TSTP Solution File: LCL839-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL839-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.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 07:58:40 EDT 2022
% Result : Unsatisfiable 2.19s 2.59s
% Output : Refutation 2.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL839-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jul 3 10:48:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.80/1.21 *** allocated 10000 integers for termspace/termends
% 0.80/1.21 *** allocated 10000 integers for clauses
% 0.80/1.21 *** allocated 10000 integers for justifications
% 0.80/1.21 Bliksem 1.12
% 0.80/1.21
% 0.80/1.21
% 0.80/1.21 Automatic Strategy Selection
% 0.80/1.21
% 0.80/1.21 Clauses:
% 0.80/1.21 [
% 0.80/1.21 [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OVar'( X ),
% 0.80/1.21 'tc_Lambda_OdB' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OVar'( X ) ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.21 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.80/1.21 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.21 , X ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.21 , X ) ) ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.80/1.21 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.80/1.21 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.80/1.21 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.21 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.80/1.21 ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.80/1.21 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.21 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.21 ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.80/1.21 ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.21 ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.21 ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.21 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.80/1.21 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 0.80/1.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 0.80/1.21 ), Z ), Y ) ],
% 0.80/1.21 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 0.80/1.21 hBOOL( hAPP( X, Z ) ) ],
% 0.80/1.21 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 0.80/1.21 hBOOL( hAPP( X, Z ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.21 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.21 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.80/1.21 , T, X ) ) ), =( Y, Z ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.80/1.21 , T, X ) ) ), =( Z, T ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.21 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.21 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.21 ) ), =( Y, Z ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.21 ) ), =( Y, Z ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.21 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.80/1.21 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.80/1.21 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.80/1.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.80/1.21 , Y ), Z ), Z, X ), Y ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.80/1.21 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.21 'tc_nat' ) ) ],
% 0.80/1.21 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X,
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( U, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.80/1.21 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, U, 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.80/1.21 ), ~( hBOOL( hAPP( hAPP( X, Z ), T ) ) ) ],
% 0.80/1.21 [ ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_ONil'( Y ), Z, Y ) ) ],
% 0.80/1.21 [ ~( 'c_ListOrder_Ostep1'( X, Y, 'c_List_Olist_ONil'( Z ), Z ) ) ],
% 0.80/1.21 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.21 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), Y ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.80/1.21 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.80/1.21 [ =( 'c_Predicate_Oconversep'( 'c_fequal'( X ), X, X ), 'c_fequal'( X )
% 0.80/1.21 ) ],
% 0.80/1.21 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.80/1.21 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.80/1.21 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.80/1.21 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.80/1.21 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.80/1.21 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ) ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.21 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.80/1.21 T, X ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.80/1.21 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 0.80/1.21 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.21 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X
% 0.80/1.21 ), 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ), X, X ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.80/1.21 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.80/1.21 [ =( 'c_Predicate_Oconversep'( 'c_Predicate_Oconversep'( X, Y, Z ), Z, Y
% 0.80/1.21 ), X ) ],
% 0.80/1.21 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.80/1.21 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.21 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.80/1.21 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.80/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 0.80/1.21 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.80/1.21 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.21 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.80/1.21 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.80/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 0.80/1.21 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.80/1.21 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.80/1.21 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.80/1.21 ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.80/1.21 , Z ), Y ), 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.80/1.21 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 0.80/1.21 ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.80/1.21 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.80/1.21 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.80/1.21 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.80/1.21 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 0.80/1.21 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.80/1.21 'tc_nat' ) ) ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.80/1.21 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), U )
% 0.80/1.21 , T ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.80/1.21 ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ],
% 0.80/1.21 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) )
% 0.80/1.21 ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.80/1.21 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) )
% 0.80/1.21 ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.80/1.21 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeE__1__1'(
% 0.80/1.21 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeD__1__1'(
% 0.80/1.21 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 0.80/1.21 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 0.80/1.21 'tc_nat' ) ) ), 'c_Lambda_Olift'( Y, T ), Z ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 0.80/1.21 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, T ), 'c_Lambda_Olift'( Y, T ),
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.80/1.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.21 T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 0.80/1.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.80/1.21 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.80/1.21 X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.80/1.21 [ =( X, hAPP( hAPP( 'c_Type_Otype_OFun',
% 0.80/1.21 'c_Type_Osko__Type__Xtyping__elims__3__1'( X, Y, Z ) ),
% 0.80/1.21 'c_Type_Osko__Type__Xtyping__elims__3__2'( X, Y, Z ) ) ), ~(
% 0.80/1.21 'c_Type_Otyping'( Y, 'c_Lambda_OdB_OAbs'( Z ), X ) ) ],
% 0.80/1.21 [ =( X, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.80/1.21 'c_Type_Osko__Type__Xvar__app__types__1__1'( Y, X, Z, T ), Y,
% 0.80/1.21 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( Z,
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ), ~( 'c_Type_Otypings'( Z, W, V0
% 0.80/1.21 ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.80/1.21 , Y ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.21 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.21 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.21 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.21 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.21 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.21 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.80/1.21 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.80/1.21 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.80/1.21 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.21 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.80/1.21 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.80/1.21 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.80/1.21 , 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.80/1.21 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 0.80/1.21 , 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.21 'c_Suc'( X ), 'tc_nat' ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.21 'c_Suc'( X ), 'tc_nat' ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.21 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.80/1.21 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.21 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.80/1.21 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.21 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.80/1.21 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.80/1.21 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.21 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.80/1.21 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 0.80/1.21 ), Z ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.21 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP(
% 0.80/1.21 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 0.80/1.21 ), Z ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.21 , 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ), 'c_Lambda_OdB_OAbs'( Y )
% 0.80/1.21 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Y ) ) ) ],
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_Lambda_OdB_OApp', X ), Y ), Z ) ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 0.80/1.21 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.80/1.21 ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.21 , 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ), 'c_Lambda_Osubst'( X
% 0.80/1.21 , T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', Y ), T ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.21 , 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ), 'c_Lambda_Osubst'( T
% 0.80/1.21 , Y, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), T ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.21 , 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ), 'c_Lambda_Osubst'( X
% 0.80/1.21 , T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y ), T ) ) ) ],
% 0.80/1.21 [ 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', X,
% 0.80/1.21 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, X, Z ),
% 0.80/1.21 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), X,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ) ) ) ],
% 0.80/1.21 [ 'c_Type_Otyping'( X, Y, 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z,
% 0.80/1.21 X, T, Y ) ), ~( 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', T )
% 0.80/1.21 , Y ), Z ) ) ],
% 0.80/1.21 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.21 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.80/1.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.21 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.80/1.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_Type_Otype_Otype__size'( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y
% 0.80/1.21 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Type_Otype_Otype__size'( X ) )
% 0.80/1.21 , 'c_Type_Otype_Otype__size'( Y ) ) ), 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.80/1.21 [ =( 'c_Nat_Osize__class_Osize'( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y
% 0.80/1.21 ), 'tc_Type_Otype' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.80/1.21 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.80/1.21 'c_Nat_Osize__class_Osize'( X, 'tc_Type_Otype' ) ),
% 0.80/1.21 'c_Nat_Osize__class_Osize'( Y, 'tc_Type_Otype' ) ) ), 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.80/1.21 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.80/1.21 'tc_nat' ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 0.80/1.21 'tc_nat' ), 'tc_nat' ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.80/1.21 [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.80/1.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.21 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OAbs'( X ),
% 0.80/1.21 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.80/1.21 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ), 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.80/1.21 [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OAbs'( X ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Lambda_OdB_OdB__size'( X ) ),
% 0.80/1.21 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.80/1.21 [ =( 'c_Nat_Osize__class_Osize'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y
% 0.80/1.21 ), 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.80/1.21 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.80/1.21 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ),
% 0.80/1.21 'c_Nat_Osize__class_Osize'( Y, 'tc_Lambda_OdB' ) ) ), 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.80/1.21 [ =( 'c_Lambda_OdB_OdB__size'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y )
% 0.80/1.21 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Lambda_OdB_OdB__size'( X ) ),
% 0.80/1.21 'c_Lambda_OdB_OdB__size'( Y ) ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ) ) ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( 'c_List_Ofoldr'(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ],
% 0.80/1.21 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.80/1.21 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.80/1.21 ) ) ],
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.80/1.21 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 0.80/1.21 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.21 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.80/1.21 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.80/1.21 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.80/1.21 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.80/1.21 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.80/1.21 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.80/1.21 X, T, 'tc_nat' ) ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.80/1.21 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.80/1.21 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.80/1.21 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.80/1.21 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.80/1.21 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.80/1.21 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.80/1.21 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.80/1.21 Y ) ) ) ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 0.80/1.21 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 0.80/1.21 ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( 'c_InductTermi_OIT', X ) ), ~( 'c_Wellfounded_Oaccp'(
% 0.80/1.21 'c_Predicate_Oconversep'( 'c_Lambda_Obeta', 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ) ) ],
% 0.80/1.21 [ 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ), ~( hBOOL( hAPP(
% 0.80/1.21 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.80/1.21 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), U )
% 0.80/1.21 , T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y
% 0.80/1.21 ), Z ), U ) ) ) ],
% 0.80/1.21 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( 'c_Wellfounded_Oaccp'( X, T, Z )
% 0.80/1.21 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Z ), Y )
% 0.80/1.21 , T ) ) ) ],
% 0.80/1.21 [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Transitive__Closure_Ortranclp'( X, Z ), Y ), T ) ) ), ~(
% 0.80/1.21 'c_Wellfounded_Oaccp'( X, T, Z ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), Z )
% 0.80/1.21 ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), Z )
% 0.80/1.21 ) ],
% 0.80/1.21 [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.21 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.80/1.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 0.80/1.21 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.80/1.21 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.80/1.21 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 X ), Y ), Z ) ), T ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 X ), Y ), Z ) ), T ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T ), U ) ),
% 0.80/1.21 ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ), T ), U ) ),
% 0.80/1.21 ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.80/1.21 [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T ), Z ) ],
% 0.80/1.21 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.80/1.21 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.80/1.21 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.80/1.21 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.80/1.21 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.80/1.21 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.80/1.21 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 0.80/1.21 Y ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), T )
% 0.80/1.21 ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Predicate_Oconversep'( X, Y, Y ), Y ), T ), Z ) ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Predicate_Oconversep'( X, Y, Y ), Y ), Z ), T ) ), ~( hBOOL( hAPP(
% 0.80/1.21 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), T ), Z ) ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.80/1.21 ) ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.80/1.21 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.80/1.21 ) ],
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 0.80/1.21 ) ],
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.80/1.21 ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.21 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.80/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.80/1.21 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y, Z ),
% 0.80/1.21 'c_Suc'( T ) ), 'c_Lambda_Osubst'( U, Y, T ), Z ), 'c_Lambda_Osubst'(
% 0.80/1.21 'c_Lambda_Osubst'( X, U, Z ), Y, T ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.80/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ),
% 0.80/1.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.80/1.21 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.80/1.21 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.80/1.21 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.80/1.21 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.80/1.21 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.80/1.21 [ =( 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Y ), 'c_Suc'( Z ) ),
% 0.80/1.21 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Z ), Y ) ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.80/1.21 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.80/1.21 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.80/1.21 [ =( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Transitive__Closure_Ortranclp'( X, Y ), Y ),
