TSTP Solution File: LCL795-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL795-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 07:58:05 EDT 2022
% Result : Timeout 300.02s 300.48s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL795-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Mon Jul 4 17:00:12 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.91/1.31 *** allocated 10000 integers for termspace/termends
% 0.91/1.31 *** allocated 10000 integers for clauses
% 0.91/1.31 *** allocated 10000 integers for justifications
% 0.91/1.31 *** allocated 15000 integers for termspace/termends
% 0.91/1.31 *** allocated 22500 integers for termspace/termends
% 0.91/1.31 Bliksem 1.12
% 0.91/1.31
% 0.91/1.31
% 0.91/1.31 Automatic Strategy Selection
% 0.91/1.31
% 0.91/1.31 Clauses:
% 0.91/1.31 [
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.31 ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( U, Z, X ) ), W ) ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ) ), T ), W ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.31 ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( U, Z, X ) ), W ) ) ), =( T, hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ) ), W ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), Z ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ) ), U ), 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T
% 0.91/1.31 , X, 'tc_nat' ), Y, 'tc_nat' ) ), U ), 'tc_nat' ) ), ~( 'c_lessequals'( X
% 0.91/1.31 , T, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y
% 0.91/1.31 , Z, 'tc_nat' ), T, 'tc_nat' ) ), U ), 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), X ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ) ), U ), 'tc_nat' ) ), ~(
% 0.91/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), Z ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ) ), U ), 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X
% 0.91/1.31 , T, 'tc_nat' ), Y, 'tc_nat' ) ), Z ), U, 'tc_nat' ) ), ~( 'c_lessequals'(
% 0.91/1.31 T, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X
% 0.91/1.31 , Y, 'tc_nat' ), Z, 'tc_nat' ) ), T ), U, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), T ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ), U ), 'tc_nat' ) ), ~(
% 0.91/1.31 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.31 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z
% 0.91/1.31 , X ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ), U ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.91/1.31 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.31 Y ) ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 0.91/1.31 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 0.91/1.31 ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.91/1.31 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.31 'v_sko__Nat__Xnat__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.91/1.31 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.91/1.31 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.91/1.31 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.31 ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( U, Z, X ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ) ), T ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.31 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 0.91/1.31 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ),
% 0.91/1.31 T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.91/1.31 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 T, X ) ) ],
% 0.91/1.31 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( X, T, Z ) ) ),
% 0.91/1.31 =( Y, T ) ],
% 0.91/1.31 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, Y, Z ) ) ),
% 0.91/1.31 =( X, T ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 0.91/1.31 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.91/1.31 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ),
% 0.91/1.31 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 0.91/1.31 ), =( X, T ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.31 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ),
% 0.91/1.31 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.91/1.31 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 0.91/1.31 Y, X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 0.91/1.31 Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ), 'c_Lambda_Osubst'( T,
% 0.91/1.31 Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 Z, X ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.31 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Y, T, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Y, Z, X ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.31 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Y, T, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Y, Z, X ) ) ) ],
% 0.91/1.31 [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.91/1.31 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) )
% 0.91/1.31 ],
% 0.91/1.31 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.91/1.31 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 0.91/1.31 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.91/1.31 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 0.91/1.31 'tc_nat' ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 Y, 'tc_nat' ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ) ), U ), 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T
% 0.91/1.31 , X, 'tc_nat' ), Y, 'tc_nat' ) ), U ), 'tc_nat' ) ), ~( 'c_lessequals'( X
% 0.91/1.31 , T, 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 Y, 'tc_nat' ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ) ), U ), 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X
% 0.91/1.31 , T, 'tc_nat' ), Y, 'tc_nat' ) ), Z ), U, 'tc_nat' ) ), ~( 'c_lessequals'(
% 0.91/1.31 T, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 0.91/1.31 ), Z ), Y ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 0.91/1.31 hBOOL( hAPP( X, Z ) ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 0.91/1.31 hBOOL( hAPP( X, Z ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.31 'tc_nat' ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 0.91/1.31 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Z, T, 'tc_nat' ), X ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.31 'v_sko__Nat__Xnat__Xinducts__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.31 Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.31 'c_Suc'( Z ), X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.31 ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.31 ), X ) ) ],
% 0.91/1.31 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.91/1.31 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 0.91/1.31 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.91/1.31 Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.91/1.31 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.91/1.31 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.91/1.31 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.91/1.31 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 0.91/1.31 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'( Y,
% 0.91/1.31 X ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.31 , Y, X ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.91/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.91/1.31 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.31 , Y, X ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.91/1.31 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.91/1.31 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.91/1.31 [ 'c_Type_Otyping'( X, Y, 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z,
% 0.91/1.31 X, T, Y ) ), ~( 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', T )
% 0.91/1.31 , Y ), Z ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 0.91/1.31 X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 0.91/1.31 X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), T ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.31 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1'( X ), 'tc_nat' ) ),
% 0.91/1.31 ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.91/1.31 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.91/1.31 ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.91/1.31 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 0.91/1.31 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.91/1.31 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.91/1.31 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.91/1.31 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ],
% 0.91/1.31 [ =( 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ), X ) ],
% 0.91/1.31 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 0.91/1.31 [ =( X, 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 0.91/1.31 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), Y, X ), Y ) ],
% 0.91/1.31 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 0.91/1.31 [ =( 'c_Nat_Onat_Onat__rec'( X, Y, 'c_Suc'( Z ), T ), hAPP( hAPP( Y, Z )
% 0.91/1.31 , 'c_Nat_Onat_Onat__rec'( X, Y, Z, T ) ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ) ), ~(
% 0.91/1.31 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.91/1.31 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.91/1.31 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.91/1.31 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.91/1.31 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.31 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.91/1.31 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.31 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.91/1.31 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.31 'v_sko__List__Xupt__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ ~( =( 'c_Type_Otype_OAtom'( X ), 'c_Type_Otype_OAtom'( Y ) ) ), =( X,
% 0.91/1.31 Y ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.31 'v_sko__List__Xreplicate__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.91/1.31 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.91/1.31 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Y, Z, X ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( U, Z, X ) ), W ), X ), ~( 'c_lessequals'( T
% 0.91/1.31 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.91/1.31 , X ) ), W ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 0.91/1.31 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.91/1.31 , X ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 0.91/1.31 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, U, X ) ), W ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Y, Z, X ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( U, Z, X ) ), W ), X ), ~( 'c_lessequals'(
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ) ), T ), W, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ) ), U ), W, X ), ~(
