/1.19 termordering = kbo
% 0.79/1.19
% 0.79/1.19 litapriori = 0
% 0.79/1.19 termapriori = 1
% 0.79/1.19 litaposteriori = 0
% 0.79/1.19 termaposteriori = 0
% 0.79/1.19 demodaposteriori = 0
% 0.79/1.19 ordereqreflfact = 0
% 0.79/1.19
% 0.79/1.19 litselect = negord
% 0.79/1.19
% 0.79/1.19 maxweight = 15
% 0.79/1.19 maxdepth = 30000
% 0.79/1.19 maxlength = 115
% 0.79/1.19 maxnrvars = 195
% 0.79/1.19 excuselevel = 1
% 0.79/1.19 increasemaxweight = 1
% 0.79/1.19
% 0.79/1.19 maxselected = 10000000
% 0.79/1.19 maxnrclauses = 10000000
% 0.79/1.19
% 0.79/1.19 showgenerated = 0
% 0.79/1.19 showkept = 0
% 0.79/1.19 showselected = 0
% 0.79/1.19 showdeleted = 0
% 0.79/1.19 showresimp = 1
% 0.79/1.19 showstatus = 2000
% 0.79/1.19
% 0.79/1.19 prologoutput = 1
% 0.79/1.19 nrgoals = 5000000
% 0.79/1.19 totalproof = 1
% 0.79/1.19
% 0.79/1.19 Symbols occurring in the translation:
% 0.79/1.19
% 0.79/1.19 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.79/1.19 . [1, 2] (w:1, o:131, a:1, s:1, b:0),
% 0.79/1.19 ! [4, 1] (w:0, o:85, a:1, s:1, b:0),
% 0.79/1.19 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.79/1.19 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.79/1.19 'c_Transitive__Closure_Ortranclp' [41, 2] (w:1, o:156, a:1, s:1, b:0)
% 0.79/1.19 ,
% 0.79/1.19 hAPP [43, 2] (w:1, o:157, a:1, s:1, b:0),
% 0.79/1.19 hBOOL [45, 1] (w:1, o:90, a:1, s:1, b:0),
% 0.79/1.19 'c_Predicate_Oconversep' [46, 3] (w:1, o:165, a:1, s:1, b:0),
% 0.79/1.19 'tc_nat' [47, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.79/1.19 'c_HOL_Oplus__class_Oplus' [48, 1] (w:1, o:92, a:1, s:1, b:0),
% 0.79/1.19 'class_Ring__and__Field_Oidom' [53, 1] (w:1, o:93, a:1, s:1, b:0),
% 0.79/1.19 'class_Int_Onumber__ring' [54, 1] (w:1, o:94, a:1, s:1, b:0),
% 0.79/1.19 'class_OrderedGroup_Ocancel__ab__semigroup__add' [55, 1] (w:1, o:96
% 0.79/1.19 , a:1, s:1, b:0),
% 0.79/1.19 'class_OrderedGroup_Ocancel__semigroup__add' [59, 1] (w:1, o:97, a:1
% 0.79/1.19 , s:1, b:0),
% 0.79/1.19 'c_Type_Osko__Type__Xvar__app__types__1__1' [64, 4] (w:1, o:176, a:1
% 0.79/1.19 , s:1, b:0),
% 0.79/1.19 'c_Type_Otypings' [65, 3] (w:1, o:168, a:1, s:1, b:0),
% 0.79/1.19 'c_Lambda_OdB_OApp' [66, 0] (w:1, o:54, a:1, s:1, b:0),
% 0.79/1.19 'c_Lambda_OdB_OVar' [68, 1] (w:1, o:98, a:1, s:1, b:0),
% 0.79/1.19 'tc_Lambda_OdB' [70, 0] (w:1, o:56, a:1, s:1, b:0),
% 0.79/1.19 'c_List_Ofoldl' [71, 5] (w:1, o:185, a:1, s:1, b:0),
% 0.79/1.19 'c_Type_Otyping' [72, 3] (w:1, o:169, a:1, s:1, b:0),
% 0.79/1.19 'c_HOL_Ozero__class_Ozero' [74, 1] (w:1, o:99, a:1, s:1, b:0),
% 0.79/1.19 'c_Suc' [75, 1] (w:1, o:100, a:1, s:1, b:0),
% 0.79/1.20 'class_Ring__and__Field_Ocomm__semiring__1' [76, 1] (w:1, o:101, a:1
% 0.79/1.20 , s:1, b:0),
% 0.79/1.20 'class_Ring__and__Field_Oordered__semidom' [78, 1] (w:1, o:104, a:1
% 0.79/1.20 , s:1, b:0),
% 0.79/1.20 'c_Nat_Osemiring__1__class_Oof__nat' [79, 2] (w:1, o:158, a:1, s:1
% 0.79/1.20 , b:0),
% 0.79/1.20 'c_lessequals' [80, 3] (w:1, o:170, a:1, s:1, b:0),
% 0.79/1.20 'class_OrderedGroup_Ocomm__monoid__add' [81, 1] (w:1, o:105, a:1, s:1
% 0.79/1.20 , b:0),
% 0.79/1.20 'class_OrderedGroup_Omonoid__add' [82, 1] (w:1, o:107, a:1, s:1, b:0)
% 0.79/1.20 ,
% 0.79/1.20 'class_Ring__and__Field_Osemiring__1' [83, 1] (w:1, o:110, a:1, s:1
% 0.79/1.20 , b:0),
% 0.79/1.20 'c_HOL_Oone__class_Oone' [84, 1] (w:1, o:91, a:1, s:1, b:0),
% 0.79/1.20 'class_Ring__and__Field_Ozero__neq__one' [85, 1] (w:1, o:111, a:1, s:
% 0.79/1.20 1, b:0),
% 0.79/1.20 'c_Power_Opower__class_Opower' [86, 3] (w:1, o:171, a:1, s:1, b:0),
% 0.79/1.20 'c_List_Olist_ONil' [89, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.79/1.20 'c_List_Ofoldr' [90, 5] (w:1, o:186, a:1, s:1, b:0),
% 0.79/1.20 'c_Type_Osko__Type__Xlist__app__typeE__1__1' [92, 4] (w:1, o:178, a:1
% 0.79/1.20 , s:1, b:0),
% 0.79/1.20 'class_OrderedGroup_Omonoid__mult' [93, 1] (w:1, o:113, a:1, s:1, b:0
% 0.79/1.20 ),
% 0.79/1.20 'class_OrderedGroup_Oab__group__add' [94, 1] (w:1, o:114, a:1, s:1
% 0.79/1.20 , b:0),
% 0.79/1.20 'class_OrderedGroup_Oab__semigroup__add' [98, 1] (w:1, o:115, a:1, s:
% 0.79/1.20 1, b:0),
% 0.79/1.20 'class_OrderedGroup_Opordered__comm__monoid__add' [99, 1] (w:1, o:116
% 0.79/1.20 , a:1, s:1, b:0),
% 0.79/1.20 'class_OrderedGroup_Olordered__ab__group__add' [100, 1] (w:1, o:106