% 0.80/1.21 'c_Transitive__Closure_Ortranclp'( X, Y ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.80/1.21 Y ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.80/1.21 Y ) ],
% 0.80/1.21 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 0.80/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.80/1.21 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.80/1.21 Y ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.80/1.21 Y ) ],
% 0.80/1.21 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.80/1.21 Y ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.80/1.21 Y ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.80/1.21 Y ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.80/1.21 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 0.80/1.21 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y,
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.80/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 0.80/1.21 'tc_nat' ) ) ) ) ) ],
% 0.80/1.21 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__types__1__1'(
% 0.80/1.21 Z, T, X, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ), T ) ), ~( 'c_Type_Otypings'( X, W, V0 ) ), ~(
% 0.80/1.21 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 0.80/1.21 , Z ) ) ],
% 0.80/1.21 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xvar__app__typesE__1__1'(
% 0.80/1.21 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ), Z ) ) ],
% 0.80/1.21 [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Type_Otyping'( X, T, Z ) ), ~(
% 0.80/1.21 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.80/1.21 'tc_Lambda_OdB' ), T ), Y ) ) ) ],
% 0.80/1.21 [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.80/1.21 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X, Y, T ), Z,
% 0.80/1.21 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ), Z ) ) ],
% 0.80/1.21 [ 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, Z,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ), ~( 'c_Type_Otypings'( X, Z, U )
% 0.80/1.21 ), ~( 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun', U, T
% 0.80/1.21 , 'tc_Type_Otype', 'tc_Type_Otype' ) ) ) ],
% 0.80/1.21 [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.80/1.21 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X, Y, T ), Z,
% 0.80/1.21 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ), Z ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.21 , 'tc_Lambda_OdB' ), 'c_Lambda_Olift'( X, Y ) ), 'c_Lambda_Olift'( Z, Y )
% 0.80/1.21 ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 0.80/1.21 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.80/1.21 [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 0.80/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 0.80/1.21 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 0.80/1.21 'c_Suc'( Y ), Z, T ) ) ],
% 0.80/1.21 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ), 'c_Type_Osko__Type__Xtyping__elims__3__1'( Y, X, Z ),
% 0.80/1.21 'tc_Type_Otype' ), Z, 'c_Type_Osko__Type__Xtyping__elims__3__2'( Y, X, Z
% 0.80/1.21 ) ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Z ), Y ) ) ],
% 0.80/1.21 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.21 'tc_nat' ), 'c_Type_Osko__Type__Xabs__typeE__1__1'( X, Y ),
% 0.80/1.21 'tc_Type_Otype' ), Y, 'c_Type_Osko__Type__Xabs__typeE__1__2'( X, Y ) ),
% 0.80/1.21 ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ) ) ],
% 0.80/1.21 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), 'c_List_Ofoldr'(
% 0.80/1.21 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X,
% 0.80/1.21 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), T,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ],
% 0.80/1.21 [ ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.21 , 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ), ~(
% 0.80/1.21 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB' ) ),
% 0.80/1.21 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.21 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.80/1.21 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Z, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ) ) ), ~( 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', Y, Z,
% 0.80/1.21 'tc_Lambda_OdB' ) ) ],
% 0.80/1.21 [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta'
% 0.80/1.21 , 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_List_Ofoldl'(
% 0.80/1.21 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~(
% 0.80/1.21 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 0.80/1.21 'tc_Lambda_OdB' ), X ), Z ) ) ) ],
% 0.80/1.21 [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.80/1.21 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 0.80/1.21 ), 'c_Lambda_OdB_OAbs'( X ) ) ],
% 0.80/1.21 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.80/1.21 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 0.80/1.21 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 0.80/1.21 [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.80/1.21 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.80/1.21 'tc_Lambda_OdB' ) ) ],
% 0.80/1.21 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 0.80/1.21 'tc_Lambda_OdB' ) ) ],
% 0.80/1.21 [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 0.80/1.21 [ 'c_Type_Otyping'( X, Y, hAPP( hAPP( 'c_Type_Otype_OFun',
% 0.80/1.21 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, Y, T ) ), Z ) ), ~(
% 0.80/1.21 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), T ), Z ) ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.80/1.21 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.80/1.21 'tc_nat' ) ) ],
% 0.80/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.80/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.80/1.21 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.80/1.21 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.80/1.21 [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ),
% 0.80/1.21 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 0.80/1.21 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( hAPP(
% 0.80/1.21 'c_Lambda_Obeta', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.21 'c_Lambda_OdB_OVar'( Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ) )
% 0.80/1.21 ) ],
% 0.80/1.21 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.21 , 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ),
% 0.80/1.21 ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y, 'tc_Lambda_OdB' ) ) ],
% 0.80/1.21 [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_ea______', 'v_ia______',
% 0.80/1.21 'v_T____', 'tc_Type_Otype' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP(
% 0.80/1.21 hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( 'v_r____' ) ), 'v_a____'
% 0.80/1.21 ), 'v_as____', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'v_T_Ha______' ) ]
% 0.80/1.21 ,
% 0.80/1.21 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OVar'(
% 0.80/1.22 Z ) ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'( X ) ),
% 0.80/1.22 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X )
% 0.80/1.22 , Y ) ) ) ],
% 0.80/1.22 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y )
% 0.80/1.22 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.80/1.22 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 0.80/1.22 , 'c_Lambda_OdB_OVar'( Y ) ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.80/1.22 ) ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Olift'( X, Y ) ),
% 0.80/1.22 'c_Lambda_Olift'( Z, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X )
% 0.80/1.22 , Z ) ) ) ],
% 0.80/1.22 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.80/1.22 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X ) ],
% 0.80/1.22 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.80/1.22 X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP(
% 0.80/1.22 hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.80/1.22 X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP(
% 0.80/1.22 hAPP( 'c_Lambda_Obeta', Y ), Z ) ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X ) ) ), ~(
% 0.80/1.22 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.22 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 0.80/1.22 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.80/1.22 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.22 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 0.80/1.22 , Y ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubst'(
% 0.80/1.22 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.80/1.22 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.22 ), 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.80/1.22 ), 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.80/1.22 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.22 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_ua______' ) ) ],
% 0.80/1.22 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.22 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.80/1.22 'tc_nat' ) ],
% 0.80/1.22 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Osubst'( X, Y, Z ) ),
% 0.80/1.22 'c_Lambda_Osubst'( T, Y, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta'
% 0.80/1.22 , X ), T ) ) ) ],
% 0.80/1.22 [ =( 'c_Lambda_Olift'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z ),
% 0.80/1.22 hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Olift'( X, Z ) ),
% 0.80/1.22 'c_Lambda_Olift'( Y, Z ) ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X ) ) ) ],
% 0.80/1.22 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.22 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 0.80/1.22 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 0.80/1.22 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 0.80/1.22 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ) ) ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Olift'( X, Y ) ) ), ~(
% 0.80/1.22 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 0.80/1.22 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.80/1.22 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.80/1.22 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ) ) ) ],
% 0.80/1.22 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.80/1.22 ) ],
% 0.80/1.22 [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.80/1.22 Z ) ) ) ],
% 0.80/1.22 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.80/1.22 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OVar'( X )
% 0.80/1.22 , Y ) ],
% 0.80/1.22 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 0.80/1.22 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 0.80/1.22 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) )
% 0.80/1.22 ) ],
% 0.80/1.22 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.80/1.22 , X ) ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.22 , Y, X ) ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.22 , Y, X ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 0.80/1.22 'c_Lambda_OdB_OAbs'( X ) ), Y ) ), 'c_Lambda_Osubst'( X, Y,
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.80/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.80/1.22 ), =( Z, Y ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.80/1.22 ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.80/1.22 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 0.80/1.22 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 0.80/1.22 [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.80/1.22 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.80/1.22 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ), X ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.80/1.22 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.22 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.22 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.80/1.22 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.80/1.22 ) ],
% 0.80/1.22 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.80/1.22 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 0.80/1.22 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.80/1.22 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 0.80/1.22 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.80/1.22 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.80/1.22 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.80/1.22 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.80/1.22 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.80/1.22 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.80/1.22 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.80/1.22 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 0.80/1.22 [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T ),
% 0.80/1.22 ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y, hAPP( hAPP(
% 0.80/1.22 'c_Type_Otype_OFun', U ), T ) ) ) ],
% 0.80/1.22 [ ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OVar'( X ) ), Y
% 0.80/1.22 ) ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( 'c_List_Ofoldl'(
% 0.80/1.22 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( 'v_r____', 'v_a____',
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_as____', 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ), X, Y ) ) ), ~( 'c_Type_Otyping'( Z, X, 'v_T____' ) ),
% 0.80/1.22 ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ), ~( 'c_Type_Otyping'(
% 0.80/1.22 'c_Type_Oshift'( Z, Y, 'v_T____', 'tc_Type_Otype' ), 'c_List_Ofoldl'(
% 0.80/1.22 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( 'v_r____', 'v_a____',
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_as____', 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ), T ) ) ],
% 0.80/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.80/1.22 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.80/1.22 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.80/1.22 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.80/1.22 ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( X,
% 0.80/1.22 'c_Lambda_OdB_OVar'( Y ), Z ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 0.80/1.22 ) ) ) ],
% 0.80/1.22 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP( hAPP(
% 0.80/1.22 'c_Type_Otype_OFun', Z ), T ) ) ), =( Y, T ) ],
% 0.80/1.22 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP( hAPP(
% 0.80/1.22 'c_Type_Otype_OFun', Z ), T ) ) ), =( X, Z ) ],
% 0.80/1.22 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.80/1.22 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.80/1.22 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.80/1.22 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.80/1.22 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.80/1.22 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.80/1.22 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.80/1.22 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.80/1.22 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.80/1.22 Z ) ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.80/1.22 , 'c_Lambda_Osubst'( 'v_r____', 'v_a____', 'c_HOL_Ozero__class_Ozero'(
% 0.80/1.22 'tc_nat' ) ), 'v_as____', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.80/1.22 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.80/1.22 ) ],
% 0.80/1.22 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 0.80/1.22 Z ) ) ) ],
% 0.80/1.22 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.80/1.22 [ =( 'c_Lambda_Osubst'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 0.80/1.22 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Z, T ) ),
% 0.80/1.22 'c_Lambda_Osubst'( Y, Z, T ) ) ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.80/1.22 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.22 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.22 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.80/1.22 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.80/1.22 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.80/1.22 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ),
% 0.80/1.22 'c_Lambda_Olift'( T, Y ), U ), ~( 'c_Type_Otyping'( X, T, U ) ) ],
% 0.80/1.22 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( 'v_a____', X, Y )
% 0.80/1.22 ) ), ~( 'c_Type_Otyping'( Z, X, 'v_T____' ) ), ~( hBOOL( hAPP(
% 0.80/1.22 'c_InductTermi_OIT', X ) ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( Z, Y
% 0.80/1.22 , 'v_T____', 'tc_Type_Otype' ), 'v_a____', T ) ) ],
% 0.80/1.22 [ 'c_Type_Otyping'( 'v_e____', 'v_u____', 'v_T____' ) ],
% 0.80/1.22 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_a____' ) ) ],
% 0.80/1.22 [ 'c_Type_Otyping'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', T
% 0.80/1.22 ), Y ) ) ), ~( 'c_Type_Otyping'( X, T, Z ) ) ],
% 0.80/1.22 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U ) ), ~(
% 0.80/1.22 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ],
% 0.80/1.22 [ ~( =( 'v_T____', hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ) ) ), hBOOL(
% 0.80/1.22 hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( Z, T, U ) ) ), ~(
% 0.80/1.22 'c_Type_Otyping'( W, T, Y ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', T ) )
% 0.80/1.22 ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( W, U, Y, 'tc_Type_Otype' ), Z,
% 0.80/1.22 V0 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', Z ) ) ) ],
% 0.80/1.22 [ ~( =( 'v_T____', hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ) ) ), hBOOL(
% 0.80/1.22 hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( Z, T, U ) ) ), ~(
% 0.80/1.22 'c_Type_Otyping'( W, T, X ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', T ) )
% 0.80/1.22 ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( W, U, X, 'tc_Type_Otype' ), Z,
% 0.80/1.22 V0 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', Z ) ) ) ],
% 0.80/1.22 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ],
% 0.80/1.22 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), hAPP( hAPP(
% 0.80/1.22 'c_Type_Otype_OFun', Z ), T ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( X
% 0.80/1.22 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_Type_Otype' ), Y, T ) )
% 0.80/1.22 ],
% 0.80/1.22 [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y )
% 0.80/1.22 , Z ) ) ],
% 0.80/1.22 [ 'c_Type_Otyping'( 'v_ea______', 'v_ua______', 'v_T____' ) ],
% 0.80/1.22 [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____', 'v_T____',
% 0.80/1.22 'tc_Type_Otype' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.80/1.22 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( 'v_r____' ) ), 'v_a____' ),
% 0.80/1.22 'v_as____', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'v_T_H____' ) ],
% 0.80/1.22 [ 'v_thesis____', ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____',
% 0.80/1.22 'v_i____', 'v_T____', 'tc_Type_Otype' ), 'v_a____', X ) ) ],
% 0.80/1.22 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y ) ) ],
% 0.80/1.22 [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 0.80/1.22 X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'( X,
% 0.80/1.22 'c_Lambda_Osubst'( U, Y, T ), W ) ],
% 0.80/1.22 [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____', 'v_T____',
% 0.80/1.22 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.80/1.22 'v_r____' ) ), 'v_a____' ), 'v_Ua____' ) ],
% 0.80/1.22 [ ~( 'v_thesis____' ) ],
% 0.80/1.22 [ 'v_thesis____', ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____',
% 0.80/1.22 'v_i____', 'v_T____', 'tc_Type_Otype' ), 'v_a____', X ) ) ],
% 0.80/1.22 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.80/1.22 'class_Orderings_Opreorder'( Y ) ) ],
% 0.80/1.22 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.80/1.22 'class_Orderings_Oorder'( Y ) ) ],
% 0.80/1.22 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.80/1.22 ],
% 0.80/1.22 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.80/1.22 ) ],
% 0.80/1.22 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.80/1.22 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 0.80/1.22 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 0.80/1.22 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 0.80/1.22 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 0.80/1.22 ] .