% 0.91/1.31 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), U ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.91/1.31 ), W ), X ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.91/1.31 , X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.91/1.31 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 X, T, 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 0.91/1.31 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1'( X ) ) ) ) ), ~( hBOOL(
% 0.91/1.31 hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.31 , T, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.31 , Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.31 , T, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.31 , Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.31 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 0.91/1.31 Y, Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.91/1.31 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Z ), T ), X ) ) ],
% 0.91/1.31 [ =( 'c_List_Odrop'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 0.91/1.31 'c_List_Olist_ONil'( Y ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1'(
% 0.91/1.31 X, Y ), Y, 'tc_nat' ), ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 0.91/1.31 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.31 Z, 'tc_nat' ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ) ), T ) ) )
% 0.91/1.31 ],
% 0.91/1.31 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.91/1.31 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.91/1.31 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.91/1.31 T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.91/1.31 T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.91/1.31 T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.91/1.31 T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.91/1.31 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.91/1.31 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.91/1.31 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( 'c_List_Ofoldr'(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), 'c_List_Ofoldl'(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z, Y, X, X ) ) ],
% 0.91/1.31 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), T ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( U, Z, X )
% 0.91/1.31 ), W ), X ), ~( 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ) ), W ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ),
% 0.91/1.31 U, X ) ), W ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 0.91/1.31 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, U, X ) ), W ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), T ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( U, Z, X )
% 0.91/1.31 ), W ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ) ), T ), W, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.91/1.31 , X ) ), U ), W, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 0.91/1.31 ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), W ), X ) ) ],
% 0.91/1.31 [ =( 'v_n____', 'v_i____' ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( T,
% 0.91/1.31 Y, 'tc_nat' ) ), U ) ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ), =( hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 0.91/1.31 'tc_nat' ), Y, 'tc_nat' ) ), Z ), U ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( T,
% 0.91/1.31 Y, 'tc_nat' ) ), U ) ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z,
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 0.91/1.31 'tc_nat' ), Y, 'tc_nat' ) ), U ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.91/1.31 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.91/1.31 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 Z, 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.91/1.31 'tc_nat' ), Z, 'tc_nat' ) ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.31 Z, 'tc_nat' ) ), T ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.31 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.31 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.31 Z, T, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), T ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Z ), T ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.31 Y, T, X ), X ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.91/1.31 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' )
% 0.91/1.31 ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 0.91/1.31 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.91/1.31 ) ],
% 0.91/1.31 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_OCons'( X, Y, Z ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ =( 'c_List_Oreplicate'( 'c_Suc'( X ), Y, Z ), 'c_List_Olist_OCons'( Y
% 0.91/1.31 , 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.91/1.31 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 0.91/1.31 X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 0.91/1.31 X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ),
% 0.91/1.31 T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.91/1.31 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.91/1.31 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeE__1__1'(
% 0.91/1.31 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.91/1.31 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.91/1.31 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.91/1.31 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.31 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.91/1.31 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.91/1.31 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1'( X ), 'tc_nat' ),
% 0.91/1.31 ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubst'(
% 0.91/1.31 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.91/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.91/1.31 'c_Type_Osko__Type__Xtype__induct__1__1'( X ) ) ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.91/1.31 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.91/1.31 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.91/1.31 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.31 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.31 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.91/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.31 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.31 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 0.91/1.31 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.91/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.91/1.31 ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.91/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.31 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.91/1.31 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.91/1.31 , T, X ) ) ), =( Y, Z ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.91/1.31 , T, X ) ) ), =( Z, T ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.91/1.31 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.91/1.31 X ), X ), Y ) ],
% 0.91/1.31 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ) ), =( Y, Z ) ],
% 0.91/1.31 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.31 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 0.91/1.31 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_OCons'( Z, T, U ), W, U ),
% 0.91/1.31 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, W, U ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.91/1.31 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 0.91/1.31 Y ) ) ) ],
% 0.91/1.31 [ =( 'c_List_Odrop'( 'c_Suc'( X ), 'c_List_Olist_OCons'( Y, Z, T ), T )
% 0.91/1.31 , 'c_List_Odrop'( X, Z, T ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.31 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.31 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 0.91/1.31 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.31 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 X ), T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 0.91/1.31 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.31 , Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.31 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.91/1.31 , T, X ), X ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 0.91/1.31 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.31 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, T
% 0.91/1.31 , X ), Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( T, Y
% 0.91/1.31 , X ), Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 0.91/1.31 'c_List_Olist_ONil'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 0.91/1.31 Z, Y, X ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.31 Y, 'tc_nat' ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.91/1.31 ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), T ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.31 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ), U ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ), U ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ) ],
% 0.91/1.31 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.31 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 0.91/1.31 , Y ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 0.91/1.31 ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 0.91/1.31 ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.31 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.91/1.31 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.91/1.31 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X )
% 0.91/1.31 ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 X ), X ) ) ],
% 0.91/1.31 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 0.91/1.31 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.91/1.31 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 0.91/1.31 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z, 'c_Suc'( T ), 't_a'
% 0.91/1.31 ) ) ) ), hBOOL( hAPP( X, hAPP( Z, T ) ) ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z, 'c_Suc'( T ), 't_a'
% 0.91/1.31 ) ) ) ), hBOOL( hAPP( X, hAPP( Z, T ) ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.91/1.31 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.91/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.91/1.31 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.91/1.31 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.91/1.31 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.91/1.31 X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.91/1.31 X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.91/1.31 X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.91/1.31 X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.91/1.31 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.91/1.31 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 0.91/1.31 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 0.91/1.31 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), 'c_HOL_Oord__class_Oless'( Y, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 Y, 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ],
% 0.91/1.31 [ 'c_InductTermi_OIT'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 0.91/1.31 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z, 'tc_Lambda_OdB'