% 0.79/1.20 , a:1, s:1, b:0),
% 0.79/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add' [101, 1] (w:1, o:
% 0.79/1.20 117, a:1, s:1, b:0),
% 0.79/1.20 'c_List_Olistsp' [103, 3] (w:1, o:172, a:1, s:1, b:0),
% 0.79/1.20 'c_Wellfounded_Oaccp' [104, 3] (w:1, o:173, a:1, s:1, b:0),
% 0.79/1.20 'c_Lambda_Obeta' [105, 0] (w:1, o:63, a:1, s:1, b:0),
% 0.79/1.20 'c_InductTermi_OIT' [106, 0] (w:1, o:64, a:1, s:1, b:0),
% 0.79/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [107, 1]
% 0.79/1.20 (w:1, o:118, a:1, s:1, b:0),
% 0.79/1.20 'class_OrderedGroup_Osemigroup__add' [108, 1] (w:1, o:119, a:1, s:1
% 0.79/1.20 , b:0),
% 0.79/1.20 'c_ListOrder_Ostep1' [111, 4] (w:1, o:179, a:1, s:1, b:0),
% 0.79/1.20 'c_fequal' [112, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.79/1.20 'class_Orderings_Oorder' [113, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.79/1.20 'class_Power_Opower' [115, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.79/1.20 'c_Type_Osko__Type__Xlist__app__typeD__1__1' [116, 4] (w:1, o:177, a:
% 0.79/1.20 1, s:1, b:0),
% 0.79/1.20 'class_Orderings_Opreorder' [117, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.79/1.20 'class_OrderedGroup_Opordered__ab__group__add' [118, 1] (w:1, o:123
% 0.79/1.20 , a:1, s:1, b:0),
% 0.79/1.20 'class_Orderings_Olinorder' [119, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.79/1.20 'c_Lambda_OdB_OAbs' [121, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.79/1.20 'c_Lambda_OdB_OdB__size' [122, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.79/1.20 'c_Lambda_Osubst' [125, 3] (w:1, o:174, a:1, s:1, b:0),
% 0.79/1.20 'c_Type_Osko__Type__Xvar__app__typesE__1__1' [126, 4] (w:1, o:180, a:
% 0.79/1.20 1, s:1, b:0),
% 0.79/1.20 'c_Type_Otype_OFun' [127, 0] (w:1, o:66, a:1, s:1, b:0),
% 0.79/1.20 'tc_Type_Otype' [130, 0] (w:1, o:67, a:1, s:1, b:0),
% 0.79/1.20 'c_Nat_Osize__class_Osize' [131, 2] (w:1, o:159, a:1, s:1, b:0),
% 0.79/1.20 'class_Ring__and__Field_Ono__zero__divisors' [133, 1] (w:1, o:103, a:
% 0.79/1.20 1, s:1, b:0),
% 0.79/1.20 'class_Ring__and__Field_Omult__zero' [134, 1] (w:1, o:102, a:1, s:1
% 0.79/1.20 , b:0),
% 0.79/1.20 'class_Ring__and__Field_Oring__1__no__zero__divisors' [135, 1] (w:1
% 0.79/1.20 , o:108, a:1, s:1, b:0),
% 0.79/1.20 'c_Type_Otype_Otype__size' [136, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.79/1.20 'c_Lambda_Olift' [139, 2] (w:1, o:160, a:1, s:1, b:0),
% 0.79/1.20 'class_Nat_Osemiring__char__0' [141, 1] (w:1, o:95, a:1, s:1, b:0),
% 0.79/1.20 'class_Ring__and__Field_Osemiring__0' [142, 1] (w:1, o:109, a:1, s:1
% 0.79/1.20 , b:0),
% 0.79/1.20 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1' [144, 3] (w:
% 0.79/1.20 1, o:175, a:1, s:1, b:0),
% 0.79/1.20 'c_Type_Otype_OAtom' [149, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.79/1.20 'c_Type_Otype_Otype__case' [150, 4] (w:1, o:183, a:1, s:1, b:0),
% 0.79/1.20 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1' [151, 2] (w:1, o:161, a:1
% 0.79/1.20 , s:1, b:0),
% 0.79/1.20 'c_Type_Oshift' [153, 4] (w:1, o:181, a:1, s:1, b:0),
% 0.79/1.20 't_a' [157, 0] (w:1, o:74, a:1, s:1, b:0),
% 0.79/1.20 'c_Type_Osko__Type__Xtype__induct__1__1' [159, 1] (w:1, o:128, a:1
% 0.79/1.20 , s:1, b:0),
% 0.79/1.20 'c_Type_Osko__Type__Xtyping__elims__2__1' [160, 4] (w:1, o:182, a:1
% 0.79/1.20 , s:1, b:0),
% 0.79/1.20 'c_Type_Osko__Type__Xtyping__elims__3__1' [161, 3] (w:1, o:166, a:1
% 0.79/1.20 , s:1, b:0),
% 0.79/1.20 'c_Type_Osko__Type__Xtyping__elims__3__2' [162, 3] (w:1, o:167, a:1
% 0.79/1.20 , s:1, b:0),
% 0.79/1.20 'v_ta____' [163, 0] (w:1, o:76, a:1, s:1, b:0),
% 0.79/1.20 'c_Type_Osko__Type__Xabs__typeE__1__1' [164, 2] (w:1, o:162, a:1, s:1
% 0.79/1.20 , b:0),
% 0.79/1.20 'c_Type_Osko__Type__Xabs__typeE__1__2' [165, 2] (w:1, o:163, a:1, s:1
% 0.79/1.20 , b:0),
% 0.79/1.20 'c_Type_Otype_Otype__rec' [167, 4] (w:1, o:184, a:1, s:1, b:0),
% 0.79/1.20 'v_s____' [175, 0] (w:1, o:75, a:1, s:1, b:0),
% 0.79/1.20 'v_ea____' [176, 0] (w:1, o:77, a:1, s:1, b:0),
% 0.79/1.20 'v_Ta____' [177, 0] (w:1, o:78, a:1, s:1, b:0),
% 0.79/1.20 'v_U____' [178, 0] (w:1, o:79, a:1, s:1, b:0),
% 0.79/1.20 'tc_fun' [183, 2] (w:1, o:164, a:1, s:1, b:0),
% 0.79/1.20 'tc_bool' [184, 0] (w:1, o:82, a:1, s:1, b:0).