% 0.80/1.22
% 0.80/1.22
% 0.80/1.22 percentage equality = 0.346591, percentage horn = 0.937853
% 0.80/1.22 This is a problem with some equality
% 0.80/1.22
% 0.80/1.22
% 0.80/1.22
% 0.80/1.22 Options Used:
% 0.80/1.22
% 0.80/1.22 useres = 1
% 0.80/1.22 useparamod = 1
% 0.80/1.22 useeqrefl = 1
% 0.80/1.22 useeqfact = 1
% 0.80/1.22 usefactor = 1
% 0.80/1.22 usesimpsplitting = 0
% 0.80/1.22 usesimpdemod = 5
% 0.80/1.22 usesimpres = 3
% 0.80/1.22
% 0.80/1.22 resimpinuse = 1000
% 0.80/1.22 resimpclauses = 20000
% 0.80/1.22 substype = eqrewr
% 0.80/1.22 backwardsubs = 1
% 0.80/1.22 selectoldest = 5
% 0.80/1.22
% 0.80/1.22 litorderings [0] = split
% 0.80/1.22 litorderings [1] = extend the termordering, first sorting on arguments
% 0.80/1.22
% 0.80/1.22 termordering = kbo
% 0.80/1.22
% 0.80/1.22 litapriori = 0
% 0.80/1.22 termapriori = 1
% 0.80/1.22 litaposteriori = 0
% 0.80/1.22 termaposteriori = 0
% 0.80/1.22 demodaposteriori = 0
% 0.80/1.22 ordereqreflfact = 0
% 0.80/1.22
% 0.80/1.22 litselect = negord
% 0.80/1.22
% 0.80/1.22 maxweight = 15
% 0.80/1.22 maxdepth = 30000
% 0.80/1.22 maxlength = 115
% 0.80/1.22 maxnrvars = 195
% 0.80/1.22 excuselevel = 1
% 0.80/1.22 increasemaxweight = 1
% 0.80/1.22
% 0.80/1.22 maxselected = 10000000
% 0.80/1.22 maxnrclauses = 10000000
% 0.80/1.22
% 0.80/1.22 showgenerated = 0
% 0.80/1.22 showkept = 0
% 0.80/1.22 showselected = 0
% 0.80/1.22 showdeleted = 0
% 0.80/1.22 showresimp = 1
% 0.80/1.22 showstatus = 2000
% 0.80/1.22
% 0.80/1.22 prologoutput = 1
% 0.80/1.22 nrgoals = 5000000
% 0.80/1.22 totalproof = 1
% 0.80/1.22
% 0.80/1.22 Symbols occurring in the translation:
% 0.80/1.22
% 0.80/1.22 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.80/1.22 . [1, 2] (w:1, o:134, a:1, s:1, b:0),
% 0.80/1.22 ! [4, 1] (w:0, o:94, a:1, s:1, b:0),
% 0.80/1.22 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.80/1.22 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.80/1.22 'c_Lambda_OdB_OVar' [40, 1] (w:1, o:99, a:1, s:1, b:0),
% 0.80/1.22 'tc_Lambda_OdB' [41, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.80/1.22 'c_Nat_Osize__class_Osize' [42, 2] (w:1, o:159, a:1, s:1, b:0),
% 0.80/1.22 'tc_nat' [43, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.80/1.22 'c_HOL_Ozero__class_Ozero' [44, 1] (w:1, o:100, a:1, s:1, b:0),
% 0.80/1.22 'c_Lambda_OdB_OdB__size' [45, 1] (w:1, o:101, a:1, s:1, b:0),
% 0.80/1.22 'c_HOL_Ominus__class_Ominus' [48, 3] (w:1, o:167, a:1, s:1, b:0),
% 0.80/1.22 'c_HOL_Oord__class_Oless' [49, 3] (w:1, o:168, a:1, s:1, b:0),
% 0.80/1.22 hAPP [51, 2] (w:1, o:160, a:1, s:1, b:0),
% 0.80/1.22 hBOOL [52, 1] (w:1, o:102, a:1, s:1, b:0),
% 0.80/1.22 'class_OrderedGroup_Opordered__ab__group__add' [56, 1] (w:1, o:104
% 0.80/1.22 , a:1, s:1, b:0),
% 0.80/1.22 'c_HOL_Oplus__class_Oplus' [57, 1] (w:1, o:106, a:1, s:1, b:0),
% 2.19/2.59 'c_Suc' [65, 1] (w:1, o:107, a:1, s:1, b:0),
% 2.19/2.59 'class_Ring__and__Field_Oidom' [66, 1] (w:1, o:108, a:1, s:1, b:0),
% 2.19/2.59 'class_Int_Onumber__ring' [67, 1] (w:1, o:109, a:1, s:1, b:0),
% 2.19/2.59 'class_OrderedGroup_Ogroup__add' [68, 1] (w:1, o:110, a:1, s:1, b:0)
% 2.19/2.59 ,
% 2.19/2.59 'class_OrderedGroup_Oab__group__add' [69, 1] (w:1, o:111, a:1, s:1
% 2.19/2.59 , b:0),
% 2.19/2.59 'c_HOL_Oone__class_Oone' [71, 1] (w:1, o:105, a:1, s:1, b:0),
% 2.19/2.59 'c_Type_Oshift' [76, 4] (w:1, o:178, a:1, s:1, b:0),
% 2.19/2.59 'c_Transitive__Closure_Ortranclp' [78, 2] (w:1, o:161, a:1, s:1, b:0)
% 2.19/2.59 ,
% 2.19/2.59 'c_List_Olist_ONil' [79, 1] (w:1, o:112, a:1, s:1, b:0),
% 2.19/2.59 'c_ListOrder_Ostep1' [81, 4] (w:1, o:179, a:1, s:1, b:0),
% 2.19/2.59 'c_List_Ofoldl' [84, 5] (w:1, o:185, a:1, s:1, b:0),
% 2.19/2.59 'class_Ring__and__Field_Ozero__neq__one' [85, 1] (w:1, o:113, a:1, s:
% 2.19/2.59 1, b:0),
% 2.19/2.59 'c_fequal' [86, 1] (w:1, o:114, a:1, s:1, b:0),
% 2.19/2.59 'c_Predicate_Oconversep' [87, 3] (w:1, o:169, a:1, s:1, b:0),
% 2.19/2.59 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [88, 1]
% 2.19/2.59 (w:1, o:115, a:1, s:1, b:0),
% 2.19/2.59 'class_OrderedGroup_Omonoid__add' [91, 1] (w:1, o:117, a:1, s:1, b:0)
% 2.19/2.59 ,
% 2.19/2.59 'c_List_Ofoldr' [92, 5] (w:1, o:186, a:1, s:1, b:0),
% 2.19/2.59 'class_Ring__and__Field_Oordered__semidom' [93, 1] (w:1, o:118, a:1
% 2.19/2.59 , s:1, b:0),
% 2.19/2.59 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [94, 1]
% 2.19/2.59 (w:1, o:119, a:1, s:1, b:0),
% 2.19/2.59 'class_Ring__and__Field_Osemiring__1' [95, 1] (w:1, o:120, a:1, s:1
% 2.19/2.59 , b:0),
% 2.19/2.59 'c_Nat_Osemiring__1__class_Oof__nat' [96, 2] (w:1, o:162, a:1, s:1
% 2.19/2.59 , b:0),
% 2.19/2.59 'c_Lambda_OdB_OAbs' [98, 1] (w:1, o:121, a:1, s:1, b:0),
% 2.19/2.59 'c_Lambda_Olift' [99, 2] (w:1, o:163, a:1, s:1, b:0),
% 2.19/2.59 'c_Wellfounded_Oaccp' [100, 3] (w:1, o:170, a:1, s:1, b:0),
% 2.19/2.59 'c_Type_Osko__Type__Xlist__app__typeE__1__1' [103, 4] (w:1, o:181, a:
% 2.19/2.59 1, s:1, b:0),
% 2.19/2.59 'c_Type_Otypings' [104, 3] (w:1, o:173, a:1, s:1, b:0),
% 2.19/2.59 'c_Lambda_OdB_OApp' [105, 0] (w:1, o:52, a:1, s:1, b:0),
% 2.19/2.59 'c_Type_Otyping' [106, 3] (w:1, o:174, a:1, s:1, b:0),
% 2.19/2.59 'c_Type_Osko__Type__Xlist__app__typeD__1__1' [107, 4] (w:1, o:180, a:
% 2.19/2.59 1, s:1, b:0),
% 2.19/2.59 'c_Lambda_Osubst' [108, 3] (w:1, o:175, a:1, s:1, b:0),
% 2.19/2.59 'c_Type_Otype_OFun' [109, 0] (w:1, o:53, a:1, s:1, b:0),
% 2.19/2.59 'c_Type_Osko__Type__Xtyping__elims__3__1' [110, 3] (w:1, o:171, a:1
% 2.19/2.59 , s:1, b:0),
% 2.19/2.59 'c_Type_Osko__Type__Xtyping__elims__3__2' [111, 3] (w:1, o:172, a:1
% 2.19/2.59 , s:1, b:0),
% 2.19/2.59 'c_Type_Osko__Type__Xvar__app__types__1__1' [114, 4] (w:1, o:182, a:1
% 2.19/2.59 , s:1, b:0),
% 2.19/2.59 'tc_Type_Otype' [115, 0] (w:1, o:67, a:1, s:1, b:0),
% 2.19/2.59 'class_OrderedGroup_Olordered__ab__group__add' [117, 1] (w:1, o:116
% 2.19/2.59 , a:1, s:1, b:0),
% 2.19/2.59 'class_OrderedGroup_Opordered__comm__monoid__add' [118, 1] (w:1, o:
% 2.19/2.59 122, a:1, s:1, b:0),
% 2.19/2.59 'class_Ring__and__Field_Oordered__idom' [119, 1] (w:1, o:123, a:1, s:
% 2.19/2.59 1, b:0),