% 0.91/1.31 , 'tc_Lambda_OdB' ) ), ~( 'c_InductTermi_OIT'( Y ) ), ~(
% 0.91/1.31 'c_InductTermi_OIT'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.31 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z,
% 0.91/1.31 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.91/1.31 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), Y ) ],
% 0.91/1.31 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.91/1.31 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.91/1.31 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.91/1.31 'tc_Lambda_OdB' ) ) ) ],
% 0.91/1.31 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_Suc'( Z ), T ), hAPP( Y, Z ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Y
% 0.91/1.31 , 'c_List_Olist_ONil'( X ) ) ],
% 0.91/1.31 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Z
% 0.91/1.31 , 'c_List_Olist_ONil'( X ) ) ],
% 0.91/1.31 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.91/1.31 'tc_nat' ), Z, 'tc_nat' ) ), T ), U, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), T ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.31 Z, 'tc_nat' ) ), U ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 0.91/1.31 ],
% 0.91/1.31 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( T,
% 0.91/1.31 Y, 'tc_nat' ) ), U ), 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ) ), Z ), U,
% 0.91/1.31 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.91/1.31 'tc_nat' ), T, 'tc_nat' ) ), U ), 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.31 T, 'tc_nat' ) ), U ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) )
% 0.91/1.31 ],
% 0.91/1.31 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( T,
% 0.91/1.31 Y, 'tc_nat' ) ), U ), 'tc_nat' ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ) ), U ),
% 0.91/1.31 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.91/1.31 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.91/1.31 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( X
% 0.91/1.31 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.91/1.31 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y
% 0.91/1.31 , 'c_List_Olist_ONil'( Z ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.31 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 T, U, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, U, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.31 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 T, U, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, U, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 0.91/1.31 =( Y, T ), =( X, Z ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.31 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 0.91/1.31 =( Y, T ), =( X, Z ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.91/1.31 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.91/1.31 Z ) ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.31 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.91/1.31 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.91/1.31 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.91/1.31 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.91/1.31 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( 'c_lessequals'( Z
% 0.91/1.31 , Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), Y ) ), ~(
% 0.91/1.31 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 0.91/1.31 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.91/1.31 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.91/1.31 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 0.91/1.31 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OVar'( X )
% 0.91/1.31 , Y ) ],
% 0.91/1.31 [ =( 'c_Type_Otype_Otype__rec'( X, Y, 'c_Type_Otype_OAtom'( Z ), T ),
% 0.91/1.31 hAPP( X, Z ) ) ],
% 0.91/1.31 [ 'c_Lambda_Obeta'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 0.91/1.31 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 0.91/1.31 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( 'c_Lambda_Obeta'( X, Z )
% 0.91/1.31 ) ],
% 0.91/1.31 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, X ) ) ],
% 0.91/1.31 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.31 'tc_nat' ) ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.91/1.31 , X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.31 , Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.31 , Y, X ) ) ],
% 0.91/1.31 [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.91/1.31 ), Y ), X ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), X, 'tc_nat' ), Y ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 0.91/1.31 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 0.91/1.31 X ) ), Y ), 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.31 ) ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , X ), Y ), 'tc_nat' ) ],
% 0.91/1.31 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , Y ), X ), 'tc_nat' ) ],
% 0.91/1.31 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , X ), Y ), 'tc_nat' ) ],
% 0.91/1.31 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ),
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 0.91/1.31 'c_List_Olist_OCons'( Y, Z, X ), X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Olistsum'( Z, X ) ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.91/1.31 ), =( Z, Y ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.91/1.31 ) ],
% 0.91/1.31 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 0.91/1.31 , Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.91/1.31 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 0.91/1.31 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 0.91/1.31 [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.91/1.31 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.91/1.31 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 0.91/1.31 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 0.91/1.31 'tc_Lambda_OdB' ), X ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.91/1.31 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.91/1.31 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.91/1.31 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.91/1.31 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.91/1.31 'c_List_Oreplicate'( T, Y, Z ), Z ), 'c_List_Oappend'(
% 0.91/1.31 'c_List_Oreplicate'( T, Y, Z ), 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.91/1.31 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.31 , X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 0.91/1.31 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.31 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.31 T, X ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.31 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 0.91/1.31 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.91/1.31 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.91/1.31 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.91/1.31 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.91/1.31 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.91/1.31 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 0.91/1.31 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.91/1.31 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 0.91/1.31 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.91/1.31 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.91/1.31 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 0.91/1.31 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 0.91/1.31 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z
% 0.91/1.31 , T, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( T
% 0.91/1.31 , Z, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.91/1.31 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.91/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.31 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 0.91/1.31 , 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.91/1.31 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 0.91/1.31 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 0.91/1.31 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 0.91/1.31 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 0.91/1.31 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.91/1.31 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 0.91/1.31 , X, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 0.91/1.31 'tc_nat' ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.31 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.31 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.91/1.31 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.91/1.31 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.91/1.31 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 0.91/1.31 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.91/1.31 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 0.91/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.31 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ), T ),
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.91/1.31 ), Y ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X )
% 0.91/1.31 ) ],
% 0.91/1.31 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), Z, 'tc_nat' ), 'tc_nat'
% 0.91/1.31 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 0.91/1.31 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 0.91/1.31 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 0.91/1.31 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 0.91/1.31 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.91/1.31 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.91/1.31 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 0.91/1.31 , V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.91/1.31 T, X, U, W, Y, V0 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.91/1.31 T, X, U, Y, W, V0 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.91/1.31 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.91/1.31 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 0.91/1.31 , V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.91/1.31 X, T, U, Y, W, V0 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.91/1.31 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 0.91/1.31 , V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.91/1.31 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 0.91/1.31 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 0.91/1.31 , V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 0.91/1.31 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 0.91/1.31 W, V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.91/1.31 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 0.91/1.31 W, V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.91/1.31 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 0.91/1.31 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 0.91/1.31 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 0.91/1.31 W, V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.91/1.31 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 0.91/1.31 , V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.91/1.31 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 0.91/1.31 W, V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 0.91/1.31 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 0.91/1.31 , V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.91/1.31 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 0.91/1.31 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.91/1.31 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 0.91/1.31 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.91/1.31 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 0.91/1.31 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.91/1.31 T, X, U, W, Z, V0 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.91/1.31 T, X, U, W, Y, V0 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.91/1.31 T, X, U, Z, W, V0 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.91/1.31 T, X, U, Y, W, V0 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 0.91/1.31 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 0.91/1.31 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.91/1.31 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.91/1.31 X, T, U, Z, W, V0 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.91/1.31 X, T, U, Y, W, V0 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 0.91/1.31 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 0.91/1.31 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 0.91/1.31 , V0, U, V1 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 0.91/1.31 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 0.91/1.31 , V0, U, V1 ) ) ],