% 0.79/1.20
% 0.79/1.20
% 0.79/1.20 Starting Search:
% 0.79/1.20
% 0.79/1.20
% 0.79/1.20 Bliksems!, er is een bewijs:
% 0.79/1.20 % SZS status Unsatisfiable
% 0.79/1.20 % SZS output start Refutation
% 0.79/1.20
% 0.79/1.20 clause( 215, [ 'c_Type_Otyping'( 'v_ea____', 'v_s____', hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', 'v_Ta____' ), 'v_U____' ) ) ] )
% 0.79/1.20 .
% 0.79/1.20 clause( 218, [] )
% 0.79/1.20 .
% 0.79/1.20
% 0.79/1.20
% 0.79/1.20 % SZS output end Refutation
% 0.79/1.20 found a proof!
% 0.79/1.20
% 0.79/1.20 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.79/1.20
% 0.79/1.20 initialclauses(
% 0.79/1.20 [ clause( 220, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.79/1.20 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Predicate_Oconversep'( X, Y, Y ), Y ), T ), Z ) ) ) ] )
% 0.79/1.20 , clause( 221, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Predicate_Oconversep'( X, Y, Y ), Y ), Z ), T ) ), ~( hBOOL( hAPP(
% 0.79/1.20 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), T ), Z ) ) ) ] )
% 0.79/1.20 , clause( 222, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) )
% 0.79/1.20 ), =( Y, Z ) ] )
% 0.79/1.20 , clause( 223, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) )
% 0.79/1.20 ), =( X, Z ) ] )
% 0.79/1.20 , clause( 224, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) )
% 0.79/1.20 ), =( Y, Z ) ] )
% 0.79/1.20 , clause( 225, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.79/1.20 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.79/1.20 , clause( 226, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) )
% 0.79/1.20 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.79/1.20 , clause( 227, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.79/1.20 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.79/1.20 , clause( 228, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.79/1.20 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ] )
% 0.79/1.20 , clause( 229, [ 'c_Type_Otypings'( X, Y,
% 0.79/1.20 'c_Type_Osko__Type__Xvar__app__types__1__1'( Z, T, X, Y ) ), ~(
% 0.79/1.20 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.20 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ) ),
% 0.79/1.20 ~( 'c_Type_Otypings'( X, W, V0 ) ), ~( 'c_Type_Otyping'( X,
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 0.79/1.20 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.79/1.20 , clause( 230, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y,
% 0.79/1.20 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 231, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.79/1.20 , clause( 232, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.20 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) )
% 0.79/1.20 ) ] )
% 0.79/1.20 , clause( 233, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.79/1.20 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.79/1.20 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 0.79/1.20 , clause( 234, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.79/1.20 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.79/1.20 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 0.79/1.20 , clause( 235, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.20 X ) ), Y ), Y ) ] )
% 0.79/1.20 , clause( 236, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.79/1.20 , Y ), Y ) ] )
% 0.79/1.20 , clause( 237, [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.79/1.20 , clause( 238, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ] )
% 0.79/1.20 , clause( 239, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.79/1.20 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ] )
% 0.79/1.20 , clause( 240, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.79/1.20 'class_Int_Onumber__ring'( X ) ), =( Y, hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 0.79/1.20 ] )
% 0.79/1.20 , clause( 241, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 0.79/1.20 ) ), Y ) ] )
% 0.79/1.20 , clause( 242, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.79/1.20 Y ) ] )
% 0.79/1.20 , clause( 243, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.79/1.20 Y ) ] )
% 0.79/1.20 , clause( 244, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 0.79/1.20 , clause( 245, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.20 X ) ), Y ), Y ) ] )
% 0.79/1.20 , clause( 246, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 X ), 'c_Suc'( Y ) ) ) ] )
% 0.79/1.20 , clause( 247, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.79/1.20 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.79/1.20 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ] )
% 0.79/1.20 , clause( 248, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.79/1.20 , clause( 249, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 0.79/1.20 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 250, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ] )
% 0.79/1.20 , clause( 251, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.79/1.20 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.79/1.20 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~( 'c_lessequals'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 0.79/1.20 ] )
% 0.79/1.20 , clause( 252, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.20 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.79/1.20 , clause( 253, [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T )
% 0.79/1.20 , Z ) ] )
% 0.79/1.20 , clause( 254, [ 'c_Type_Otypings'( X, Y,
% 0.79/1.20 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X, T, Y ) ), ~(
% 0.79/1.20 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', T, Y,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.79/1.20 , clause( 255, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.79/1.20 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.79/1.20 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.79/1.20 , clause( 256, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ] )
% 0.79/1.20 , clause( 257, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ] )
% 0.79/1.20 , clause( 258, [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T
% 0.79/1.20 ), U ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ] )
% 0.79/1.20 , clause( 259, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ] )
% 0.79/1.20 , clause( 260, [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T
% 0.79/1.20 ), U ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ] )
% 0.79/1.20 , clause( 261, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.79/1.20 , clause( 262, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.79/1.20 , clause( 263, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.20 X ), Y ), T ) ), Z ) ) ] )
% 0.79/1.20 , clause( 264, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.20 X ), Y ), Z ) ), T ) ) ] )
% 0.79/1.20 , clause( 265, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.79/1.20 , clause( 266, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.79/1.20 , clause( 267, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.79/1.20 , clause( 268, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ] )
% 0.79/1.20 , clause( 269, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.79/1.20 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ] )
% 0.79/1.20 , clause( 270, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.79/1.20 , clause( 271, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.20 X ), Y ), Z ) ), T ) ) ] )
% 0.79/1.20 , clause( 272, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.79/1.20 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.79/1.20 , clause( 273, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.79/1.20 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.79/1.20 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.79/1.20 , clause( 274, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.20 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 275, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.79/1.20 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.79/1.20 , clause( 276, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 0.79/1.20 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 0.79/1.20 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.79/1.20 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.79/1.20 , clause( 277, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.79/1.20 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.79/1.20 , clause( 278, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.79/1.20 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.79/1.20 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 0.79/1.20 , clause( 279, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.79/1.20 , clause( 280, [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ] )