% 2.19/2.59 'c_Lambda_Obeta' [121, 0] (w:1, o:69, a:1, s:1, b:0),
% 2.19/2.59 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1' [126, 3] (w:
% 2.19/2.59 1, o:176, a:1, s:1, b:0),
% 2.19/2.59 'c_Type_Osko__Type__Xtyping__elims__2__1' [128, 4] (w:1, o:183, a:1
% 2.19/2.59 , s:1, b:0),
% 2.19/2.59 'c_Type_Otype_Otype__size' [131, 1] (w:1, o:124, a:1, s:1, b:0),
% 2.19/2.59 'class_OrderedGroup_Oab__semigroup__add' [135, 1] (w:1, o:125, a:1
% 2.19/2.59 , s:1, b:0),
% 2.19/2.59 'class_Nat_Osemiring__char__0' [136, 1] (w:1, o:103, a:1, s:1, b:0),
% 2.19/2.59
% 2.19/2.59 'class_OrderedGroup_Osemigroup__add' [137, 1] (w:1, o:126, a:1, s:1
% 2.19/2.59 , b:0),
% 2.19/2.59 'class_Ring__and__Field_Ocomm__semiring__1' [138, 1] (w:1, o:127, a:1
% 2.19/2.59 , s:1, b:0),
% 2.19/2.59 'class_OrderedGroup_Ocomm__monoid__add' [139, 1] (w:1, o:128, a:1, s:
% 2.19/2.59 1, b:0),
% 2.19/2.59 'c_InductTermi_OIT' [141, 0] (w:1, o:73, a:1, s:1, b:0),
% 2.19/2.59 'c_List_Olistsp' [143, 3] (w:1, o:177, a:1, s:1, b:0),
% 2.19/2.59 'class_OrderedGroup_Ocancel__ab__semigroup__add' [146, 1] (w:1, o:129
% 2.19/2.59 , a:1, s:1, b:0),
% 2.19/2.59 'class_OrderedGroup_Ocancel__semigroup__add' [147, 1] (w:1, o:130, a:
% 2.19/2.59 1, s:1, b:0),
% 2.19/2.59 'c_Type_Osko__Type__Xvar__app__typesE__1__1' [148, 4] (w:1, o:184, a:
% 2.19/2.59 1, s:1, b:0),
% 2.19/2.59 'c_Type_Osko__Type__Xabs__typeE__1__1' [149, 2] (w:1, o:164, a:1, s:1
% 2.19/2.59 , b:0),
% 2.19/2.59 'c_Type_Osko__Type__Xabs__typeE__1__2' [150, 2] (w:1, o:165, a:1, s:1
% 2.19/2.59 , b:0),
% 2.19/2.59 'v_ea______' [152, 0] (w:1, o:75, a:1, s:1, b:0),
% 2.19/2.59 'v_ia______' [153, 0] (w:1, o:76, a:1, s:1, b:0),
% 2.19/2.59 'v_T____' [154, 0] (w:1, o:77, a:1, s:1, b:0),
% 2.19/2.59 'v_r____' [155, 0] (w:1, o:78, a:1, s:1, b:0),
% 2.19/2.59 'v_a____' [156, 0] (w:1, o:79, a:1, s:1, b:0),
% 2.19/2.59 'v_as____' [157, 0] (w:1, o:80, a:1, s:1, b:0),
% 2.19/2.59 'v_T_Ha______' [158, 0] (w:1, o:81, a:1, s:1, b:0),
% 2.19/2.59 'v_u____' [161, 0] (w:1, o:83, a:1, s:1, b:0),
% 2.19/2.59 'class_Orderings_Oorder' [162, 1] (w:1, o:131, a:1, s:1, b:0),
% 2.19/2.59 'class_Orderings_Opreorder' [163, 1] (w:1, o:132, a:1, s:1, b:0),
% 2.19/2.59 'v_ua______' [164, 0] (w:1, o:84, a:1, s:1, b:0),
% 2.19/2.59 'class_Orderings_Olinorder' [166, 1] (w:1, o:133, a:1, s:1, b:0),
% 2.19/2.59 'v_e____' [171, 0] (w:1, o:85, a:1, s:1, b:0),
% 2.19/2.59 'v_i____' [175, 0] (w:1, o:86, a:1, s:1, b:0),
% 2.19/2.59 'v_T_H____' [176, 0] (w:1, o:87, a:1, s:1, b:0),
% 2.19/2.59 'v_thesis____' [177, 0] (w:1, o:82, a:1, s:1, b:0),
% 2.19/2.59 'v_Ua____' [180, 0] (w:1, o:88, a:1, s:1, b:0),
% 2.19/2.59 'tc_fun' [183, 2] (w:1, o:166, a:1, s:1, b:0),
% 2.19/2.59 'tc_bool' [184, 0] (w:1, o:91, a:1, s:1, b:0).
% 2.19/2.59
% 2.19/2.59
% 2.19/2.59 Starting Search:
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59
% 2.19/2.59 Intermediate Status:
% 2.19/2.59 Generated: 8167
% 2.19/2.59 Kept: 2421
% 2.19/2.59 Inuse: 143
% 2.19/2.59 Deleted: 14
% 2.19/2.59 Deletedinuse: 1
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59
% 2.19/2.59 Intermediate Status:
% 2.19/2.59 Generated: 20474
% 2.19/2.59 Kept: 4843
% 2.19/2.59 Inuse: 216
% 2.19/2.59 Deleted: 19
% 2.19/2.59 Deletedinuse: 4
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59
% 2.19/2.59 Intermediate Status:
% 2.19/2.59 Generated: 31181
% 2.19/2.59 Kept: 6951
% 2.19/2.59 Inuse: 286
% 2.19/2.59 Deleted: 20
% 2.19/2.59 Deletedinuse: 4
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59
% 2.19/2.59 Intermediate Status:
% 2.19/2.59 Generated: 40573
% 2.19/2.59 Kept: 8952
% 2.19/2.59 Inuse: 352
% 2.19/2.59 Deleted: 55
% 2.19/2.59 Deletedinuse: 5
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59
% 2.19/2.59 Intermediate Status:
% 2.19/2.59 Generated: 51055
% 2.19/2.59 Kept: 11021
% 2.19/2.59 Inuse: 406
% 2.19/2.59 Deleted: 56
% 2.19/2.59 Deletedinuse: 6
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59
% 2.19/2.59 Intermediate Status:
% 2.19/2.59 Generated: 61018
% 2.19/2.59 Kept: 13039
% 2.19/2.59 Inuse: 448
% 2.19/2.59 Deleted: 59
% 2.19/2.59 Deletedinuse: 6
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59
% 2.19/2.59 Intermediate Status:
% 2.19/2.59 Generated: 68442
% 2.19/2.59 Kept: 15088
% 2.19/2.59 Inuse: 471
% 2.19/2.59 Deleted: 60
% 2.19/2.59 Deletedinuse: 6
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59
% 2.19/2.59 Intermediate Status:
% 2.19/2.59 Generated: 82413
% 2.19/2.59 Kept: 17392
% 2.19/2.59 Inuse: 520
% 2.19/2.59 Deleted: 67
% 2.19/2.59 Deletedinuse: 6
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59
% 2.19/2.59 Intermediate Status:
% 2.19/2.59 Generated: 92024
% 2.19/2.59 Kept: 19520
% 2.19/2.59 Inuse: 535
% 2.19/2.59 Deleted: 67
% 2.19/2.59 Deletedinuse: 6
% 2.19/2.59
% 2.19/2.59 Resimplifying inuse:
% 2.19/2.59 Done
% 2.19/2.59
% 2.19/2.59 Resimplifying clauses:
% 2.19/2.59
% 2.19/2.59 Bliksems!, er is een bewijs:
% 2.19/2.59 % SZS status Unsatisfiable
% 2.19/2.59 % SZS output start Refutation
% 2.19/2.59
% 2.19/2.59 clause( 119, [ 'c_Type_Otyping'( X, Y,
% 2.19/2.59 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, T, Y ) ), ~(
% 2.19/2.59 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', T ), Y ), Z ) ) ]
% 2.19/2.59 )
% 2.19/2.59 .
% 2.19/2.59 clause( 303, [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____',
% 2.19/2.59 'v_T____', 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 2.19/2.59 'c_Lambda_OdB_OAbs'( 'v_r____' ) ), 'v_a____' ), 'v_Ua____' ) ] )
% 2.19/2.59 .
% 2.19/2.59 clause( 304, [ ~( 'v_thesis____' ) ] )
% 2.19/2.59 .
% 2.19/2.59 clause( 305, [ ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____',
% 2.19/2.59 'v_T____', 'tc_Type_Otype' ), 'v_a____', X ) ) ] )
% 2.19/2.59 .
% 2.19/2.59 clause( 15094, [ ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____'
% 2.19/2.59 , 'v_T____', 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ),
% 2.19/2.59 'v_a____' ), Y ) ) ] )
% 2.19/2.59 .
% 2.19/2.59 clause( 20203, [] )
% 2.19/2.59 .
% 2.19/2.59
% 2.19/2.59
% 2.19/2.59 % SZS output end Refutation
% 2.19/2.59 found a proof!