% 0.91/1.31 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 0.91/1.31 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 0.91/1.31 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_Type_Otype_Otype__case'( Y, Z,
% 0.91/1.31 'c_Type_Otype_OAtom'( T ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, T ) )
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( hBOOL( hAPP( X, 'c_Type_Otype_Otype__case'( Y, Z,
% 0.91/1.31 'c_Type_Otype_OAtom'( T ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, T ) )
% 0.91/1.31 ) ],
% 0.91/1.31 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 0.91/1.31 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 0.91/1.31 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.31 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.31 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.31 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.91/1.31 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.91/1.31 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.91/1.31 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 0.91/1.31 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 0.91/1.31 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.91/1.31 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Y,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 0.91/1.31 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Z,
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.31 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 0.91/1.31 'c_InductTermi_OIT'( X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.31 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.91/1.31 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.91/1.31 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.91/1.31 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 0.91/1.31 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ]
% 0.91/1.31 ,
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 0.91/1.31 Z, Y, X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.91/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.31 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.91/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.91/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.31 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.31 [ =( 'c_List_Odrop'( X, 'c_List_Oreplicate'( Y, Z, T ), T ),
% 0.91/1.31 'c_List_Oreplicate'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, T
% 0.91/1.31 ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.91/1.31 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 0.91/1.31 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.91/1.31 X ), X ), X ) ],
% 0.91/1.31 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 0.91/1.31 , 'c_List_Olist_ONil'( Y ) ) ],
% 0.91/1.31 [ =( 'c_nat_Onat__size'( 'c_Suc'( X ) ), hAPP( hAPP(
% 0.91/1.31 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_nat_Onat__size'( X ) ),
% 0.91/1.31 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.31 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.91/1.31 X ), X ), Y ) ],
% 0.91/1.31 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 0.91/1.31 'tc_nat' ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.91/1.31 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.91/1.31 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.91/1.31 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.91/1.31 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.91/1.31 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.91/1.31 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.91/1.32 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 0.91/1.32 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ],
% 0.91/1.32 [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Z ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y
% 0.91/1.32 , 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.32 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.32 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.91/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.91/1.32 'c_lessequals'( Y, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.91/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.91/1.32 'c_lessequals'( Z, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.91/1.32 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.91/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.91/1.32 'c_lessequals'( Y, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.91/1.32 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.91/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.91/1.32 'c_lessequals'( Z, T, X ) ) ],
% 0.91/1.32 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.91/1.32 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 0.91/1.32 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.91/1.32 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 0.91/1.32 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y,
% 0.91/1.32 X, 'tc_nat' ) ), X ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), ~( 'c_lessequals'(
% 0.91/1.32 X, Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ), X ), ~(
% 0.91/1.32 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 0.91/1.32 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0,
% 0.91/1.32 V1 ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 0.91/1.32 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0,
% 0.91/1.32 V1 ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 0.91/1.32 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 0.91/1.32 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.91/1.32 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 0.91/1.32 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ =( 'c_List_Odrop'( X, 'c_List_Odrop'( Y, Z, T ), T ), 'c_List_Odrop'(
% 0.91/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, T ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.91/1.32 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 0.91/1.32 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 0.91/1.32 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 0.91/1.32 [ =( 'c_List_Oreplicate'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Y ), Z, T ), 'c_List_Oappend'( 'c_List_Oreplicate'( X, Z
% 0.91/1.32 , T ), 'c_List_Oreplicate'( Y, Z, T ), T ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.32 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.32 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.91/1.32 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.91/1.32 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ),
% 0.91/1.32 =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.91/1.32 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.32 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 0.91/1.32 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'( Y, Z, X ) ) ),
% 0.91/1.32 =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.91/1.32 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.91/1.32 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_Type_Otypings'( X, Y, 'c_Type_Osko__Type__Xlist__app__typeD__1__1'(
% 0.91/1.32 Z, X, T, Y ) ), ~( 'c_Type_Otyping'( X, 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', T, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), Z ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.91/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.32 ) ), X, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.32 ) ), X, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 0.91/1.32 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.91/1.32 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.91/1.32 ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.91/1.32 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.32 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.91/1.32 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 0.91/1.32 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( X, 'c_Lambda_OdB_OVar'( Y ), Z
% 0.91/1.32 ) ), ~( 'c_InductTermi_OIT'( X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.32 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.32 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.32 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 0.91/1.32 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.91/1.32 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 0.91/1.32 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.91/1.32 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 0.91/1.32 , Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.32 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.91/1.32 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.32 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.91/1.32 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.32 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.91/1.32 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.32 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.91/1.32 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.32 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.91/1.32 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.91/1.32 [ ~( =( 'c_List_Oappend'( X, Y, Z ), X ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( =( X, 'c_List_Oappend'( X, Y, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( =( 'c_List_Oappend'( X, Y, Z ), Y ) ), =( X, 'c_List_Olist_ONil'( Z