% 0.79/1.20 , clause( 281, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.79/1.20 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.79/1.20 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.79/1.20 , clause( 282, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Transitive__Closure_Ortranclp'( X, Z ), Y ), T ) ) ), ~(
% 0.79/1.20 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 0.79/1.20 , clause( 283, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( 'c_Wellfounded_Oaccp'(
% 0.79/1.20 X, T, Z ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X,
% 0.79/1.20 Z ), Y ), T ) ) ) ] )
% 0.79/1.20 , clause( 284, [ 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'(
% 0.79/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB'
% 0.79/1.20 ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.79/1.20 , clause( 285, [ hBOOL( hAPP( 'c_InductTermi_OIT', X ) ), ~(
% 0.79/1.20 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ) ) ] )
% 0.79/1.20 , clause( 286, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.79/1.20 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 0.79/1.20 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.79/1.20 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 0.79/1.20 , clause( 287, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.79/1.20 , 'c_Suc'( Y ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.20 'tc_nat' ), X ), Y ) ) ) ] )
% 0.79/1.20 , clause( 288, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 'c_Suc'( X ) ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.20 'tc_nat' ), X ), Y ) ) ) ] )
% 0.79/1.20 , clause( 289, [ ~(
% 0.79/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.79/1.20 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 0.79/1.20 Y, T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.79/1.20 ] )
% 0.79/1.20 , clause( 290, [ ~(
% 0.79/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.79/1.20 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 0.79/1.20 Y, Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 0.79/1.20 ] )
% 0.79/1.20 , clause( 291, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.79/1.20 , clause( 292, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.79/1.20 , clause( 293, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.79/1.20 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ]
% 0.79/1.20 )
% 0.79/1.20 , clause( 294, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.79/1.20 , clause( 295, [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =(
% 0.79/1.20 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), T, X, X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ] )
% 0.79/1.20 , clause( 296, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.79/1.20 'class_Int_Onumber__ring'( X ) ), ~( =( Y, hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), =( Z,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.79/1.20 , clause( 297, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 X ), Y ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 298, [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.79/1.20 ), X ), Y ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 299, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.79/1.20 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.79/1.20 , clause( 300, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.79/1.20 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.79/1.20 , clause( 301, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 302, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 303, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.79/1.20 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.79/1.20 ) ) ] )
% 0.79/1.20 , clause( 304, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.79/1.20 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ),
% 0.79/1.20 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ] )
% 0.79/1.20 , clause( 305, [ ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_ONil'( Y ), Z, Y
% 0.79/1.20 ) ) ] )
% 0.79/1.20 , clause( 306, [ ~( 'c_ListOrder_Ostep1'( X, Y, 'c_List_Olist_ONil'( Z ), Z
% 0.79/1.20 ) ) ] )
% 0.79/1.20 , clause( 307, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 0.79/1.20 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.79/1.20 , clause( 308, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 309, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.79/1.20 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.79/1.20 )
% 0.79/1.20 , clause( 310, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z )
% 0.79/1.20 , Y ) ] )
% 0.79/1.20 , clause( 311, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.79/1.20 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 0.79/1.20 , clause( 312, [ =( 'c_Predicate_Oconversep'( 'c_fequal'( X ), X, X ),
% 0.79/1.20 'c_fequal'( X ) ) ] )
% 0.79/1.20 , clause( 313, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.79/1.20 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'(
% 0.79/1.20 X ), X ) ] )
% 0.79/1.20 , clause( 314, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.20 'tc_nat' ) ) ) ] )
% 0.79/1.20 , clause( 315, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.79/1.20 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.20 X ), X ) ) ] )
% 0.79/1.20 , clause( 316, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 0.79/1.20 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.79/1.20 , clause( 317, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 0.79/1.20 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.79/1.20 , clause( 318, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 0.79/1.20 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 0.79/1.20 , clause( 319, [ ~(
% 0.79/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.79/1.20 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.79/1.20 'c_lessequals'( Y, T, X ) ) ] )
% 0.79/1.20 , clause( 320, [ ~(
% 0.79/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.79/1.20 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 0.79/1.20 , clause( 321, [ ~(
% 0.79/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.79/1.20 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.79/1.20 'c_lessequals'( Z, T, X ) ) ] )
% 0.79/1.20 , clause( 322, [ ~(
% 0.79/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.79/1.20 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 0.79/1.20 , clause( 323, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 0.79/1.20 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 0.79/1.20 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.79/1.20 'c_lessequals'( Y, T, X ) ) ] )
% 0.79/1.20 , clause( 324, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 0.79/1.20 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 0.79/1.20 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.79/1.20 'c_lessequals'( Z, T, X ) ) ] )
% 0.79/1.20 , clause( 325, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'(
% 0.79/1.20 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.79/1.20 'c_Lambda_OdB_OApp', X ), Y ), Z ) ] )
% 0.79/1.20 , clause( 326, [ ~( 'class_Power_Opower'( X ) ), =(
% 0.79/1.20 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.79/1.20 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.79/1.20 , clause( 327, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.79/1.20 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.79/1.20 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.79/1.20 , clause( 328, [ 'c_Type_Otypings'( X, Y,
% 0.79/1.20 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X, T, Y ) ), ~(
% 0.79/1.20 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', T, Y,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.79/1.20 , clause( 329, [ =( 'c_Predicate_Oconversep'( 'c_Predicate_Oconversep'( X,
% 0.79/1.20 Y, Z ), Z, Y ), X ) ] )
% 0.79/1.20 , clause( 330, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.79/1.20 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.79/1.20 , clause( 331, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.79/1.20 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.79/1.20 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.79/1.20 , clause( 332, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z,