% 2.19/2.59
% 2.19/2.59 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.19/2.59
% 2.19/2.59 initialclauses(
% 2.19/2.59 [ clause( 20205, [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OVar'( X )
% 2.19/2.59 , 'tc_Lambda_OdB' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20206, [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OVar'( X ) )
% 2.19/2.59 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20207, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.19/2.59 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.19/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 2.19/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.19/2.59 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20208, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.19/2.59 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 2.19/2.59 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20209, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.19/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20210, [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.19/2.59 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ] )
% 2.19/2.59 , clause( 20211, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.19/2.59 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.19/2.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 2.19/2.59 , X ) ) ] )
% 2.19/2.59 , clause( 20212, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.19/2.59 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.19/2.59 , X ) ) ] )
% 2.19/2.59 , clause( 20213, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 2.19/2.59 ), 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 2.19/2.59 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 2.19/2.59 , clause( 20214, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.19/2.59 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 2.19/2.59 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 2.19/2.59 , clause( 20215, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.19/2.59 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 2.19/2.59 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.19/2.59 , clause( 20216, [ 'c_HOL_Oord__class_Oless'( X,
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 2.19/2.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.19/2.59 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20217, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 2.19/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~(
% 2.19/2.59 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 2.19/2.59 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20218, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.19/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 2.19/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 2.19/2.59 , clause( 20219, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.19/2.59 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 2.19/2.59 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20220, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'(
% 2.19/2.59 Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20221, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.19/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 2.19/2.59 , clause( 20222, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 2.19/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20223, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.19/2.59 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 2.19/2.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.19/2.59 , clause( 20224, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.19/2.59 ) ] )
% 2.19/2.59 , clause( 20225, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 2.19/2.59 ) ] )
% 2.19/2.59 , clause( 20226, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.19/2.59 ) ] )
% 2.19/2.59 , clause( 20227, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.19/2.59 ) ] )
% 2.19/2.59 , clause( 20228, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.19/2.59 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 2.19/2.59 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 2.19/2.59 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20229, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 2.19/2.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 2.19/2.59 , clause( 20230, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 2.19/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z
% 2.19/2.59 , X ) ), Z ), Y ) ] )
% 2.19/2.59 , clause( 20231, [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP(
% 2.19/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) )
% 2.19/2.59 ), hBOOL( hAPP( X, Z ) ) ] )
% 2.19/2.59 , clause( 20232, [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP(
% 2.19/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) )
% 2.19/2.59 ), hBOOL( hAPP( X, Z ) ) ] )
% 2.19/2.59 , clause( 20233, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.19/2.59 X, Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.19/2.59 , clause( 20234, [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 2.19/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 2.19/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20235, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.19/2.59 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20236, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 2.19/2.59 , T, X ) ) ), =( Y, Z ) ] )
% 2.19/2.59 , clause( 20237, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.19/2.59 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 2.19/2.59 , T, X ) ) ), =( Z, T ) ] )
% 2.19/2.59 , clause( 20238, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.19/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 2.19/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.19/2.59 , clause( 20239, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 2.24/2.59 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20240, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 2.24/2.59 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20241, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.24/2.59 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 2.24/2.59 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 2.24/2.59 , clause( 20242, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.24/2.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.24/2.59 ) ), =( Y, Z ) ] )
% 2.24/2.59 , clause( 20243, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.24/2.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.24/2.59 ) ), =( Y, Z ) ] )
% 2.24/2.59 , clause( 20244, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.24/2.59 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.24/2.59 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 2.24/2.59 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20245, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.24/2.59 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 2.24/2.59 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 2.24/2.59 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20246, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ),
% 2.24/2.59 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 2.24/2.59 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20247, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ] )
% 2.24/2.59 , clause( 20248, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ] )
% 2.24/2.59 , clause( 20249, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.24/2.59 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 2.24/2.59 , Y ), Z ), Z, X ), Y ) ] )
% 2.24/2.59 , clause( 20250, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.24/2.59 X, 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20251, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.24/2.59 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20252, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X,
% 2.24/2.59 'c_HOL_Ominus__class_Ominus'( U, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.24/2.59 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, U, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20253, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.24/2.59 , clause( 20254, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 2.24/2.59 , Y ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( X, Z ), T ) ) ) ] )
% 2.24/2.59 , clause( 20255, [ ~( 'c_ListOrder_Ostep1'( X, 'c_List_Olist_ONil'( Y ), Z
% 2.24/2.59 , Y ) ) ] )
% 2.24/2.59 , clause( 20256, [ ~( 'c_ListOrder_Ostep1'( X, Y, 'c_List_Olist_ONil'( Z )
% 2.24/2.59 , Z ) ) ] )
% 2.24/2.59 , clause( 20257, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.24/2.59 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y
% 2.24/2.59 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.24/2.59 , clause( 20258, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.24/2.59 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X
% 2.24/2.59 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20259, [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z
% 2.24/2.59 ), Y ) ] )
% 2.24/2.59 , clause( 20260, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.24/2.59 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20261, [ =( 'c_Predicate_Oconversep'( 'c_fequal'( X ), X, X ),
% 2.24/2.59 'c_fequal'( X ) ) ] )
% 2.24/2.59 , clause( 20262, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 2.24/2.59 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20263, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X )
% 2.24/2.59 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20264, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 2.24/2.59 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20265, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 2.24/2.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ) ) ) ] )
% 2.24/2.59 , clause( 20266, [ ~(
% 2.24/2.59 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 2.24/2.59 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.24/2.59 T, X ) ) ] )
% 2.24/2.59 , clause( 20267, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20268, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.24/2.59 ) ) ) ] )
% 2.24/2.59 , clause( 20269, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.24/2.59 ) ) ) ] )
% 2.24/2.59 , clause( 20270, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20271, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20272, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 2.24/2.59 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20273, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 2.24/2.59 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ), 'c_List_Ofoldr'(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 2.24/2.59 ) ) ] )
% 2.24/2.59 , clause( 20274, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 2.24/2.59 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ] )
% 2.24/2.59 , clause( 20275, [ =( 'c_Predicate_Oconversep'( 'c_Predicate_Oconversep'( X
% 2.24/2.59 , Y, Z ), Z, Y ), X ) ] )
% 2.24/2.59 , clause( 20276, [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20277, [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20278, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 2.24/2.59 , clause( 20279, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 2.24/2.59 , clause( 20280, [ ~(
% 2.24/2.59 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 2.24/2.59 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.24/2.59 , clause( 20281, [ ~(
% 2.24/2.59 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 2.24/2.59 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.24/2.59 , clause( 20282, [ ~(
% 2.24/2.59 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 2.24/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 2.24/2.59 , clause( 20283, [ ~(
% 2.24/2.59 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 2.24/2.59 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.24/2.59 , clause( 20284, [ ~(
% 2.24/2.59 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 2.24/2.59 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.24/2.59 , clause( 20285, [ ~(
% 2.24/2.59 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 2.24/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 2.24/2.59 , clause( 20286, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20287, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , Z ), Y ), 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20288, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20289, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.24/2.59 , clause( 20290, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20291, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 2.24/2.59 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20292, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 2.24/2.59 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 2.24/2.59 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ] )
% 2.24/2.59 , clause( 20293, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y,
% 2.24/2.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.24/2.59 , clause( 20294, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20295, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 2.24/2.59 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), 'c_HOL_Oone__class_Oone'(
% 2.24/2.59 'tc_nat' ) ) ) ) ) ] )
% 2.24/2.59 , clause( 20296, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 2.24/2.59 , Y ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Transitive__Closure_Ortranclp'( X, Y ), U ), T ) ) ), ~( hBOOL( hAPP(
% 2.24/2.59 hAPP( X, Z ), U ) ) ) ] )
% 2.24/2.59 , clause( 20297, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 2.24/2.59 , Y ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP(
% 2.24/2.59 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ] )
% 2.24/2.59 , clause( 20298, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 X, Y ), T ) ) ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 2.24/2.59 , clause( 20299, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 X, Y ), T ) ) ), ~( 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 2.24/2.59 , clause( 20300, [ 'c_Type_Otypings'( X, Y,
% 2.24/2.59 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X, T, Y ) ), ~(
% 2.24/2.59 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', T, Y,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 2.24/2.59 , clause( 20301, [ 'c_Type_Otypings'( X, Y,
% 2.24/2.59 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X, T, Y ) ), ~(
% 2.24/2.59 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', T, Y,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 2.24/2.59 , clause( 20302, [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 2.24/2.59 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 2.24/2.59 'tc_nat' ) ) ), 'c_Lambda_Olift'( Y, T ), Z ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20303, [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 2.24/2.59 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, T ), 'c_Lambda_Olift'( Y, T ),
% 2.24/2.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 2.24/2.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.24/2.59 T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 2.24/2.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20304, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 2.24/2.59 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20305, [ =( X, hAPP( hAPP( 'c_Type_Otype_OFun',
% 2.24/2.59 'c_Type_Osko__Type__Xtyping__elims__3__1'( X, Y, Z ) ),
% 2.24/2.59 'c_Type_Osko__Type__Xtyping__elims__3__2'( X, Y, Z ) ) ), ~(
% 2.24/2.59 'c_Type_Otyping'( Y, 'c_Lambda_OdB_OAbs'( Z ), X ) ) ] )
% 2.24/2.59 , clause( 20306, [ =( X, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 2.24/2.59 'c_Type_Osko__Type__Xvar__app__types__1__1'( Y, X, Z, T ), Y,
% 2.24/2.59 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( Z,
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X ) ), ~( 'c_Type_Otypings'( Z, W, V0
% 2.24/2.59 ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 2.24/2.59 , Y ) ) ] )
% 2.24/2.59 , clause( 20307, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.24/2.59 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.24/2.59 , clause( 20308, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.24/2.59 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 2.24/2.59 , clause( 20309, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.24/2.59 ~( 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X