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( =( X, 'c_List_Oappend'( Y, X, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.32 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Otimes__class_Otimes'( Z, U
% 0.91/1.32 , X ) ) ) ), =( T, U ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 Y, T, 'tc_nat' ) ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y
% 0.91/1.32 , Z, X ), X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 0.91/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.91/1.32 , X ) ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 0.91/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.91/1.32 , X ) ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.91/1.32 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.91/1.32 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.32 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 0.91/1.32 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.32 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 0.91/1.32 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.32 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.91/1.32 ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.32 , Z ), Y ), 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.91/1.32 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 0.91/1.32 ],
% 0.91/1.32 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.32 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 0.91/1.32 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.91/1.32 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.91/1.32 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.91/1.32 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.91/1.32 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.91/1.32 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.91/1.32 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.91/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 0.91/1.32 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.91/1.32 [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ],
% 0.91/1.32 [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 0.91/1.32 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat' ) ) )
% 0.91/1.32 ],
% 0.91/1.32 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.91/1.32 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.32 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.32 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.32 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.32 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.32 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.32 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 0.91/1.32 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.32 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.91/1.32 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.32 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.32 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 X ), T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.91/1.32 [ =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Oappend'(
% 0.91/1.32 'c_List_Olist_ONil'( Z ), 'c_List_Olist_OCons'( X, Y, Z ), Z ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.32 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ), T ),
% 0.91/1.32 'c_Orderings_Oord__class_Omax'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.91/1.32 ), Y ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X )
% 0.91/1.32 ) ],
% 0.91/1.32 [ 'c_InductTermi_OIT'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ),
% 0.91/1.32 'c_Lambda_OdB_OVar'( Y ) ) ), ~( 'c_InductTermi_OIT'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.91/1.32 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.91/1.32 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 0.91/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.91/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.32 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.32 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.91/1.32 ],
% 0.91/1.32 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.32 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.91/1.32 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.91/1.32 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.32 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.91/1.32 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.91/1.32 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.32 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.91/1.32 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 0.91/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.32 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.91/1.32 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 0.91/1.32 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.91/1.32 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( 'c_List_Olist_ONil'( X
% 0.91/1.32 ), 'c_List_Olist_ONil'( X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.32 ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), T ), Z, X ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y )
% 0.91/1.32 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.91/1.32 , X ), X ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.91/1.32 , X ), X ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), X ) ) ],
% 0.91/1.32 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 0.91/1.32 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.32 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.91/1.32 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ],
% 0.91/1.32 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.91/1.32 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( Z ), Z ), Z ),
% 0.91/1.32 'c_List_Olist_OCons'( Y, 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), Z ), Z, X ), Y ) ],
% 0.91/1.32 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Oappend'( Z, T, U ), W, U ),
% 0.91/1.32 'c_List_Ofoldl'( X, 'c_List_Ofoldl'( X, Y, Z, W, U ), T, W, U ) ) ],
% 0.91/1.32 [ =( 'c_Type_Otype_Otype__case'( X, Y, 'c_Type_Otype_OAtom'( Z ), T ),
% 0.91/1.32 hAPP( X, Z ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.32 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.91/1.32 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.91/1.32 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OVar'(
% 0.91/1.32 Z ) ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.91/1.32 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 0.91/1.32 , 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.91/1.32 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.91/1.32 , 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ =( X, hAPP( hAPP( 'c_Type_Otype_OFun',
% 0.91/1.32 'c_Type_Osko__Type__Xtyping__elims__3__1'( X, Y, Z ) ),
% 0.91/1.32 'c_Type_Osko__Type__Xtyping__elims__3__2'( X, Y, Z ) ) ), ~(
% 0.91/1.32 'c_Type_Otyping'( Y, 'c_Lambda_OdB_OAbs'( Z ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.91/1.32 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.91/1.32 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.91/1.32 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 0.91/1.32 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.91/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.32 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.91/1.32 ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.32 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.91/1.32 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.91/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.91/1.32 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.32 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ) ), =( Y, Z ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ) ), =( Y, Z ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.91/1.32 Y ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.91/1.32 Y ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.32 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.91/1.32 Y ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.91/1.32 Y ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.91/1.32 Y ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.91/1.32 Y ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.91/1.32 Y ) ],
% 0.91/1.32 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 0.91/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.32 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.32 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.32 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.32 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.91/1.32 , X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.91/1.32 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 0.91/1.32 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 0.91/1.32 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 0.91/1.32 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 0.91/1.32 ) ), =( X, T ) ],
% 0.91/1.32 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 0.91/1.32 ) ), =( Y, U ) ],
% 0.91/1.32 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.91/1.32 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 0.91/1.32 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 0.91/1.32 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 0.91/1.32 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 0.91/1.32 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 0.91/1.32 Z ) ) ) ],
% 0.91/1.32 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.91/1.32 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.91/1.32 , 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 0.91/1.32 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.91/1.32 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 0.91/1.32 ) ],
% 0.91/1.32 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.91/1.32 'c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1'( X, Z ), 'tc_nat' )
% 0.91/1.32 ), ~( hBOOL( hAPP( X, Z ) ) ), hBOOL( hAPP( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.91/1.32 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.91/1.32 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 0.91/1.32 Z ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 0.91/1.32 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.32 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.32 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.32 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.32 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 0.91/1.32 'c_List_Olist_OCons'( Y, T, Z ), Z ), 'c_List_Olist_OCons'( Y,
% 0.91/1.32 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ), T, Z ), Z ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 0.91/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.91/1.32 ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.32 , Y, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.32 , T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.32 , T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.32 , Y, X ), X ) ) ],