% 0.79/1.20 X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 0.79/1.20 , clause( 333, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.79/1.20 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 0.79/1.20 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.79/1.20 , clause( 334, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 0.79/1.20 Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 0.79/1.20 )
% 0.79/1.20 , clause( 335, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y,
% 0.79/1.20 X ) ] )
% 0.79/1.20 , clause( 336, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 0.79/1.20 Y, X ) ] )
% 0.79/1.20 , clause( 337, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.79/1.20 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 0.79/1.20 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ] )
% 0.79/1.20 , clause( 338, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.79/1.20 , clause( 339, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.79/1.20 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.79/1.20 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ] )
% 0.79/1.20 , clause( 340, [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 0.79/1.20 ), Y ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 0.79/1.20 'tc_Lambda_OdB' ) ) ] )
% 0.79/1.20 , clause( 341, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y,
% 0.79/1.20 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.79/1.20 , clause( 342, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 343, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X
% 0.79/1.20 , Y ), T ) ) ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 0.79/1.20 , clause( 344, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.79/1.20 Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 0.79/1.20 , clause( 345, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X
% 0.79/1.20 , Y ), T ) ) ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 0.79/1.20 , clause( 346, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.79/1.20 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP(
% 0.79/1.20 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ] )
% 0.79/1.20 , clause( 347, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.79/1.20 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 X, Y ), U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ) ] )
% 0.79/1.20 , clause( 348, [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OAbs'( X ) ),
% 0.79/1.20 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 'c_Lambda_OdB_OdB__size'( X ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.20 'tc_nat' ) ) ) ) ] )
% 0.79/1.20 , clause( 349, [ =( 'c_Lambda_OdB_OdB__size'( hAPP( hAPP(
% 0.79/1.20 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.20 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 'c_Lambda_OdB_OdB__size'( X ) ), 'c_Lambda_OdB_OdB__size'( Y ) ) ),
% 0.79/1.20 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.79/1.20 , clause( 350, [ =( 'c_Lambda_Osubst'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.79/1.20 , Y ), Z, T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Z,
% 0.79/1.20 T ) ), 'c_Lambda_Osubst'( Y, Z, T ) ) ) ] )
% 0.79/1.20 , clause( 351, [ 'c_Type_Otypings'( X, Y,
% 0.79/1.20 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X, T, Y ) ), ~(
% 0.79/1.20 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.20 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.79/1.20 )
% 0.79/1.20 , clause( 352, [ =( 'c_Nat_Osize__class_Osize'( hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', X ), Y ), 'tc_Type_Otype' ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Nat_Osize__class_Osize'( X,
% 0.79/1.20 'tc_Type_Otype' ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_Type_Otype' ) ) )
% 0.79/1.20 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.79/1.20 , clause( 353, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y
% 0.79/1.20 ) ] )
% 0.79/1.20 , clause( 354, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 0.79/1.20 , clause( 355, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 0.79/1.20 , clause( 356, [ =( X, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.79/1.20 'c_Type_Osko__Type__Xvar__app__types__1__1'( Y, X, Z, T ), Y,
% 0.79/1.20 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( Z,
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ), ~( 'c_Type_Otypings'( Z, W, V0
% 0.79/1.20 ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.79/1.20 , Y ) ) ] )
% 0.79/1.20 , clause( 357, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.79/1.20 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~(
% 0.79/1.20 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.79/1.20 'tc_Lambda_OdB' ), X ), Z ) ) ) ] )
% 0.79/1.20 , clause( 358, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.79/1.20 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.79/1.20 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.79/1.20 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.79/1.20 ) ) ] )
% 0.79/1.20 , clause( 359, [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.79/1.20 X ) ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.79/1.20 ) ) ] )
% 0.79/1.20 , clause( 360, [ =( 'c_Type_Otype_Otype__size'( hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', X ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.79/1.20 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 'c_Type_Otype_Otype__size'( X ) ), 'c_Type_Otype_Otype__size'( Y ) ) ),
% 0.79/1.20 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.79/1.20 , clause( 361, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.79/1.20 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.20 X ), Z, X ) ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 0.79/1.20 'c_Suc'( T ), X ), 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ),
% 0.79/1.20 X ) ) ] )
% 0.79/1.20 , clause( 362, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.79/1.20 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ), 'c_List_Ofoldr'(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.79/1.20 ) ) ] )
% 0.79/1.20 , clause( 363, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.79/1.20 ) ) ] )
% 0.79/1.20 , clause( 364, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.79/1.20 ) ) ] )
% 0.79/1.20 , clause( 365, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Z, 'tc_Lambda_OdB',
% 0.79/1.20 'tc_Lambda_OdB' ) ) ), ~( 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', Y, Z,
% 0.79/1.20 'tc_Lambda_OdB' ) ) ] )
% 0.79/1.20 , clause( 366, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Olift'( X, Y ) ),
% 0.79/1.20 'c_Lambda_Olift'( Z, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.79/1.20 ), Z ) ) ) ] )
% 0.79/1.20 , clause( 367, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 0.79/1.20 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.79/1.20 , clause( 368, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Olift'( X, Y )
% 0.79/1.20 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.79/1.20 , clause( 369, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.79/1.20 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( X, Z ), T ) ) ) ] )
% 0.79/1.20 , clause( 370, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 0.79/1.20 , clause( 371, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 0.79/1.20 , clause( 372, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.79/1.20 'c_Lambda_Osubst'( X, T, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.79/1.20 ), T ) ) ) ] )
% 0.79/1.20 , clause( 373, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.79/1.20 'c_Lambda_Osubst'( T, Y, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.79/1.20 ), T ) ) ) ] )
% 0.79/1.20 , clause( 374, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.79/1.20 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.79/1.20 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 0.79/1.20 , clause( 375, [ =( 'c_Lambda_Olift'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.79/1.20 , Y ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Olift'( X, Z ) ),
% 0.79/1.20 'c_Lambda_Olift'( Y, Z ) ) ) ] )
% 0.79/1.20 , clause( 376, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.79/1.20 'c_Lambda_Osubst'( X, T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta'