% 2.24/2.59 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.24/2.59 , clause( 20310, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.24/2.59 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.24/2.59 , clause( 20311, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.24/2.59 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 2.24/2.59 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.24/2.59 , clause( 20312, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.24/2.59 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 2.24/2.59 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.24/2.59 , clause( 20313, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 2.24/2.59 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.24/2.59 , clause( 20314, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 2.24/2.59 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.24/2.59 , clause( 20315, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.24/2.59 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.24/2.59 , clause( 20316, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.24/2.59 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 2.24/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.24/2.59 , clause( 20317, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.24/2.59 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 2.24/2.59 , clause( 20318, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 2.24/2.59 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.24/2.59 , clause( 20319, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 2.24/2.59 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.24/2.59 , clause( 20320, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 2.24/2.59 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20321, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.24/2.59 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 2.24/2.59 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 2.24/2.59 , clause( 20322, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 2.24/2.59 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20323, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 2.24/2.59 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20324, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20325, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20326, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 2.24/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20327, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20328, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 2.24/2.59 ] )
% 2.24/2.59 , clause( 20329, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 2.24/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 2.24/2.59 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20330, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 2.24/2.59 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 2.24/2.59 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), ~( hBOOL( hAPP(
% 2.24/2.59 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 2.24/2.59 'tc_Lambda_OdB' ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 2.24/2.59 ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20331, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 2.24/2.59 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 2.24/2.59 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ) ), ~( hBOOL( hAPP(
% 2.24/2.59 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 2.24/2.59 'tc_Lambda_OdB' ), X ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20332, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 2.24/2.59 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 2.24/2.59 , Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ) ), ~( hBOOL( hAPP(
% 2.24/2.59 hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 2.24/2.59 'tc_Lambda_OdB' ), Y ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20333, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 2.24/2.59 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ),
% 2.24/2.59 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 2.24/2.59 ), Y ) ) ) ] )
% 2.24/2.59 , clause( 20334, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'(
% 2.24/2.59 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 2.24/2.59 'c_Lambda_OdB_OApp', X ), Y ), Z ) ] )
% 2.24/2.59 , clause( 20335, [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 2.24/2.59 ), Y ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 2.24/2.59 'tc_Lambda_OdB' ) ) ] )
% 2.24/2.59 , clause( 20336, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 2.24/2.59 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ),
% 2.24/2.59 'c_Lambda_Osubst'( X, T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta'
% 2.24/2.59 , Y ), T ) ) ) ] )
% 2.24/2.59 , clause( 20337, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 2.24/2.59 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ),
% 2.24/2.59 'c_Lambda_Osubst'( T, Y, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 2.24/2.59 ), T ) ) ) ] )
% 2.24/2.59 , clause( 20338, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 2.24/2.59 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Osubst'( X, Y, Z ) ),
% 2.24/2.59 'c_Lambda_Osubst'( X, T, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), Y
% 2.24/2.59 ), T ) ) ) ] )
% 2.24/2.59 , clause( 20339, [ 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', X,
% 2.24/2.59 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, X, Z ),
% 2.24/2.59 'tc_Lambda_OdB' ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), X,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20340, [ 'c_Type_Otyping'( X, Y,
% 2.24/2.59 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, T, Y ) ), ~(
% 2.24/2.59 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', T ), Y ), Z ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20341, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 2.24/2.59 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.24/2.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20342, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 2.24/2.59 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.24/2.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20343, [ =( 'c_Type_Otype_Otype__size'( hAPP( hAPP(
% 2.24/2.59 'c_Type_Otype_OFun', X ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 'c_Type_Otype_Otype__size'( X ) ), 'c_Type_Otype_Otype__size'( Y ) ) ),
% 2.24/2.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 2.24/2.59 , clause( 20344, [ =( 'c_Nat_Osize__class_Osize'( hAPP( hAPP(
% 2.24/2.59 'c_Type_Otype_OFun', X ), Y ), 'tc_Type_Otype' ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Nat_Osize__class_Osize'( X,
% 2.24/2.59 'tc_Type_Otype' ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_Type_Otype' ) ) )
% 2.24/2.59 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 2.24/2.59 , clause( 20345, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 2.24/2.59 ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.24/2.59 'tc_nat' ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20346, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.24/2.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.24/2.59 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20347, [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.24/2.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.24/2.59 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20348, [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OAbs'( X )
% 2.24/2.59 , 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ), 'c_Suc'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 2.24/2.59 , clause( 20349, [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OAbs'( X ) )
% 2.24/2.59 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 'c_Lambda_OdB_OdB__size'( X ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ) ) ) ) ] )
% 2.24/2.59 , clause( 20350, [ =( 'c_Nat_Osize__class_Osize'( hAPP( hAPP(
% 2.24/2.59 'c_Lambda_OdB_OApp', X ), Y ), 'tc_Lambda_OdB' ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Nat_Osize__class_Osize'( X,
% 2.24/2.59 'tc_Lambda_OdB' ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_Lambda_OdB' ) ) )
% 2.24/2.59 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 2.24/2.59 , clause( 20351, [ =( 'c_Lambda_OdB_OdB__size'( hAPP( hAPP(
% 2.24/2.59 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 'c_Lambda_OdB_OdB__size'( X ) ), 'c_Lambda_OdB_OdB__size'( Y ) ) ),
% 2.24/2.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 2.24/2.59 , clause( 20352, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 2.24/2.59 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ),
% 2.24/2.59 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ] )
% 2.24/2.59 , clause( 20353, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 2.24/2.59 , clause( 20354, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 2.24/2.59 , clause( 20355, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.24/2.59 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 2.24/2.59 ) ) ] )
% 2.24/2.59 , clause( 20356, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20357, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20358, [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.24/2.59 ] )
% 2.24/2.59 , clause( 20359, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , X ), Y ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20360, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.24/2.59 'class_Int_Onumber__ring'( X ) ), ~( =( Y, hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), =( Z,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.24/2.59 , clause( 20361, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 2.24/2.59 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 2.24/2.59 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 2.24/2.59 , clause( 20362, [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =(
% 2.24/2.59 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), T, X, X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ] )
% 2.24/2.59 , clause( 20363, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.24/2.59 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 2.24/2.59 , clause( 20364, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T )
% 2.24/2.59 ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( X, T, 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20365, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 2.24/2.59 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20366, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.24/2.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 2.24/2.59 , clause( 20367, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.24/2.59 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 2.24/2.59 , clause( 20368, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20369, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20370, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20371, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20372, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20373, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20374, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20375, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20376, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 2.24/2.59 ) ) ) ] )
% 2.24/2.59 , clause( 20377, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 2.24/2.59 ) ) ) ] )
% 2.24/2.59 , clause( 20378, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 'c_Suc'( X ) ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 'tc_nat' ), X ), Y ) ) ) ] )
% 2.24/2.59 , clause( 20379, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 2.24/2.59 ), 'c_Suc'( Y ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 'tc_nat' ), X ), Y ) ) ) ] )
% 2.24/2.59 , clause( 20380, [ hBOOL( hAPP( 'c_InductTermi_OIT', X ) ), ~(
% 2.24/2.59 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB' ) ) ] )
% 2.24/2.59 , clause( 20381, [ 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'(
% 2.24/2.59 'c_Lambda_Obeta', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB'
% 2.24/2.59 ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 2.24/2.59 , clause( 20382, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 2.24/2.59 , Y ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Transitive__Closure_Ortranclp'( X, Y ), U ), T ) ) ), ~( hBOOL( hAPP(
% 2.24/2.59 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), Z ), U ) ) ) ] )
% 2.24/2.59 , clause( 20383, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~(
% 2.24/2.59 'c_Wellfounded_Oaccp'( X, T, Z ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Transitive__Closure_Ortranclp'( X, Z ), Y ), T ) ) ) ] )
% 2.24/2.59 , clause( 20384, [ 'c_Wellfounded_Oaccp'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Transitive__Closure_Ortranclp'( X, Z ), Y ), T ) ) ), ~(
% 2.24/2.59 'c_Wellfounded_Oaccp'( X, T, Z ) ) ] )
% 2.24/2.59 , clause( 20385, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 2.24/2.59 , Y ), Z ), Z ) ) ] )
% 2.24/2.59 , clause( 20386, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 2.24/2.59 , Y ), Z ), Z ) ) ] )
% 2.24/2.59 , clause( 20387, [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ] )
% 2.24/2.59 , clause( 20388, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.24/2.59 , clause( 20389, [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ] )
% 2.24/2.59 , clause( 20390, [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ] )
% 2.24/2.59 , clause( 20391, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.24/2.59 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.24/2.59 , clause( 20392, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20393, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.24/2.59 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 X ), Y ), Z ) ), T ) ) ] )
% 2.24/2.59 , clause( 20394, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 2.24/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 2.24/2.59 , clause( 20395, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 2.24/2.59 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP(
% 2.24/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20396, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP(
% 2.24/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20397, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.24/2.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 2.24/2.59 , clause( 20398, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.24/2.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 2.24/2.59 , clause( 20399, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 2.24/2.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 2.24/2.59 , clause( 20400, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.24/2.59 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 X ), Y ), Z ) ), T ) ) ] )
% 2.24/2.59 , clause( 20401, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.24/2.59 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 X ), Y ), T ) ), Z ) ) ] )
% 2.24/2.59 , clause( 20402, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.24/2.59 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 2.24/2.59 , clause( 20403, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.24/2.59 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 2.24/2.59 , clause( 20404, [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ),
% 2.24/2.59 T ), U ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ] )
% 2.24/2.59 , clause( 20405, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ] )
% 2.24/2.59 , clause( 20406, [ hBOOL( hAPP( hAPP( 'c_Predicate_Oconversep'( X, Y, Z ),
% 2.24/2.59 T ), U ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ) ] )
% 2.24/2.59 , clause( 20407, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Predicate_Oconversep'( X, T, U ), Z ), Y ) ) ) ] )
% 2.24/2.59 , clause( 20408, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.24/2.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ] )
% 2.24/2.59 , clause( 20409, [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T
% 2.24/2.59 ), Z ) ] )
% 2.24/2.59 , clause( 20410, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 2.24/2.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 2.24/2.59 , clause( 20411, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 2.24/2.59 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 2.24/2.59 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.24/2.59 , clause( 20412, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.24/2.59 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20413, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.24/2.59 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y
% 2.24/2.59 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20414, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.24/2.59 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X
% 2.24/2.59 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.24/2.59 , clause( 20415, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 2.24/2.59 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 2.24/2.59 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ] )
% 2.24/2.59 , clause( 20416, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 X ), 'c_Suc'( Y ) ) ) ] )
% 2.24/2.59 , clause( 20417, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( X
% 2.24/2.59 , Y ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Transitive__Closure_Ortranclp'( 'c_Predicate_Oconversep'( X, Y, Y ), Y
% 2.24/2.59 ), T ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20418, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 2.24/2.59 'c_Predicate_Oconversep'( X, Y, Y ), Y ), Z ), T ) ), ~( hBOOL( hAPP(