% 0.91/1.32 [ =( 'c_Lambda_Osubst'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 0.91/1.32 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Z, T ) ),
% 0.91/1.32 'c_Lambda_Osubst'( Y, Z, T ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 0.91/1.32 ],
% 0.91/1.32 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.91/1.32 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.91/1.32 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.91/1.32 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.91/1.32 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.91/1.32 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.91/1.32 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.91/1.32 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.91/1.32 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.91/1.32 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.91/1.32 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.32 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.32 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.91/1.32 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 0.91/1.32 'c_List_Oappend'( Y, Z, X ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 X ), 'c_List_Olistsum'( Y, X ) ), 'c_List_Olistsum'( Z, X ) ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.91/1.32 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.91/1.32 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.91/1.32 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( X, T
% 0.91/1.32 ) ],
% 0.91/1.32 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 0.91/1.32 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 0.91/1.32 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( Y, U
% 0.91/1.32 ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.32 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.32 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.91/1.32 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.91/1.32 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.91/1.32 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.91/1.32 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.91/1.32 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.91/1.32 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.91/1.32 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 0.91/1.32 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.91/1.32 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.91/1.32 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.91/1.32 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.91/1.32 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.91/1.32 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.91/1.32 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.91/1.32 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.91/1.32 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.91/1.32 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.91/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.91/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.32 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.32 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.91/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.91/1.32 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.91/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.32 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_ONil'( X
% 0.91/1.32 ), X ), 'c_List_Olist_ONil'( X ) ) ],
% 0.91/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 0.91/1.32 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.91/1.32 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.32 T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.91/1.32 X ), Z, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.91/1.32 T, X ), X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.91/1.32 X ), T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.91/1.32 T, X ), X ) ) ],
% 0.91/1.32 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.91/1.32 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.91/1.32 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.91/1.32 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 0.91/1.32 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 0.91/1.32 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 0.91/1.32 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 0.91/1.32 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.91/1.32 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.91/1.32 X ), T, X ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 Z, T, X ) ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.91/1.32 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 Z, T, X ) ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.91/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( X, hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.91/1.32 Y, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.32 X ), Z ), T ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.32 Y, T, X ) ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.32 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.32 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.91/1.32 'c_lessequals'( Z, Y, X ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.32 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.32 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.32 [ =( 'c_Nat_Onat_Onat__rec'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.32 ), Z ), X ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, 'c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1'(
% 0.91/1.32 X, Y ) ) ), ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.91/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.91/1.32 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.91/1.32 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1'( X ) ) ), ~( hBOOL( hAPP( X
% 0.91/1.32 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.32 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.32 ), Z ), X ) ],
% 0.91/1.32 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.32 ), Z ), X ) ],
% 0.91/1.32 [ =( 'c_Orderings_Oord__class_Omin'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.91/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.91/1.32 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 0.91/1.32 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.91/1.32 'v_sko__List__Xreplicate__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.91/1.32 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 't_a' ) ) ) ), hBOOL( hAPP( X, Y
% 0.91/1.32 ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__Nat__Xnat__Xinducts__1'(
% 0.91/1.32 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 0.91/1.32 ],
% 0.91/1.32 [ =( 'c_Nitpick_Onat__gcd'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.91/1.32 , X ) ],
% 0.91/1.32 [ =( 'c_nat_Onat__size'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_String_Ochar_Ochar__size'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__Nat__Xnat__Xinduct__1'(
% 0.91/1.32 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 0.91/1.32 ],
% 0.91/1.32 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.32 ), 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.32 ), 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__List__Xupt__Xinduct__1'(
% 0.91/1.32 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 0.91/1.32 ],
% 0.91/1.32 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ), X )
% 0.91/1.32 ],
% 0.91/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.91/1.32 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.91/1.32 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1'( X ) ) ) ), ~( hBOOL(
% 0.91/1.32 hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.91/1.32 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 0.91/1.32 ],
% 0.91/1.32 [ =( 'c_Nat_Osize__class_Osize'( X, 'tc_String_Ochar' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 0.91/1.32 , 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, Y ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ =( 'c_Orderings_Oord__class_Omax'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.91/1.32 [ =( 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), X, 'tc_nat' ), X ) ],
% 0.91/1.32 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 0.91/1.32 ), =( Y, U ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 0.91/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.91/1.32 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 0.91/1.32 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'( Y,
% 0.91/1.32 X ), 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X
% 0.91/1.32 ), 'c_List_Ofoldr'( 'c_HOL_Oplus__class_Oplus'( X ), Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), X, X ) ) ],
% 0.91/1.32 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ), hAPP( hAPP(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldr'(
% 0.91/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z, 'c_HOL_Ozero__class_Ozero'( X ), X, X
% 0.91/1.32 ) ) ) ],
% 0.91/1.32 [ 'c_Type_Otypings'( 'c_Type_Oshift'( 'v_e____', 'v_i____', 'v_T____',
% 0.91/1.32 'tc_Type_Otype' ), 'v_as____', 'v_Ts____' ) ],
% 0.91/1.32 [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Lambda_Obeta'( T, Y ) ), ~(
% 0.91/1.32 'c_Type_Otyping'( X, T, Z ) ) ],
% 0.91/1.32 [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y )
% 0.91/1.32 , Z ) ) ],
% 0.91/1.32 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y ) ) ],
% 0.91/1.32 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), 'c_Type_Osko__Type__Xabs__typeE__1__1'( X, Y ),
% 0.91/1.32 'tc_Type_Otype' ), Y, 'c_Type_Osko__Type__Xabs__typeE__1__2'( X, Y ) ),
% 0.91/1.32 ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ) ) ],
% 0.91/1.32 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.32 'tc_nat' ), 'c_Type_Osko__Type__Xtyping__elims__3__1'( Y, X, Z ),
% 0.91/1.32 'tc_Type_Otype' ), Z, 'c_Type_Osko__Type__Xtyping__elims__3__2'( Y, X, Z
% 0.91/1.32 ) ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Z ), Y ) ) ],
% 0.91/1.32 [ 'c_Type_Otyping'( X, Y, hAPP( hAPP( 'c_Type_Otype_OFun',
% 0.91/1.32 'c_Type_Osko__Type__Xtyping__elims__2__1'( Z, X, Y, T ) ), Z ) ), ~(
% 0.91/1.32 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), T ), Z ) ) ]
% 0.91/1.32 ,
% 0.91/1.32 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), 'c_Type_Otype_OAtom'(
% 0.91/1.32 Z ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_Type_Osko__Type__Xtype__induct__1__1'( X ), hAPP( hAPP(
% 0.91/1.32 'c_Type_Otype_OFun', Y ), Z ) ) ), hBOOL( hAPP( X, T ) ), hBOOL( hAPP( X
% 0.91/1.32 , Z ) ) ],
% 0.91/1.32 [ ~( =( 'c_Type_Osko__Type__Xtype__induct__1__1'( X ), hAPP( hAPP(
% 0.91/1.32 'c_Type_Otype_OFun', Y ), Z ) ) ), hBOOL( hAPP( X, T ) ), hBOOL( hAPP( X
% 0.91/1.32 , Y ) ) ],
% 0.91/1.32 [ =( 'c_Type_Otype_Otype__rec'( X, Y, hAPP( hAPP( 'c_Type_Otype_OFun', Z
% 0.91/1.32 ), T ), U ), hAPP( hAPP( hAPP( hAPP( Y, Z ), T ),
% 0.91/1.32 'c_Type_Otype_Otype__rec'( X, Y, Z, U ) ), 'c_Type_Otype_Otype__rec'( X,