% 0.79/1.20 , Y ), T ) ) ) ] )
% 0.79/1.20 , clause( 377, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X )
% 0.79/1.20 ) ) ] )
% 0.79/1.20 , clause( 378, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X )
% 0.79/1.20 ) ) ] )
% 0.79/1.20 , clause( 379, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.79/1.20 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.79/1.20 , clause( 380, [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 0.79/1.20 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X,
% 0.79/1.20 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.79/1.20 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.79/1.20 , clause( 381, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.79/1.20 ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 X, Y ), U ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ] )
% 0.79/1.20 , clause( 382, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.79/1.20 ), Z ), Z ) ) ] )
% 0.79/1.20 , clause( 383, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.79/1.20 ), Z ), Z ) ) ] )
% 0.79/1.20 , clause( 384, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Osubst'( X
% 0.79/1.20 , Y, Z ) ), 'c_Lambda_Osubst'( T, Y, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Lambda_Obeta', X ), T ) ) ) ] )
% 0.79/1.20 , clause( 385, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.79/1.20 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.79/1.20 X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.79/1.20 , clause( 386, [ ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'(
% 0.79/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.20 'tc_nat' ) ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) )
% 0.79/1.20 , ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB' ) ),
% 0.79/1.20 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.79/1.20 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ] )
% 0.79/1.20 , clause( 387, [ 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.79/1.20 , Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ), ~( 'c_Type_Otypings'( X
% 0.79/1.20 , Z, U ) ), ~( 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 0.79/1.20 'c_Type_Otype_OFun', U, T, 'tc_Type_Otype', 'tc_Type_Otype' ) ) ) ] )
% 0.79/1.20 , clause( 388, [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'(
% 0.79/1.20 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.79/1.20 , clause( 389, [ =( 'c_Nat_Osize__class_Osize'( hAPP( hAPP(
% 0.79/1.20 'c_Lambda_OdB_OApp', X ), Y ), 'tc_Lambda_OdB' ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Nat_Osize__class_Osize'( X,
% 0.79/1.20 'tc_Lambda_OdB' ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_Lambda_OdB' ) ) )
% 0.79/1.20 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.79/1.20 , clause( 390, [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'(
% 0.79/1.20 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 0.79/1.20 , clause( 391, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.79/1.20 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP(
% 0.79/1.20 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 0.79/1.20 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.79/1.20 ) ) ) ] )
% 0.79/1.20 , clause( 392, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.79/1.20 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.79/1.20 , clause( 393, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.79/1.20 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.79/1.20 , clause( 394, [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OAbs'( X ),
% 0.79/1.20 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.79/1.20 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ), 'c_Suc'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.79/1.20 , clause( 395, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X
% 0.79/1.20 ) ] )
% 0.79/1.20 , clause( 396, [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.20 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ) ] )
% 0.79/1.20 , clause( 397, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Olift'( X,
% 0.79/1.20 Y ) ), 'c_Lambda_Olift'( Z, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Lambda_Obeta', X ), Z ) ) ) ] )
% 0.79/1.20 , clause( 398, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 0.79/1.20 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 0.79/1.20 , clause( 399, [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 0.79/1.20 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X,
% 0.79/1.20 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.79/1.20 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.79/1.20 , clause( 400, [ 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', X,
% 0.79/1.20 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, X, Z ),
% 0.79/1.20 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), X,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ) ) ) ] )
% 0.79/1.20 , clause( 401, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.79/1.20 =( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.79/1.20 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 0.79/1.20 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.79/1.20 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.79/1.20 , clause( 402, [ =( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Transitive__Closure_Ortranclp'( X, Y ), Y ),
% 0.79/1.20 'c_Transitive__Closure_Ortranclp'( X, Y ) ) ] )
% 0.79/1.20 , clause( 403, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.79/1.20 'c_Lambda_OdB_OVar'( Z ) ) ) ] )
% 0.79/1.20 , clause( 404, [ =( 'c_Type_Otype_Otype__case'( X, Y, 'c_Type_Otype_OAtom'(
% 0.79/1.20 Z ), T ), hAPP( X, Z ) ) ] )
% 0.79/1.20 , clause( 405, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'(
% 0.79/1.20 X ) ), 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Lambda_Obeta', X ), Y ) ) ) ] )
% 0.79/1.20 , clause( 406, [ =( X, 'c_Lambda_OdB_OAbs'(
% 0.79/1.20 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'( Y, X ) ) ), ~( hBOOL( hAPP(
% 0.79/1.20 hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'( Y ) ), X ) ) ) ] )
% 0.79/1.20 , clause( 407, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.79/1.20 X ) ), Y ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z
% 0.79/1.20 ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.79/1.20 , clause( 408, [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'(
% 0.79/1.20 'c_Type_Oshift'( X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'(
% 0.79/1.20 X, 'c_Lambda_Osubst'( U, Y, T ), W ) ] )
% 0.79/1.20 , clause( 409, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 0.79/1.20 'c_Lambda_OdB_OApp', X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ), ~( hBOOL( hAPP(
% 0.79/1.20 'c_InductTermi_OIT', X ) ) ) ] )
% 0.79/1.20 , clause( 410, [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Type_Otyping'( X, T, Z
% 0.79/1.20 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), T ), Y ) ) ) ] )
% 0.79/1.20 , clause( 411, [ =( 'c_Type_Otype_Otype__size'( 'c_Type_Otype_OAtom'( X ) )
% 0.79/1.20 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 412, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.79/1.20 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y
% 0.79/1.20 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ] )
% 0.79/1.20 , clause( 413, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.79/1.20 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z
% 0.79/1.20 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', Y ), Z ) ) ) ] )
% 0.79/1.20 , clause( 414, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.79/1.20 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), ~( hBOOL( hAPP(
% 0.79/1.20 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.79/1.20 'tc_Lambda_OdB' ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.79/1.20 ), Z ) ) ) ] )
% 0.79/1.20 , clause( 415, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X )
% 0.79/1.20 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 0.79/1.20 , clause( 416, [ ~( hBOOL( hAPP( X, 'c_Type_Otype_Otype__case'( Y, Z,
% 0.79/1.20 'c_Type_Otype_OAtom'( T ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, T ) )
% 0.79/1.20 ) ] )
% 0.79/1.20 , clause( 417, [ ~( hBOOL( hAPP( X, 'c_Type_Otype_Otype__case'( Y, Z,
% 0.79/1.20 'c_Type_Otype_OAtom'( T ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, T ) )
% 0.79/1.20 ) ] )
% 0.79/1.20 , clause( 418, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.79/1.20 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP(