% 2.24/2.59 hAPP( 'c_Transitive__Closure_Ortranclp'( X, Y ), T ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20419, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 2.24/2.59 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP(
% 2.24/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 2.24/2.59 ) ) ) ] )
% 2.24/2.59 , clause( 20420, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 2.24/2.59 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20421, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z )
% 2.24/2.59 ) ), =( Y, Z ) ] )
% 2.24/2.59 , clause( 20422, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y )
% 2.24/2.59 ) ), =( X, Z ) ] )
% 2.24/2.59 , clause( 20423, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z )
% 2.24/2.59 ) ), =( Y, Z ) ] )
% 2.24/2.59 , clause( 20424, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.24/2.59 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 2.24/2.59 , clause( 20425, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 2.24/2.59 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 2.24/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 2.24/2.59 , clause( 20426, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 2.24/2.59 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 2.24/2.59 , clause( 20427, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 2.24/2.59 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ] )
% 2.24/2.59 , clause( 20428, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X,
% 2.24/2.59 'c_Lambda_Olift'( Y, Z ), 'c_Suc'( T ) ), 'c_Lambda_Osubst'( U, Y, T ), Z
% 2.24/2.59 ), 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X, U, Z ), Y, T ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20429, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y,
% 2.24/2.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20430, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.24/2.59 , clause( 20431, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.24/2.59 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) )
% 2.24/2.59 ) ] )
% 2.24/2.59 , clause( 20432, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20433, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20434, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20435, [ =( 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Y ), 'c_Suc'(
% 2.24/2.59 Z ) ), 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Z ), Y ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 2.24/2.59 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20436, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 2.24/2.59 'c_HOL_Oone__class_Oone'( X ) ), X ) ] )
% 2.24/2.59 , clause( 20437, [ =( 'c_Transitive__Closure_Ortranclp'(
% 2.24/2.59 'c_Transitive__Closure_Ortranclp'( X, Y ), Y ),
% 2.24/2.59 'c_Transitive__Closure_Ortranclp'( X, Y ) ) ] )
% 2.24/2.59 , clause( 20438, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.24/2.59 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y ) ] )
% 2.24/2.59 , clause( 20439, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.24/2.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 X ) ), Y ), Y ) ] )
% 2.24/2.59 , clause( 20440, [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 2.24/2.59 , X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.24/2.59 , clause( 20441, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ] )
% 2.24/2.59 , clause( 20442, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 2.24/2.59 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ] )
% 2.24/2.59 , clause( 20443, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.24/2.59 'class_Int_Onumber__ring'( X ) ), =( Y, hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 2.24/2.59 ] )
% 2.24/2.59 , clause( 20444, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.24/2.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 2.24/2.59 , clause( 20445, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 2.24/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 2.24/2.59 , Y ), Y ) ] )
% 2.24/2.59 , clause( 20446, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 2.24/2.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 2.24/2.59 ) ), Y ) ] )
% 2.24/2.59 , clause( 20447, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.24/2.59 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 2.24/2.59 , clause( 20448, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.24/2.59 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y ) ] )
% 2.24/2.59 , clause( 20449, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 2.24/2.59 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20450, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20451, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 2.24/2.59 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20452, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 2.24/2.59 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 2.24/2.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 2.24/2.59 'tc_nat' ) ) ) ) ) ] )
% 2.24/2.59 , clause( 20453, [ 'c_Type_Otypings'( X, Y,
% 2.24/2.59 'c_Type_Osko__Type__Xvar__app__types__1__1'( Z, T, X, Y ) ), ~(
% 2.24/2.59 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ) ),
% 2.24/2.59 ~( 'c_Type_Otypings'( X, W, V0 ) ), ~( 'c_Type_Otyping'( X,
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( U ), W, 'tc_Lambda_OdB',
% 2.24/2.59 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 2.24/2.59 , clause( 20454, [ 'c_Type_Otypings'( X, Y,
% 2.24/2.59 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X, T, Y ) ), ~(
% 2.24/2.59 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OVar'( T ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20455, [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Type_Otyping'( X, T,
% 2.24/2.59 Z ) ), ~( hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 2.24/2.59 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), T ), Y ) ) ) ] )
% 2.24/2.59 , clause( 20456, [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 2.24/2.59 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X,
% 2.24/2.59 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 2.24/2.59 'tc_Lambda_OdB' ), Z ) ) ] )
% 2.24/2.59 , clause( 20457, [ 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ), ~(
% 2.24/2.59 'c_Type_Otypings'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y,
% 2.24/2.59 'c_List_Ofoldr'( 'c_Type_Otype_OFun', U, T, 'tc_Type_Otype',
% 2.24/2.59 'tc_Type_Otype' ) ) ) ] )
% 2.24/2.59 , clause( 20458, [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'(
% 2.24/2.59 'c_Type_Otype_OFun', 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X,
% 2.24/2.59 Y, T ), Z, 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 2.24/2.59 'tc_Lambda_OdB' ), Z ) ) ] )
% 2.24/2.59 , clause( 20459, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 2.24/2.59 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_Lambda_Olift'( X, Y ) ),
% 2.24/2.59 'c_Lambda_Olift'( Z, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), X
% 2.24/2.59 ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20460, [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 2.24/2.59 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 2.24/2.59 'c_Suc'( Y ), Z, T ) ) ] )
% 2.24/2.59 , clause( 20461, [ 'c_Type_Otyping'( 'c_Type_Oshift'( X,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.24/2.59 'c_Type_Osko__Type__Xtyping__elims__3__1'( Y, X, Z ), 'tc_Type_Otype' ),
% 2.24/2.59 Z, 'c_Type_Osko__Type__Xtyping__elims__3__2'( Y, X, Z ) ), ~(
% 2.24/2.59 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Z ), Y ) ) ] )
% 2.24/2.59 , clause( 20462, [ 'c_Type_Otyping'( 'c_Type_Oshift'( X,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.24/2.59 'c_Type_Osko__Type__Xabs__typeE__1__1'( X, Y ), 'tc_Type_Otype' ), Y,
% 2.24/2.59 'c_Type_Osko__Type__Xabs__typeE__1__2'( X, Y ) ), ~( 'c_Type_Otyping'( X
% 2.24/2.59 , 'c_Lambda_OdB_OAbs'( Y ), Z ) ) ] )
% 2.24/2.59 , clause( 20463, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ),
% 2.24/2.59 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 2.24/2.59 'c_Type_Osko__Type__Xvar__app__typesE__1__1'( Z, X, Y, T ), Z,
% 2.24/2.59 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Y ), T,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ] )
% 2.24/2.59 , clause( 20464, [ ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'(
% 2.24/2.59 'c_Lambda_Obeta', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ) ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) )
% 2.24/2.59 , ~( 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB' ) ),
% 2.24/2.59 'c_Wellfounded_Oaccp'( 'c_Predicate_Oconversep'( 'c_Lambda_Obeta',
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 2.24/2.59 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB' ) ] )
% 2.24/2.59 , clause( 20465, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Z, 'tc_Lambda_OdB',
% 2.24/2.59 'tc_Lambda_OdB' ) ) ), ~( 'c_ListOrder_Ostep1'( 'c_Lambda_Obeta', Y, Z,
% 2.24/2.59 'tc_Lambda_OdB' ) ) ] )
% 2.24/2.59 , clause( 20466, [ hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'(
% 2.24/2.59 'c_Lambda_Obeta', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 2.24/2.59 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~(
% 2.24/2.59 hBOOL( hAPP( hAPP( 'c_Transitive__Closure_Ortranclp'( 'c_Lambda_Obeta',
% 2.24/2.59 'tc_Lambda_OdB' ), X ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20467, [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( X ) ) ] )
% 2.24/2.59 , clause( 20468, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 2.24/2.59 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 2.24/2.59 , clause( 20469, [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'(
% 2.24/2.59 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 2.24/2.59 , clause( 20470, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 2.24/2.59 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 2.24/2.59 , clause( 20471, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 2.24/2.59 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ] )
% 2.24/2.59 , clause( 20472, [ =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), 'c_List_Olist_ONil'(
% 2.24/2.59 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ] )
% 2.24/2.59 , clause( 20473, [ 'c_Type_Otyping'( X, Y, hAPP( hAPP( 'c_Type_Otype_OFun'
% 2.24/2.59 , 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, Y, T ) ), Z ) ), ~(
% 2.24/2.59 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), T ), Z ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20474, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.24/2.59 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.24/2.59 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20475, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.24/2.59 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 2.24/2.59 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 2.24/2.59 , clause( 20476, [ =( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OVar'( Y ),
% 2.24/2.59 'c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1'( Y, Z, X ),
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Lambda_Obeta', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OVar'( Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), X ) )
% 2.24/2.59 ) ] )
% 2.24/2.59 , clause( 20477, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB',
% 2.24/2.59 'tc_Lambda_OdB' ) ) ), ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y,
% 2.24/2.59 'tc_Lambda_OdB' ) ) ] )
% 2.24/2.59 , clause( 20478, [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_ea______',
% 2.24/2.59 'v_ia______', 'v_T____', 'tc_Type_Otype' ), 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 2.24/2.59 'v_r____' ) ), 'v_a____' ), 'v_as____', 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 2.24/2.59 ), 'v_T_Ha______' ) ] )
% 2.24/2.59 , clause( 20479, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 2.24/2.59 'c_Lambda_OdB_OVar'( Z ) ) ) ] )
% 2.24/2.59 , clause( 20480, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_OdB_OAbs'(
% 2.24/2.59 X ) ), 'c_Lambda_OdB_OAbs'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Lambda_Obeta', X ), Y ) ) ) ] )
% 2.24/2.59 , clause( 20481, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OAbs'( X ) ), Y ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 2.24/2.59 , clause( 20482, [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP(
% 2.24/2.59 'c_Lambda_OdB_OApp', X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ), ~( hBOOL( hAPP(
% 2.24/2.59 'c_InductTermi_OIT', X ) ) ) ] )
% 2.24/2.59 , clause( 20483, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Olift'( X
% 2.24/2.59 , Y ) ), 'c_Lambda_Olift'( Z, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Lambda_Obeta', X ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20484, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 2.24/2.59 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 2.24/2.59 ) ) ] )
% 2.24/2.59 , clause( 20485, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ),
% 2.24/2.59 X ) ] )
% 2.24/2.59 , clause( 20486, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_u____' ) ) ] )
% 2.24/2.59 , clause( 20487, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 2.24/2.59 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Z ), Y
% 2.24/2.59 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20488, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 2.24/2.59 'c_Lambda_OdB_OApp', X ), Y ) ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Z
% 2.24/2.59 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', Y ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20489, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X
% 2.24/2.59 ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 2.24/2.59 , clause( 20490, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 2.24/2.59 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 2.24/2.59 , clause( 20491, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 2.24/2.59 'c_Lambda_OdB_OAbs'( X ), Y ) ] )
% 2.24/2.59 , clause( 20492, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 2.24/2.59 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ] )
% 2.24/2.59 , clause( 20493, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20494, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20495, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 2.24/2.59 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.24/2.59 , clause( 20496, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 2.24/2.59 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.24/2.59 , clause( 20497, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_ua______' ) ) ] )
% 2.24/2.59 , clause( 20498, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 2.24/2.59 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 2.24/2.59 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20499, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_Lambda_Osubst'(
% 2.24/2.59 X, Y, Z ) ), 'c_Lambda_Osubst'( T, Y, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Lambda_Obeta', X ), T ) ) ) ] )
% 2.24/2.59 , clause( 20500, [ =( 'c_Lambda_Olift'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 2.24/2.59 ), Y ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Olift'( X, Z ) )
% 2.24/2.59 , 'c_Lambda_Olift'( Y, Z ) ) ) ] )
% 2.24/2.59 , clause( 20501, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OVar'( X
% 2.24/2.59 ) ) ) ] )
% 2.24/2.59 , clause( 20502, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 2.24/2.59 ) ) ] )
% 2.24/2.59 , clause( 20503, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 2.24/2.59 X ) ), Y ), Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 2.24/2.59 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y,
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB',
% 2.24/2.59 'tc_Lambda_OdB' ) ) ) ) ] )
% 2.24/2.59 , clause( 20504, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Olift'( X, Y
% 2.24/2.59 ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ] )
% 2.24/2.59 , clause( 20505, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ] )
% 2.24/2.59 , clause( 20506, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 2.24/2.59 ) ), =( X, Y ) ] )
% 2.24/2.59 , clause( 20507, [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP(
% 2.24/2.59 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20508, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 2.24/2.59 'c_Lambda_OdB_OVar'( X ), Y ) ] )
% 2.24/2.59 , clause( 20509, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ),
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y, 'tc_Lambda_OdB',
% 2.24/2.59 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', X ), Z ) )
% 2.24/2.59 ) ] )
% 2.24/2.59 , clause( 20510, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20511, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20512, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.24/2.59 , clause( 20513, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.24/2.59 , clause( 20514, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.24/2.59 , clause( 20515, [ hBOOL( hAPP( hAPP( 'c_Lambda_Obeta', hAPP( hAPP(