% 0.91/1.32 Y, T, U ) ) ) ],
% 0.91/1.32 [ =( 'c_Type_Otype_Otype__case'( X, Y, hAPP( hAPP( 'c_Type_Otype_OFun',
% 0.91/1.32 Z ), T ), U ), hAPP( hAPP( Y, Z ), T ) ) ],
% 0.91/1.32 [ ~( hBOOL( hAPP( X, 'c_Type_Otype_Otype__case'( Y, Z, hAPP( hAPP(
% 0.91/1.32 'c_Type_Otype_OFun', T ), U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.91/1.32 Z, T ), U ) ) ) ],
% 0.91/1.32 [ ~( hBOOL( hAPP( X, 'c_Type_Otype_Otype__case'( Y, Z, hAPP( hAPP(
% 0.91/1.32 'c_Type_Otype_OFun', T ), U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 0.91/1.32 Z, T ), U ) ) ) ],
% 0.91/1.32 [ ~( =( 'c_Type_Otype_OAtom'( X ), hAPP( hAPP( 'c_Type_Otype_OFun', Y )
% 0.91/1.32 , Z ) ) ) ],
% 0.91/1.32 [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_OCons'( Y, Z, T ), U, T, W ),
% 0.91/1.32 hAPP( hAPP( X, Y ), 'c_List_Ofoldr'( X, Z, U, T, W ) ) ) ],
% 0.91/1.32 [ =( 'c_List_Ofoldr'( X, 'c_List_Oappend'( Y, Z, T ), U, T, W ),
% 0.91/1.32 'c_List_Ofoldr'( X, Y, 'c_List_Ofoldr'( X, Z, U, T, W ), T, W ) ) ],
% 0.91/1.32 [ =( 'c_List_Ofoldr'( X, 'c_List_Olist_ONil'( Y ), Z, Y, T ), Z ) ],
% 0.91/1.32 [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 0.91/1.32 'c_InductTermi_OIT'( X ) ) ],
% 0.91/1.32 [ =( 'c_Lambda_Olift'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z ),
% 0.91/1.32 hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Olift'( X, Z ) ),
% 0.91/1.32 'c_Lambda_Olift'( Y, Z ) ) ) ],
% 0.91/1.32 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X ) ],
% 0.91/1.32 [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ), 'c_Lambda_Olift'( Z, Y ) )
% 0.91/1.32 , ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 0.91/1.32 [ ~( =( 'v_T____', hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ) ) ),
% 0.91/1.32 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( Z, T, U ) ), ~( 'c_Type_Otyping'(
% 0.91/1.32 W, T, Y ) ), ~( 'c_InductTermi_OIT'( T ) ), ~( 'c_Type_Otyping'(
% 0.91/1.32 'c_Type_Oshift'( W, U, Y, 'tc_Type_Otype' ), Z, V0 ) ), ~(
% 0.91/1.32 'c_InductTermi_OIT'( Z ) ) ],
% 0.91/1.32 [ ~( =( 'v_T____', hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ) ) ),
% 0.91/1.32 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( Z, T, U ) ), ~( 'c_Type_Otyping'(
% 0.91/1.32 W, T, X ) ), ~( 'c_InductTermi_OIT'( T ) ), ~( 'c_Type_Otyping'(
% 0.91/1.32 'c_Type_Oshift'( W, U, X, 'tc_Type_Otype' ), Z, V0 ) ), ~(
% 0.91/1.32 'c_InductTermi_OIT'( Z ) ) ],
% 0.91/1.32 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U ) ), ~(
% 0.91/1.32 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ],
% 0.91/1.32 [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.91/1.32 'c_Type_Osko__Type__Xlist__app__typeE__1__1'( Z, X, Y, T ), Z,
% 0.91/1.32 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.91/1.32 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ), Z ) ) ],
% 0.91/1.32 [ 'c_Type_Otyping'( X, 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, Z,
% 0.91/1.32 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), T ), ~( 'c_Type_Otypings'( X, Z, U )
% 0.91/1.32 ), ~( 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun', U, T
% 0.91/1.32 , 'tc_Type_Otype', 'tc_Type_Otype' ) ) ) ],
% 0.91/1.32 [ 'c_Type_Otyping'( X, Y, 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.91/1.32 'c_Type_Osko__Type__Xlist__app__typeD__1__1'( Z, X, Y, T ), Z,
% 0.91/1.32 'tc_Type_Otype', 'tc_Type_Otype' ) ), ~( 'c_Type_Otyping'( X,
% 0.91/1.32 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Y, T, 'tc_Lambda_OdB',
% 0.91/1.32 'tc_Lambda_OdB' ), Z ) ) ],
% 0.91/1.32 [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____', 'v_T____',
% 0.91/1.32 'tc_Type_Otype' ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'(
% 0.91/1.32 'v_n____' ) ), 'v_a____' ), 'c_List_Ofoldr'( 'c_Type_Otype_OFun',
% 0.91/1.32 'v_Ts____', 'v_T_H____', 'tc_Type_Otype', 'tc_Type_Otype' ) ) ],
% 0.91/1.32 [ 'c_InductTermi_OIT'( 'v_u____' ) ],
% 0.91/1.32 [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____', 'v_T____',
% 0.91/1.32 'tc_Type_Otype' ), 'v_a____', 'v_T_H_H____' ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.91/1.32 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.91/1.32 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.91/1.32 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.91/1.32 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.91/1.32 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.91/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.32 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.91/1.32 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.91/1.32 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.91/1.32 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.94/1.32 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.32 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.94/1.32 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.94/1.32 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.32 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.32 [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 0.94/1.32 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 0.94/1.32 'c_Suc'( Y ), Z, T ) ) ],
% 0.94/1.32 [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T ),
% 0.94/1.32 ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y, hAPP( hAPP(
% 0.94/1.32 'c_Type_Otype_OFun', U ), T ) ) ) ],
% 0.94/1.32 [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 0.94/1.32 X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'( X,
% 0.94/1.32 'c_Lambda_Osubst'( U, Y, T ), W ) ],
% 0.94/1.32 [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____', 'v_T____',
% 0.94/1.32 'tc_Type_Otype' ), 'c_Lambda_OdB_OVar'( 'v_n____' ), hAPP( hAPP(
% 0.94/1.32 'c_Type_Otype_OFun', 'v_T_H_H____' ), 'c_List_Ofoldr'(
% 0.94/1.32 'c_Type_Otype_OFun', 'v_Ts____', 'v_T_H____', 'tc_Type_Otype',
% 0.94/1.32 'tc_Type_Otype' ) ) ) ],
% 0.94/1.32 [ 'c_Type_Otyping'( 'v_e____', 'v_u____', 'v_T____' ) ],
% 0.94/1.32 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), hAPP( hAPP(
% 0.94/1.32 'c_Type_Otype_OFun', Z ), T ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( X
% 0.94/1.32 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_Type_Otype' ), Y, T ) )
% 0.94/1.32 ],
% 0.94/1.32 [ =( 'v_T____', hAPP( hAPP( 'c_Type_Otype_OFun', 'v_T_H_H____' ),
% 0.94/1.32 'c_List_Ofoldr'( 'c_Type_Otype_OFun', 'v_Ts____', 'v_T_H____',
% 0.94/1.32 'tc_Type_Otype', 'tc_Type_Otype' ) ) ) ],
% 0.94/1.32 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ),
% 0.94/1.32 'c_Lambda_Olift'( T, Y ), U ), ~( 'c_Type_Otyping'( X, T, U ) ) ],
% 0.94/1.32 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP( hAPP(
% 0.94/1.32 'c_Type_Otype_OFun', Z ), T ) ) ), =( X, Z ) ],
% 0.94/1.32 [ ~( =( hAPP( hAPP( 'c_Type_Otype_OFun', X ), Y ), hAPP( hAPP(
% 0.94/1.32 'c_Type_Otype_OFun', Z ), T ) ) ), =( Y, T ) ],
% 0.94/1.32 [ 'c_Type_Otyping'( 'v_e____', 'v_u____', hAPP( hAPP(
% 0.94/1.32 'c_Type_Otype_OFun', 'v_T_H_H____' ), 'c_List_Ofoldr'(
% 0.94/1.32 'c_Type_Otype_OFun', 'v_Ts____', 'v_T_H____', 'tc_Type_Otype',
% 0.94/1.32 'tc_Type_Otype' ) ) ) ],
% 0.94/1.32 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ],
% 0.94/1.32 [ ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____',
% 0.94/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'v_T_H_H____', 'tc_Type_Otype' )
% 0.94/1.32 , 'c_Lambda_Olift'( 'v_u____', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.32 hAPP( hAPP( 'c_Type_Otype_OFun', 'v_T_H_H____' ), 'c_List_Ofoldr'(
% 0.94/1.32 'c_Type_Otype_OFun', 'v_Ts____', 'v_T_H____', 'tc_Type_Otype',
% 0.94/1.32 'tc_Type_Otype' ) ) ) ) ],
% 0.94/1.32 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.94/1.32 'class_Orderings_Opreorder'( Y ) ) ],
% 0.94/1.32 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.94/1.32 'class_Orderings_Oorder'( Y ) ) ],
% 0.94/1.32 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 0.94/1.32 Y ) ) ],
% 0.94/1.32 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.94/1.32 ],
% 0.94/1.32 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.94/1.32 ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.94/1.32 ],
% 0.94/1.32 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 0.94/1.32 ,
% 0.94/1.32 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 0.94/1.32 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 0.94/1.32 [ 'c_fequal'( X, X, Y ) ],
% 0.94/1.32 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 0.94/1.32 ] .
% 0.94/1.32
% 0.94/1.32
% 0.94/1.32 percentage equality = 0.271481, percentage horn = 0.903870
% 0.94/1.32 This is a problem with some equality
% 0.94/1.32
% 0.94/1.32
% 0.94/1.32
% 0.94/1.32 Options Used:
% 0.94/1.32
% 0.94/1.32 useres = 1
% 0.94/1.32 useparamod = 1
% 0.94/1.32 useeqrefl = 1
% 0.94/1.32 useeqfact = 1
% 0.94/1.32 usefactor = 1
% 0.94/1.32 usesimpsplitting = 0
% 0.94/1.32 usesimpdemod = 5
% 0.94/1.32 usesimpres = 3
% 0.94/1.32
% 0.94/1.32 resimpinuse = 1000
% 0.94/1.32 resimpclauses = 20000
% 0.94/1.32 substype = eqrewr
% 0.94/1.32 backwardsubs = 1
% 0.94/1.32 selectoldest = 5
% 0.94/1.32
% 0.94/1.32 litorderings [0] = split
% 0.94/1.32 litorderings [1] = extend the termordering, first sorting on arguments
% 0.94/1.32
% 0.94/1.32 termordering = kbo
% 0.94/1.32
% 0.94/1.32 litapriori = 0
% 0.94/1.32 termapriori = 1
% 0.94/1.32 litaposteriori = 0
% 0.94/1.32 termaposteriori = 0
% 0.94/1.32 demodaposteriori = 0
% 0.94/1.32 ordereqreflfact = 0
% 0.94/1.32
% 0.94/1.32 litselect = negord
% 0.94/1.32
% 0.94/1.32 maxweight = 15
% 0.94/1.32 maxdepth = 30000
% 0.94/1.32 maxlength = 115
% 0.94/1.32 maxnrvars = 195
% 0.94/1.32 excuselevel = 1
% 0.94/1.32 increasemaxweight = 1
% 0.94/1.32
% 0.94/1.32 maxselected = 10000000
% 0.94/1.32 maxnrclauses = 10000000
% 0.94/1.32
% 0.94/1.32 showgenerated = 0
% 0.94/1.32 showkept = 0
% 0.94/1.32 showselected = 0
% 0.94/1.32 showdeleted = 0
% 0.94/1.32 showresimp = 1
% 0.94/1.32 showstatus = 2000
% 0.94/1.32
% 0.94/1.32 prologoutput = 1
% 0.94/1.32 nrgoals = 5000000
% 0.94/1.32 totalproof = 1
% 0.94/1.32
% 0.94/1.32 Symbols occurring in the translation:
% 0.94/1.32
% 0.94/1.32 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.94/1.32 . [1, 2] (w:1, o:177, a:1, s:1, b:0),
% 0.94/1.32 ! [4, 1] (w:0, o:104, a:1, s:1, b:0),
% 0.94/1.32 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.32 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.32 'class_Ring__and__Field_Oring' [40, 1] (w:1, o:109, a:1, s:1, b:0),
% 0.94/1.32 'c_HOL_Oplus__class_Oplus' [41, 1] (w:1, o:110, a:1, s:1, b:0),
% 0.94/1.32 'c_HOL_Otimes__class_Otimes' [44, 3] (w:1, o:213, a:1, s:1, b:0),
% 0.94/1.32 hAPP [45, 2] (w:1, o:202, a:1, s:1, b:0),
% 0.94/1.32 'c_HOL_Ominus__class_Ominus' [49, 3] (w:1, o:214, a:1, s:1, b:0),
% 0.94/1.32 'tc_nat' [50, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.94/1.32 'c_HOL_Oord__class_Oless' [56, 3] (w:1, o:215, a:1, s:1, b:0),
% 0.94/1.32 'c_lessequals' [57, 3] (w:1, o:216, a:1, s:1, b:0),
% 0.94/1.32 'c_Suc' [58, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.94/1.32 'class_Ring__and__Field_Osemiring__0' [59, 1] (w:1, o:116, a:1, s:1