% 0.79/1.20 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.79/1.20 'tc_Lambda_OdB' ), X ), Z ) ) ) ] )
% 0.79/1.20 , clause( 419, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.79/1.20 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP(
% 0.79/1.20 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.79/1.20 'tc_Lambda_OdB' ), Y ), Z ) ) ) ] )
% 0.79/1.20 , clause( 420, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 0.79/1.20 'c_Lambda_OdB_OAbs'( X ), Y ) ] )
% 0.79/1.20 , clause( 421, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.79/1.20 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.20 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.79/1.20 , clause( 422, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.79/1.20 'c_Type_Osko__Type__Xtype__induct__1__1'( X ) ) ) ) ] )
% 0.79/1.20 , clause( 423, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.79/1.20 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.79/1.20 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.79/1.20 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.79/1.20 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 0.79/1.20 , clause( 424, [ 'c_Type_Otyping'( X, Y,
% 0.79/1.20 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, T, Y ) ), ~(
% 0.79/1.20 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', T ), Y ), Z ) ) ]
% 0.79/1.20 )
% 0.79/1.20 , clause( 425, [ 'c_Type_Otyping'( 'c_Type_Oshift'( X,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.79/1.20 'c_Type_Osko__Type__Xtyping__elims__3__1'( Y, X, Z ), 'tc_Type_Otype' ),
% 0.79/1.20 Z, 'c_Type_Osko__Type__Xtyping__elims__3__2'( Y, X, Z ) ), ~(
% 0.79/1.20 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Z ), Y ) ) ] )
% 0.79/1.20 , clause( 426, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_ta____' ) ) ] )
% 0.79/1.20 , clause( 427, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.20 'c_Lambda_OdB_OVar'( Y ),
% 0.79/1.20 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Lambda_Obeta', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.20 'c_Lambda_OdB_OVar'( Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ) )
% 0.79/1.20 ) ] )
% 0.79/1.20 , clause( 428, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.79/1.20 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ),
% 0.79/1.20 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.79/1.20 ), Y ) ) ) ] )
% 0.79/1.20 , clause( 429, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ),
% 0.79/1.20 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.79/1.20 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X, Y, T ), Z,
% 0.79/1.20 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), T,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 0.79/1.20 , clause( 430, [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OVar'( X ) ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 431, [ 'c_Type_Otyping'( 'c_Type_Oshift'( X,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.79/1.20 'c_Type_Osko__Type__Xabs__typeE__1__1'( X, Y ), 'tc_Type_Otype' ), Y,
% 0.79/1.20 'c_Type_Osko__Type__Xabs__typeE__1__2'( X, Y ) ), ~( 'c_Type_Otyping'( X
% 0.79/1.20 , 'c_Lambda_OdB_OAbs'( Y ), Z ) ) ] )
% 0.79/1.20 , clause( 432, [ ~( =( 'c_Type_Otype_OAtom'( X ), 'c_Type_Otype_OAtom'( Y )
% 0.79/1.20 ) ), =( X, Y ) ] )
% 0.79/1.20 , clause( 433, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X )
% 0.79/1.20 ) ) ] )
% 0.79/1.20 , clause( 434, [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 0.79/1.20 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 0.79/1.20 'c_Suc'( Y ), Z, T ) ) ] )
% 0.79/1.20 , clause( 435, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.79/1.20 ) ] )
% 0.79/1.20 , clause( 436, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.79/1.20 X ) ), Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.79/1.20 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB',
% 0.79/1.20 'tc_Lambda_OdB' ) ) ) ) ] )
% 0.79/1.20 , clause( 437, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ] )
% 0.79/1.20 , clause( 438, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.20 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 0.79/1.20 , clause( 439, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.79/1.20 ), =( X, Y ) ] )
% 0.79/1.20 , clause( 440, [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP(
% 0.79/1.20 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 0.79/1.20 , clause( 441, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 0.79/1.20 'c_Lambda_OdB_OVar'( X ), Y ) ] )
% 0.79/1.20 , clause( 442, [ =( 'c_Type_Otype_Otype__rec'( X, Y, 'c_Type_Otype_OAtom'(
% 0.79/1.20 Z ), T ), hAPP( X, Z ) ) ] )
% 0.79/1.20 , clause( 443, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB',
% 0.79/1.20 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) )
% 0.79/1.20 ) ] )
% 0.79/1.20 , clause( 444, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 0.79/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ) ), 'c_Lambda_Osubst'(
% 0.79/1.20 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.79/1.20 , clause( 445, [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.79/1.20 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.79/1.20 'tc_Lambda_OdB' ), X ) ) ] )
% 0.79/1.20 , clause( 446, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.79/1.20 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ] )
% 0.79/1.20 , clause( 447, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.79/1.20 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ] )
% 0.79/1.20 , clause( 448, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 0.79/1.20 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB',
% 0.79/1.20 'tc_Lambda_OdB' ) ) ), ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y,
% 0.79/1.20 'tc_Lambda_OdB' ) ) ] )
% 0.79/1.20 , clause( 449, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.20 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 0.79/1.20 , clause( 450, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.20 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.79/1.20 , clause( 451, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.79/1.20 'c_Lambda_OdB_OAbs'( Z ) ) ] )
% 0.79/1.20 , clause( 452, [ ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.79/1.20 'c_Lambda_OdB_OVar'( X ) ), Y ) ) ) ] )
% 0.79/1.20 , clause( 453, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ),
% 0.79/1.20 'c_Lambda_Osko__Lambda__Xbeta__cases__2__1'( X, Y ) ) ), ~( hBOOL( hAPP(
% 0.79/1.20 hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'( X ) ), Y ) ) ) ] )
% 0.79/1.20 , clause( 454, [ =( 'c_Nat_Osize__class_Osize'( 'c_Type_Otype_OAtom'( X ),
% 0.79/1.20 'tc_Type_Otype' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 455, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.79/1.20 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.79/1.20 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 456, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.79/1.20 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.79/1.20 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.79/1.20 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.79/1.20 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.79/1.20 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 457, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( X,
% 0.79/1.20 'c_Lambda_OdB_OVar'( Y ), Z ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.79/1.20 ) ) ) ] )
% 0.79/1.20 , clause( 458, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.20 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 0.79/1.20 , clause( 459, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.79/1.20 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 0.79/1.20 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.79/1.20 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 0.79/1.20 , clause( 460, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP(
% 0.79/1.20 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 0.79/1.20 , clause( 461, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) )
% 0.79/1.20 ), =( X, Y ) ] )
% 0.79/1.20 , clause( 462, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.79/1.20 'c_Lambda_OdB_OAbs'( Z ) ) ) ] )
% 0.79/1.20 , clause( 463, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) )
% 0.79/1.20 ) ] )
% 0.79/1.20 , clause( 464, [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OVar'( X ),