% 2.24/2.59 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ) ), 'c_Lambda_Osubst'(
% 2.24/2.59 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 2.24/2.59 , clause( 20516, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 2.24/2.59 ), =( Z, Y ) ] )
% 2.24/2.59 , clause( 20517, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 2.24/2.59 ) ] )
% 2.24/2.59 , clause( 20518, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 2.24/2.59 , clause( 20519, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), =( Z, Y ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20520, [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 2.24/2.59 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 2.24/2.59 'tc_Lambda_OdB' ), X ) ) ] )
% 2.24/2.59 , clause( 20521, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 2.24/2.59 , clause( 20522, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 2.24/2.59 ), =( Z, Y ) ] )
% 2.24/2.59 , clause( 20523, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 2.24/2.59 , clause( 20524, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 2.24/2.59 ) ] )
% 2.24/2.59 , clause( 20525, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 2.24/2.59 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ] )
% 2.24/2.59 , clause( 20526, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 2.24/2.59 hAPP( 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ] )
% 2.24/2.59 , clause( 20527, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 2.24/2.59 , clause( 20528, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OAbs'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 2.24/2.59 , clause( 20529, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 2.24/2.59 'c_Lambda_OdB_OAbs'( Z ) ) ] )
% 2.24/2.59 , clause( 20530, [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y
% 2.24/2.59 ), Z ), T ), ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y
% 2.24/2.59 , hAPP( hAPP( 'c_Type_Otype_OFun', U ), T ) ) ) ] )
% 2.24/2.59 , clause( 20531, [ ~( hBOOL( hAPP( hAPP( 'c_Lambda_Obeta',
% 2.24/2.59 'c_Lambda_OdB_OVar'( X ) ), Y ) ) ) ] )
% 2.24/2.59 , clause( 20532, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'(
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( 'v_r____',
% 2.24/2.59 'v_a____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_as____',
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), X, Y ) ) ), ~( 'c_Type_Otyping'( Z, X
% 2.24/2.59 , 'v_T____' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ), ~(
% 2.24/2.59 'c_Type_Otyping'( 'c_Type_Oshift'( Z, Y, 'v_T____', 'tc_Type_Otype' ),
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( 'v_r____',
% 2.24/2.59 'v_a____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_as____',
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ) ) ] )
% 2.24/2.59 , clause( 20533, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.24/2.59 ] )
% 2.24/2.59 , clause( 20534, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.24/2.59 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20535, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 2.24/2.59 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 2.24/2.59 ) ) ] )
% 2.24/2.59 , clause( 20536, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( X,
% 2.24/2.59 'c_Lambda_OdB_OVar'( Y ), Z ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X
% 2.24/2.59 ) ) ) ] )
% 2.24/2.59 , clause( 20537, [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP(
% 2.24/2.59 hAPP( 'c_Type_Otype_OFun', Z ), T ) ) ), =( Y, T ) ] )
% 2.24/2.59 , clause( 20538, [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP(
% 2.24/2.59 hAPP( 'c_Type_Otype_OFun', Z ), T ) ) ), =( X, Z ) ] )
% 2.24/2.59 , clause( 20539, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ),
% 2.24/2.59 Y ) ] )
% 2.24/2.59 , clause( 20540, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Y, T ) ] )
% 2.24/2.59 , clause( 20541, [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OVar'( X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 2.24/2.59 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 2.24/2.59 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ] )
% 2.24/2.59 , clause( 20542, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP(
% 2.24/2.59 'c_Lambda_OdB_OApp', Y ), Z ) ) ) ] )
% 2.24/2.59 , clause( 20543, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 2.24/2.59 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( 'v_r____', 'v_a____',
% 2.24/2.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'v_as____', 'tc_Lambda_OdB',
% 2.24/2.59 'tc_Lambda_OdB' ) ) ) ] )
% 2.24/2.59 , clause( 20544, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y )
% 2.24/2.59 ) ), =( X, Y ) ] )
% 2.24/2.59 , clause( 20545, [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 2.24/2.59 'c_Lambda_OdB_OAbs'( Z ) ) ) ] )
% 2.24/2.59 , clause( 20546, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y )
% 2.24/2.59 ) ) ] )
% 2.24/2.59 , clause( 20547, [ =( 'c_Lambda_Osubst'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X
% 2.24/2.59 ), Y ), Z, T ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Z
% 2.24/2.59 , T ) ), 'c_Lambda_Osubst'( Y, Z, T ) ) ) ] )
% 2.24/2.59 , clause( 20548, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.24/2.59 Y, X ) ) ] )
% 2.24/2.59 , clause( 20549, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.24/2.59 Y, X ) ) ] )
% 2.24/2.59 , clause( 20550, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.24/2.59 Y, X ) ) ] )
% 2.24/2.59 , clause( 20551, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.24/2.59 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.24/2.59 Y, X ) ) ] )
% 2.24/2.59 , clause( 20552, [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z,
% 2.24/2.59 'tc_Type_Otype' ), 'c_Lambda_Olift'( T, Y ), U ), ~( 'c_Type_Otyping'( X
% 2.24/2.59 , T, U ) ) ] )
% 2.24/2.59 , clause( 20553, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'(
% 2.24/2.59 'v_a____', X, Y ) ) ), ~( 'c_Type_Otyping'( Z, X, 'v_T____' ) ), ~( hBOOL(
% 2.24/2.59 hAPP( 'c_InductTermi_OIT', X ) ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 2.24/2.59 Z, Y, 'v_T____', 'tc_Type_Otype' ), 'v_a____', T ) ) ] )
% 2.24/2.59 , clause( 20554, [ 'c_Type_Otyping'( 'v_e____', 'v_u____', 'v_T____' ) ] )
% 2.24/2.59 , clause( 20555, [ hBOOL( hAPP( 'c_InductTermi_OIT', 'v_a____' ) ) ] )
% 2.24/2.59 , clause( 20556, [ 'c_Type_Otyping'( X, Y, Z ), ~( hBOOL( hAPP( hAPP(
% 2.24/2.59 'c_Lambda_Obeta', T ), Y ) ) ), ~( 'c_Type_Otyping'( X, T, Z ) ) ] )
% 2.24/2.59 , clause( 20557, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U
% 2.24/2.59 ) ), ~( 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ] )
% 2.24/2.59 , clause( 20558, [ ~( =( 'v_T____', hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y
% 2.24/2.59 ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( Z, T, U ) )
% 2.24/2.59 ), ~( 'c_Type_Otyping'( W, T, Y ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT'
% 2.24/2.59 , T ) ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( W, U, Y, 'tc_Type_Otype'
% 2.24/2.59 ), Z, V0 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', Z ) ) ) ] )
% 2.24/2.59 , clause( 20559, [ ~( =( 'v_T____', hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y
% 2.24/2.59 ) ) ), hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_Osubst'( Z, T, U ) )
% 2.24/2.59 ), ~( 'c_Type_Otyping'( W, T, X ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT'
% 2.24/2.59 , T ) ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( W, U, X, 'tc_Type_Otype'
% 2.24/2.59 ), Z, V0 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', Z ) ) ) ] )
% 2.24/2.59 , clause( 20560, [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ] )
% 2.24/2.59 , clause( 20561, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), hAPP(
% 2.24/2.59 hAPP( 'c_Type_Otype_OFun', Z ), T ) ), ~( 'c_Type_Otyping'(
% 2.24/2.59 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.24/2.59 'tc_Type_Otype' ), Y, T ) ) ] )
% 2.24/2.59 , clause( 20562, [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X,
% 2.24/2.59 'c_Lambda_OdB_OVar'( Y ), Z ) ) ] )
% 2.24/2.59 , clause( 20563, [ 'c_Type_Otyping'( 'v_ea______', 'v_ua______', 'v_T____'
% 2.24/2.59 ) ] )
% 2.24/2.59 , clause( 20564, [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____'
% 2.24/2.59 , 'v_T____', 'tc_Type_Otype' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 2.24/2.59 hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( 'v_r____' ) ),
% 2.24/2.59 'v_a____' ), 'v_as____', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'v_T_H____'
% 2.24/2.59 ) ] )
% 2.24/2.59 , clause( 20565, [ 'v_thesis____', ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 2.24/2.59 'v_e____', 'v_i____', 'v_T____', 'tc_Type_Otype' ), 'v_a____', X ) ) ] )
% 2.24/2.59 , clause( 20566, [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X,
% 2.24/2.59 Y ) ) ] )
% 2.24/2.59 , clause( 20567, [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'(
% 2.24/2.59 'c_Type_Oshift'( X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'(
% 2.24/2.59 X, 'c_Lambda_Osubst'( U, Y, T ), W ) ] )
% 2.24/2.59 , clause( 20568, [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____'
% 2.24/2.59 , 'v_T____', 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 2.24/2.59 'c_Lambda_OdB_OAbs'( 'v_r____' ) ), 'v_a____' ), 'v_Ua____' ) ] )
% 2.24/2.59 , clause( 20569, [ ~( 'v_thesis____' ) ] )
% 2.24/2.59 , clause( 20570, [ 'v_thesis____', ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 2.24/2.59 'v_e____', 'v_i____', 'v_T____', 'tc_Type_Otype' ), 'v_a____', X ) ) ] )
% 2.24/2.59 , clause( 20571, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 2.24/2.59 'class_Orderings_Opreorder'( Y ) ) ] )
% 2.24/2.59 , clause( 20572, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 2.24/2.59 'class_Orderings_Oorder'( Y ) ) ] )
% 2.24/2.59 , clause( 20573, [
% 2.24/2.59 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20574, [
% 2.24/2.59 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20575, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 2.24/2.59 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20576, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 2.24/2.59 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20577, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 2.24/2.59 ] )
% 2.24/2.59 , clause( 20578, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20579, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 2.24/2.59 ] )
% 2.24/2.59 , clause( 20580, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20581, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20582, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20583, [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20584, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20585, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20586, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20587, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20588, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20589, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 2.24/2.59 , clause( 20590, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 2.24/2.59 , clause( 20591, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 2.24/2.59 , clause( 20592, [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ] )
% 2.24/2.59 , clause( 20593, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y
% 2.24/2.59 ) ) ) ] )
% 2.24/2.59 ] ).
% 2.24/2.59
% 2.24/2.59
% 2.24/2.59
% 2.24/2.59 subsumption(
% 2.24/2.59 clause( 119, [ 'c_Type_Otyping'( X, Y,
% 2.24/2.59 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, T, Y ) ), ~(
% 2.24/2.59 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', T ), Y ), Z ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , clause( 20340, [ 'c_Type_Otyping'( X, Y,
% 2.24/2.59 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, T, Y ) ), ~(
% 2.24/2.59 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', T ), Y ), Z ) ) ]
% 2.24/2.59 )
% 2.24/2.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.24/2.59 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 2.24/2.59
% 2.24/2.59
% 2.24/2.59 subsumption(
% 2.24/2.59 clause( 303, [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____',
% 2.24/2.59 'v_T____', 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 2.24/2.60 'c_Lambda_OdB_OAbs'( 'v_r____' ) ), 'v_a____' ), 'v_Ua____' ) ] )
% 2.24/2.60 , clause( 20568, [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____'
% 2.24/2.60 , 'v_T____', 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 2.24/2.60 'c_Lambda_OdB_OAbs'( 'v_r____' ) ), 'v_a____' ), 'v_Ua____' ) ] )
% 2.24/2.60 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.24/2.60
% 2.24/2.60
% 2.24/2.60 subsumption(
% 2.24/2.60 clause( 304, [ ~( 'v_thesis____' ) ] )
% 2.24/2.60 , clause( 20569, [ ~( 'v_thesis____' ) ] )
% 2.24/2.60 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.24/2.60
% 2.24/2.60
% 2.24/2.60 resolution(
% 2.24/2.60 clause( 21694, [ ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____'
% 2.24/2.60 , 'v_T____', 'tc_Type_Otype' ), 'v_a____', X ) ) ] )
% 2.24/2.60 , clause( 304, [ ~( 'v_thesis____' ) ] )
% 2.24/2.60 , 0, clause( 20565, [ 'v_thesis____', ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 2.24/2.60 'v_e____', 'v_i____', 'v_T____', 'tc_Type_Otype' ), 'v_a____', X ) ) ] )
% 2.24/2.60 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, X )] )).
% 2.24/2.60
% 2.24/2.60
% 2.24/2.60 subsumption(
% 2.24/2.60 clause( 305, [ ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____',
% 2.24/2.60 'v_T____', 'tc_Type_Otype' ), 'v_a____', X ) ) ] )
% 2.24/2.60 , clause( 21694, [ ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____',
% 2.24/2.60 'v_i____', 'v_T____', 'tc_Type_Otype' ), 'v_a____', X ) ) ] )
% 2.24/2.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.24/2.60
% 2.24/2.60
% 2.24/2.60 resolution(
% 2.24/2.60 clause( 21695, [ ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____'
% 2.24/2.60 , 'v_T____', 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 2.24/2.60 'v_a____' ), X ) ) ] )
% 2.24/2.60 , clause( 305, [ ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____'
% 2.24/2.60 , 'v_T____', 'tc_Type_Otype' ), 'v_a____', X ) ) ] )
% 2.24/2.60 , 0, clause( 119, [ 'c_Type_Otyping'( X, Y,
% 2.24/2.60 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, T, Y ) ), ~(
% 2.24/2.60 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', T ), Y ), Z ) ) ]
% 2.24/2.60 )
% 2.24/2.60 , 0, substitution( 0, [ :=( X, 'c_Type_Osko__Type__Xtyping__elims__2__1'( X
% 2.24/2.60 , 'c_Type_Oshift'( 'v_e____', 'v_i____', 'v_T____', 'tc_Type_Otype' ), Y
% 2.24/2.60 , 'v_a____' ) )] ), substitution( 1, [ :=( X, 'c_Type_Oshift'( 'v_e____'
% 2.24/2.60 , 'v_i____', 'v_T____', 'tc_Type_Otype' ) ), :=( Y, 'v_a____' ), :=( Z, X
% 2.24/2.60 ), :=( T, Y )] )).
% 2.24/2.60
% 2.24/2.60
% 2.24/2.60 subsumption(
% 2.24/2.60 clause( 15094, [ ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____'
% 2.24/2.60 , 'v_T____', 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', X ),
% 2.24/2.60 'v_a____' ), Y ) ) ] )
% 2.24/2.60 , clause( 21695, [ ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____',
% 2.24/2.60 'v_i____', 'v_T____', 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_OdB_OApp'
% 2.24/2.60 , Y ), 'v_a____' ), X ) ) ] )
% 2.24/2.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.24/2.60 )] ) ).
% 2.24/2.60
% 2.24/2.60
% 2.24/2.60 resolution(
% 2.24/2.60 clause( 21696, [] )
% 2.24/2.60 , clause( 15094, [ ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____',
% 2.24/2.60 'v_i____', 'v_T____', 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_OdB_OApp'
% 2.24/2.60 , X ), 'v_a____' ), Y ) ) ] )
% 2.24/2.60 , 0, clause( 303, [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____'
% 2.24/2.60 , 'v_T____', 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 2.24/2.60 'c_Lambda_OdB_OAbs'( 'v_r____' ) ), 'v_a____' ), 'v_Ua____' ) ] )
% 2.24/2.60 , 0, substitution( 0, [ :=( X, 'c_Lambda_OdB_OAbs'( 'v_r____' ) ), :=( Y,
% 2.24/2.60 'v_Ua____' )] ), substitution( 1, [] )).
% 2.24/2.60
% 2.24/2.60
% 2.24/2.60 subsumption(
% 2.24/2.60 clause( 20203, [] )
% 2.24/2.60 , clause( 21696, [] )
% 2.24/2.60 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.24/2.60
% 2.24/2.60
% 2.24/2.60 end.
% 2.24/2.60
% 2.24/2.60 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.24/2.60
% 2.24/2.60 Memory use:
% 2.24/2.60
% 2.24/2.60 space for terms: 441851
% 2.24/2.60 space for clauses: 967897
% 2.24/2.60
% 2.24/2.60
% 2.24/2.60 clauses generated: 95375
% 2.24/2.60 clauses kept: 20204
% 2.24/2.60 clauses selected: 540
% 2.24/2.60 clauses deleted: 375
% 2.24/2.60 clauses inuse deleted: 6
% 2.24/2.60
% 2.24/2.60 subsentry: 268195
% 2.24/2.60 literals s-matched: 183524
% 2.24/2.60 literals matched: 176851
% 2.24/2.60 full subsumption: 64688
% 2.24/2.60
% 2.24/2.60 checksum: -670472360
% 2.24/2.60
% 2.24/2.60
% 2.24/2.60 Bliksem ended
%------------------------------------------------------------------------------