% 0.79/1.20 'tc_Lambda_OdB' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.79/1.20 , clause( 465, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( X, Y
% 0.79/1.20 , Z ) ) ), ~( 'c_Type_Otyping'( T, Y, U ) ), ~( hBOOL( hAPP(
% 0.79/1.20 'c_InductTermi_OIT', Y ) ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( T, Z
% 0.79/1.20 , U, 'tc_Type_Otype' ), X, W ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.79/1.20 ) ) ) ] )
% 0.79/1.20 , clause( 466, [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z,
% 0.79/1.20 'tc_Type_Otype' ), 'c_Lambda_Olift'( T, Y ), U ), ~( 'c_Type_Otyping'( X
% 0.79/1.20 , T, U ) ) ] )
% 0.79/1.20 , clause( 467, [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ),
% 0.79/1.20 'c_Type_Otype_OAtom'( Z ) ) ) ] )
% 0.79/1.20 , clause( 468, [ =( X, hAPP( hAPP( 'c_Type_Otype_OFun',
% 0.79/1.20 'c_Type_Osko__Type__Xtyping__elims__3__1'( X, Y, Z ) ),
% 0.79/1.20 'c_Type_Osko__Type__Xtyping__elims__3__2'( X, Y, Z ) ) ), ~(
% 0.79/1.20 'c_Type_Otyping'( Y, 'c_Lambda_OdB_OAbs'( Z ), X ) ) ] )
% 0.79/1.20 , clause( 469, [ 'c_Type_Otyping'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.79/1.20 'c_Lambda_Obeta', T ), Y ) ) ), ~( 'c_Type_Otyping'( X, T, Z ) ) ] )
% 0.79/1.20 , clause( 470, [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP(
% 0.79/1.20 hAPP( 'c_Type_Otype_OFun', Z ), T ) ) ), =( X, Z ) ] )
% 0.79/1.20 , clause( 471, [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP(
% 0.79/1.20 hAPP( 'c_Type_Otype_OFun', Z ), T ) ) ), =( Y, T ) ] )
% 0.79/1.20 , clause( 472, [ ~( =( 'c_Type_Osko__Type__Xtype__induct__1__1'( X ), hAPP(
% 0.79/1.20 hAPP( 'c_Type_Otype_OFun', Y ), Z ) ) ), hBOOL( hAPP( X, T ) ), hBOOL(
% 0.79/1.20 hAPP( X, Z ) ) ] )
% 0.79/1.20 , clause( 473, [ ~( =( 'c_Type_Osko__Type__Xtype__induct__1__1'( X ), hAPP(
% 0.79/1.20 hAPP( 'c_Type_Otype_OFun', Y ), Z ) ) ), hBOOL( hAPP( X, T ) ), hBOOL(
% 0.79/1.20 hAPP( X, Y ) ) ] )
% 0.79/1.20 , clause( 474, [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y )
% 0.79/1.20 , Z ), T ), ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y,
% 0.79/1.20 hAPP( hAPP( 'c_Type_Otype_OFun', U ), T ) ) ) ] )
% 0.79/1.20 , clause( 475, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_s____' ) ) ] )
% 0.79/1.20 , clause( 476, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', Z ), T ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( X
% 0.79/1.20 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_Type_Otype' ), Y, T ) )
% 0.79/1.20 ] )
% 0.79/1.20 , clause( 477, [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X,
% 0.79/1.20 'c_Lambda_OdB_OVar'( Y ), Z ) ) ] )
% 0.79/1.20 , clause( 478, [ 'c_Type_Otyping'( 'v_ea____', 'v_ta____', 'v_Ta____' ) ]
% 0.79/1.20 )
% 0.79/1.20 , clause( 479, [ =( 'c_Type_Otype_Otype__rec'( X, Y, hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', Z ), T ), U ), hAPP( hAPP( hAPP( hAPP( Y, Z ), T ),
% 0.79/1.20 'c_Type_Otype_Otype__rec'( X, Y, Z, U ) ), 'c_Type_Otype_Otype__rec'( X,
% 0.79/1.20 Y, T, U ) ) ) ] )
% 0.79/1.20 , clause( 480, [ =( 'c_Type_Otype_Otype__case'( X, Y, hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', Z ), T ), U ), hAPP( hAPP( Y, Z ), T ) ) ] )
% 0.79/1.20 , clause( 481, [ 'c_Type_Otyping'( 'v_ea____', 'v_s____', hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', 'v_Ta____' ), 'v_U____' ) ) ] )
% 0.79/1.20 , clause( 482, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y
% 0.79/1.20 ) ) ] )
% 0.79/1.20 , clause( 483, [ ~( hBOOL( hAPP( X, 'c_Type_Otype_Otype__case'( Y, Z, hAPP(
% 0.79/1.20 hAPP( 'c_Type_Otype_OFun', T ), U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP(
% 0.79/1.20 hAPP( Z, T ), U ) ) ) ] )
% 0.79/1.20 , clause( 484, [ ~( hBOOL( hAPP( X, 'c_Type_Otype_Otype__case'( Y, Z, hAPP(
% 0.79/1.20 hAPP( 'c_Type_Otype_OFun', T ), U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP(
% 0.79/1.20 hAPP( Z, T ), U ) ) ) ] )
% 0.79/1.20 , clause( 485, [ ~( =( 'c_Type_Otype_OAtom'( X ), hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', Y ), Z ) ) ) ] )
% 0.79/1.20 , clause( 486, [ 'c_Type_Otyping'( X, Y, hAPP( hAPP( 'c_Type_Otype_OFun',
% 0.79/1.20 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, Y, T ) ), Z ) ), ~(
% 0.79/1.20 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), T ), Z ) ) ]
% 0.79/1.20 )
% 0.79/1.20 , clause( 487, [ ~( 'c_Type_Otyping'( 'v_ea____', 'v_s____', hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', 'v_Ta____' ), 'v_U____' ) ) ) ] )
% 0.79/1.20 , clause( 488, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.79/1.20 'class_Orderings_Opreorder'( Y ) ) ] )
% 0.79/1.20 , clause( 489, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.79/1.20 'class_Orderings_Oorder'( Y ) ) ] )
% 0.79/1.20 , clause( 490, [
% 0.79/1.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 0.79/1.20 )
% 0.79/1.20 , clause( 491, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 0.79/1.20 'tc_nat' ) ] )
% 0.79/1.20 , clause( 492, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.79/1.20 'tc_nat' ) ] )
% 0.79/1.20 , clause( 493, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat'
% 0.79/1.20 ) ] )
% 0.79/1.20 , clause( 494, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ]
% 0.79/1.20 )
% 0.79/1.20 , clause( 495, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ]
% 0.79/1.20 )
% 0.79/1.20 , clause( 496, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 0.79/1.20 )
% 0.79/1.20 , clause( 497, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ]
% 0.79/1.20 )
% 0.79/1.20 , clause( 498, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 499, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 500, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 501, [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 502, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 503, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 504, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 505, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 506, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 507, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 508, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 509, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 510, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 511, [ 'class_Power_Opower'( 'tc_nat' ) ] )
% 0.79/1.20 , clause( 512, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 0.79/1.20 , clause( 513, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 0.79/1.20 , clause( 514, [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ] )
% 0.79/1.20 , clause( 515, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y )
% 0.79/1.20 ) ) ] )
% 0.79/1.20 ] ).
% 0.79/1.20
% 0.79/1.20
% 0.79/1.20
% 0.79/1.20 subsumption(
% 0.79/1.20 clause( 215, [ 'c_Type_Otyping'( 'v_ea____', 'v_s____', hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', 'v_Ta____' ), 'v_U____' ) ) ] )
% 0.79/1.20 , clause( 481, [ 'c_Type_Otyping'( 'v_ea____', 'v_s____', hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', 'v_Ta____' ), 'v_U____' ) ) ] )
% 0.79/1.20 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.79/1.20
% 0.79/1.20
% 0.79/1.20 resolution(
% 0.79/1.20 clause( 1083, [] )
% 0.79/1.20 , clause( 487, [ ~( 'c_Type_Otyping'( 'v_ea____', 'v_s____', hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', 'v_Ta____' ), 'v_U____' ) ) ) ] )
% 0.79/1.20 , 0, clause( 215, [ 'c_Type_Otyping'( 'v_ea____', 'v_s____', hAPP( hAPP(
% 0.79/1.20 'c_Type_Otype_OFun', 'v_Ta____' ), 'v_U____' ) ) ] )
% 0.79/1.20 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.79/1.20
% 0.79/1.20
% 0.79/1.20 subsumption(
% 0.79/1.20 clause( 218, [] )
% 0.79/1.20 , clause( 1083, [] )
% 0.79/1.20 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.79/1.20
% 0.79/1.20
% 0.79/1.20 end.
% 0.79/1.20
% 0.79/1.20 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.79/1.20
% 0.79/1.20 Memory use:
% 0.79/1.20
% 0.79/1.20 space for terms: 14752
% 0.79/1.20 space for clauses: 20116
% 0.79/1.20
% 0.79/1.20
% 0.79/1.20 clauses generated: 268
% 0.79/1.20 clauses kept: 219
% 0.79/1.20 clauses selected: 0
% 0.79/1.20 clauses deleted: 0
% 0.79/1.20 clauses inuse deleted: 0
% 0.79/1.20
% 0.79/1.20 subsentry: 5135
% 0.79/1.20 literals s-matched: 1948
% 0.79/1.20 literals matched: 1948
% 0.79/1.20 full subsumption: 222
% 0.79/1.20
% 0.79/1.20 checksum: 1549146023
% 0.79/1.20
% 0.79/1.20
% 0.79/1.20 Bliksem ended
%------------------------------------------------------------------------------