% 0.94/1.32 , b:0),
% 0.94/1.32 'class_Power_Opower' [60, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.94/1.32 'c_HOL_Ozero__class_Ozero' [61, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.94/1.32 'c_Power_Opower__class_Opower' [62, 3] (w:1, o:219, a:1, s:1, b:0),
% 0.94/1.32 'class_Ring__and__Field_Oordered__semiring__strict' [63, 1] (w:1, o:
% 0.94/1.32 145, a:1, s:1, b:0),
% 0.94/1.32 hBOOL [66, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.94/1.32 'v_sko__Nat__Xnat__Xinduct__1' [67, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.94/1.32 'class_Orderings_Olinorder' [68, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.94/1.32 'c_Orderings_Oord__class_Omin' [71, 3] (w:1, o:217, a:1, s:1, b:0),
% 0.94/1.32 'class_Ring__and__Field_Oordered__semidom' [73, 1] (w:1, o:148, a:1
% 0.94/1.32 , s:1, b:0),
% 0.94/1.32 'class_OrderedGroup_Opordered__ab__group__add' [74, 1] (w:1, o:119
% 0.94/1.32 , a:1, s:1, b:0),
% 0.94/1.32 'c_Orderings_Oord__class_Omax' [75, 3] (w:1, o:218, a:1, s:1, b:0),
% 0.94/1.32 'c_List_Oappend' [78, 3] (w:1, o:220, a:1, s:1, b:0),
% 0.94/1.32 'c_List_Oreplicate' [81, 3] (w:1, o:221, a:1, s:1, b:0),
% 0.94/1.32 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [82, 1]
% 0.94/1.57 (w:1, o:120, a:1, s:1, b:0),
% 0.94/1.57 'class_OrderedGroup_Ocomm__monoid__add' [83, 1] (w:1, o:121, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 'c_Nat_Osemiring__1__class_Oof__nat' [84, 2] (w:1, o:203, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 'c_Lambda_Osubst' [87, 3] (w:1, o:222, a:1, s:1, b:0),
% 0.94/1.57 'c_Lambda_Obeta' [89, 2] (w:1, o:204, a:1, s:1, b:0),
% 0.94/1.57 'class_Ring__and__Field_Oidom' [90, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.94/1.57 'class_Int_Onumber__ring' [91, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.94/1.57 'class_OrderedGroup_Olordered__ab__group__add' [92, 1] (w:1, o:122
% 0.94/1.57 , a:1, s:1, b:0),
% 0.94/1.57 'c_Lambda_OdB_OVar' [93, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.94/1.57 'class_OrderedGroup_Ogroup__add' [94, 1] (w:1, o:123, a:1, s:1, b:0)
% 0.94/1.57 ,
% 0.94/1.57 'class_Ring__and__Field_Ocomm__semiring__1' [95, 1] (w:1, o:152, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 'v_sko__Nat__Xnat__Xinducts__1' [98, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.94/1.57
% 0.94/1.57 'class_OrderedGroup_Omonoid__mult' [99, 1] (w:1, o:124, a:1, s:1, b:0
% 0.94/1.57 ),
% 0.94/1.57 'class_OrderedGroup_Opordered__ab__semigroup__add' [101, 1] (w:1, o:
% 0.94/1.57 125, a:1, s:1, b:0),
% 0.94/1.57 'class_OrderedGroup_Omonoid__add' [102, 1] (w:1, o:126, a:1, s:1, b:0
% 0.94/1.57 ),
% 0.94/1.57 'c_List_Olistsum' [103, 2] (w:1, o:205, a:1, s:1, b:0),
% 0.94/1.57 'c_List_Ofoldl' [104, 5] (w:1, o:238, a:1, s:1, b:0),
% 0.94/1.57 'class_OrderedGroup_Opordered__comm__monoid__add' [105, 1] (w:1, o:
% 0.94/1.57 127, a:1, s:1, b:0),
% 0.94/1.57 'class_Orderings_Opreorder' [106, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.94/1.57 'class_Orderings_Oorder' [107, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.94/1.57 'c_Type_Osko__Type__Xtyping__elims__2__1' [109, 4] (w:1, o:230, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 'c_Type_Otyping' [110, 3] (w:1, o:225, a:1, s:1, b:0),
% 0.94/1.57 'c_Lambda_OdB_OApp' [111, 0] (w:1, o:70, a:1, s:1, b:0),
% 0.94/1.57 'class_OrderedGroup_Oab__group__add' [112, 1] (w:1, o:130, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1' [113, 1] (w:1
% 0.94/1.57 , o:154, a:1, s:1, b:0),
% 0.94/1.57 'c_List_Olist_ONil' [114, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.94/1.57 'class_Orderings_Obot' [115, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.94/1.57 'c_Orderings_Obot__class_Obot' [116, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.94/1.57
% 0.94/1.57 'c_Nat_Onat_Onat__rec' [119, 4] (w:1, o:231, a:1, s:1, b:0),
% 0.94/1.57 'c_Groebner__Basis_Ogb__semiring' [125, 6] (w:1, o:240, a:1, s:1, b:0
% 0.94/1.57 ),
% 0.94/1.57 'v_sko__List__Xupt__Xinduct__1' [126, 1] (w:1, o:157, a:1, s:1, b:0)
% 0.94/1.57 ,
% 0.94/1.57 'c_Type_Otype_OAtom' [127, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.94/1.57 'v_sko__List__Xreplicate__Xinduct__1' [129, 1] (w:1, o:160, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 'class_Ring__and__Field_Opordered__ring' [130, 1] (w:1, o:164, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 'class_Ring__and__Field_Oordered__ring__strict' [131, 1] (w:1, o:144
% 0.94/1.57 , a:1, s:1, b:0),
% 0.94/1.57 'class_OrderedGroup_Osemigroup__add' [132, 1] (w:1, o:132, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1' [133, 1] (w:1, o:165
% 0.94/1.57 , a:1, s:1, b:0),
% 0.94/1.57 'class_Nat_Osemiring__char__0' [134, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.94/1.57
% 0.94/1.57 'class_Ring__and__Field_Oordered__semiring' [135, 1] (w:1, o:161, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 'c_List_Odrop' [136, 3] (w:1, o:226, a:1, s:1, b:0),
% 0.94/1.57 'c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1' [137, 2] (w:1
% 0.94/1.57 , o:206, a:1, s:1, b:0),
% 0.94/1.57 'c_InductTermi_OIT' [138, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.94/1.57 'class_OrderedGroup_Oab__semigroup__add' [139, 1] (w:1, o:133, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 'c_List_Ofoldr' [140, 5] (w:1, o:239, a:1, s:1, b:0),
% 0.94/1.57 'c_Lambda_OdB_OAbs' [142, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.94/1.57 'v_n____' [143, 0] (w:1, o:76, a:1, s:1, b:0),
% 0.94/1.57 'v_i____' [144, 0] (w:1, o:77, a:1, s:1, b:0),
% 0.94/1.57 'class_Ring__and__Field_Oordered__idom' [145, 1] (w:1, o:162, a:1, s:
% 0.94/1.57 1, b:0),
% 0.94/1.57 'c_List_Olist_OCons' [146, 3] (w:1, o:227, a:1, s:1, b:0),
% 0.94/1.57 'c_Type_Osko__Type__Xlist__app__typeE__1__1' [148, 4] (w:1, o:233, a:
% 0.94/1.57 1, s:1, b:0),
% 0.94/1.57 'c_Type_Otypings' [149, 3] (w:1, o:228, a:1, s:1, b:0),
% 0.94/1.57 'tc_Lambda_OdB' [150, 0] (w:1, o:78, a:1, s:1, b:0),
% 0.94/1.57 'c_Type_Osko__Type__Xtype__induct__1__1' [151, 1] (w:1, o:158, a:1
% 11.01/11.41 , s:1, b:0),
% 11.01/11.41 'class_Ring__and__Field_Osemiring' [157, 1] (w:1, o:168, a:1, s:1, b:
% 11.01/11.41 0),
% 11.01/11.41 't_a' [159, 0] (w:1, o:81, a:1, s:1, b:0),
% 11.01/11.41 'c_Nat_Onat_Onat__case' [160, 4] (w:1, o:234, a:1, s:1, b:0),
% 11.01/11.41 'class_Ring__and__Field_Osemiring__1' [162, 1] (w:1, o:169, a:1, s:1
% 11.01/11.41 , b:0),
% 11.01/11.41 'c_Type_Otype_Otype__rec' [170, 4] (w:1, o:236, a:1, s:1, b:0),
% 11.01/11.41 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [174, 1]
% 11.01/11.41 (w:1, o:134, a:1, s:1, b:0),
% 11.01/11.41 'class_Ring__and__Field_Opordered__cancel__semiring' [178, 1] (w:1
% 11.01/11.41 , o:170, a:1, s:1, b:0),
% 11.01/11.41 'class_OrderedGroup_Ocancel__ab__semigroup__add' [179, 1] (w:1, o:135
% 11.01/11.41 , a:1, s:1, b:0),
% 11.01/11.41 'class_OrderedGroup_Ocancel__semigroup__add' [180, 1] (w:1, o:136, a:
% 11.01/11.41 1, s:1, b:0),
% 11.01/11.41 'c_Type_Otype_Otype__case' [183, 4] (w:1, o:237, a:1, s:1, b:0),
% 11.01/11.41 'c_nat_Onat__size' [184, 1] (w:1, o:171, a:1, s:1, b:0),
% 11.01/11.41 'c_Lambda_Olift' [185, 2] (w:1, o:207, a:1, s:1, b:0),
% 11.01/11.41 'class_OrderedGroup_Oab__semigroup__idem__mult' [186, 1] (w:1, o:137
% 11.01/11.41 , a:1, s:1, b:0),
% 11.01/11.41 'c_Type_Osko__Type__Xlist__app__typeD__1__1' [187, 4] (w:1, o:232, a:
% 11.01/11.41 1, s:1, b:0),
% 11.01/11.41 'class_Ring__and__Field_Oring__1' [188, 1] (w:1, o:113, a:1, s:1, b:0
% 11.01/11.41 ),
% 11.01/11.41 'class_Ring__and__Field_Omult__mono' [189, 1] (w:1, o:172, a:1, s:1
% 11.01/11.41 , b:0),
% 11.01/11.41 'class_Ring__and__Field_Omult__mono1' [190, 1] (w:1, o:173, a:1, s:1
% 11.01/11.41 , b:0),
% 11.01/11.41 'class_Ring__and__Field_Oordered__comm__semiring__strict' [191, 1]
% 11.01/11.41 (w:1, o:163, a:1, s:1, b:0),
% 11.01/11.41 'class_Ring__and__Field_Opordered__semiring' [192, 1] (w:1, o:174, a:
% 11.01/11.41 1, s:1, b:0),
% 11.01/11.41 'c_Type_Otype_OFun' [193, 0] (w:1, o:88, a:1, s:1, b:0),
% 11.01/11.41 'c_Type_Osko__Type__Xtyping__elims__3__1' [194, 3] (w:1, o:223, a:1
% 11.01/11.41 , s:1, b:0),
% 11.01/11.41 'c_Type_Osko__Type__Xtyping__elims__3__2' [195, 3] (w:1, o:224, a:1
% 11.01/11.41 , s:1, b:0),
% 11.01/11.41 'class_Ring__and__Field_Ozero__neq__one' [196, 1] (w:1, o:175, a:1
% 11.01/11.41 , s:1, b:0),
% 11.01/11.41 'class_Ring__and__Field_Ono__zero__divisors' [197, 1] (w:1, o:143, a:
% 11.01/11.41 1, s:1, b:0),
% 11.01/11.41 'class_Ring__and__Field_Omult__zero' [198, 1] (w:1, o:142, a:1, s:1
% 11.01/11.41 , b:0),
% 11.01/11.41 'class_Ring__and__Field_Oring__1__no__zero__divisors' [199, 1] (w:1
% 11.01/11.41 , o:114, a:1, s:1, b:0),
% 11.01/11.41 'class_Ring__and__Field_Oring__no__zero__divisors' [200, 1] (w:1, o:
% 11.01/11.41 115, a:1, s:1, b:0),
% 11.01/11.41 'class_OrderedGroup_Ocomm__monoid__mult' [202, 1] (w:1, o:138, a:1
% 11.01/11.41 , s:1, b:0),
% 11.01/11.41 'class_OrderedGroup_Oab__semigroup__mult' [203, 1] (w:1, o:139, a:1
% 11.01/11.41 , s:1, b:0),
% 11.01/11.41 'class_Ring__and__Field_Ocomm__semiring' [205, 1] (w:1, o:176, a:1
% 11.01/11.41 , s:1, b:0),
% 11.01/11.41 'c_Nitpick_Onat__gcd' [206, 2] (w:1, o:208, a:1, s:1, b:0),
% 11.01/11.41 'c_String_Ochar_Ochar__size' [207, 1] (w:1, o:111, a:1, s:1, b:0),
% 11.01/11.41 'tc_String_Ochar' [208, 0] (w:1, o:90, a:1, s:1, b:0),
% 11.01/11.41 'c_Nat_Osize__class_Osize' [209, 2] (w:1, o:209, a:1, s:1, b:0),
% 11.01/11.41 'v_e____' [210, 0] (w:1, o:91, a:1, s:1, b:0),
% 11.01/11.41 'v_T____' [211, 0] (w:1, o:92, a:1, s:1, b:0),
% 11.01/11.41 'tc_Type_Otype' [212, 0] (w:1, o:93, a:1, s:1, b:0),
% 11.01/11.41 'c_Type_Oshift' [213, 4] (w:1, o:235, a:1, s:1, b:0),
% 11.01/11.41 'v_as____' [214, 0] (w:1, o:94, a:1, s:1, b:0),
% 11.01/11.41 'v_Ts____' [215, 0] (w:1, o:95, a:1, s:1, b:0),
% 11.01/11.41 'c_Type_Osko__Type__Xabs__typeE__1__1' [218, 2] (w:1, o:210, a:1, s:1
% 11.01/11.41 , b:0),
% 11.01/11.41 'c_Type_Osko__Type__Xabs__typeE__1__2' [219, 2] (w:1, o:211, a:1, s:1
% 11.01/11.41 , b:0),
% 11.01/11.41 'v_a____' [230, 0] (w:1, o:96, a:1, s:1, b:0),
% 11.01/11.41 'v_T_H____' [231, 0] (w:1, o:97, a:1, s:1, b:0),
% 11.01/11.41 'v_u____' [232, 0] (w:1, o:98, a:1, s:1, b:0),
% 11.01/11.41 'v_T_H_H____' [233, 0] (w:1, o:99, a:1, s:1, b:0),
% 11.01/11.41 'tc_fun' [237, 2] (w:1, o:212, a:1, s:1, b:0),
% 11.01/11.41 'c_fequal' [238, 3] (w:1, o:229, a:1, s:1, b:0).
% 11.01/11.41
% 11.01/11.41
% 11.01/11.41 Starting Search:
% 11.01/11.41
% 11.01/11.41 Resimplifying inuse:
% 11.01/11.41 Done
% 11.01/11.41
% 11.01/11.41
% 11.01/11.41 Intermediate Status:
% 11.01/11.41 Generated: 5831
% 11.01/11.41 Kept: 2020
% 11.01/11.41 Inuse: 120
% 11.01/11.41 Deleted: 1
% 11.01/11.41 Deletedinuse: 0
% 11.01/11.41
% 11.01/11.41 Resimplifying inuse:
% 11.01/11.41 Done
% 11.01/11.41
% 11.01/11.41 Resimplifying inuse:
% 11.01/11.41 Done
% 11.01/11.41
% 11.01/11.41
% 11.01/11.41 Intermediate Status:
% 11.01/11.41 Generated: 11283
% 11.01/11.41 Kept: 4315
% 11.01/11.41 Inuse: 186
% 11.01/11.41 Deleted: 5
% 11.01/11.41 Deletedinuse: 0
% 11.01/11.41
% 11.01/11.41 Resimplifying inuse:
% 11.01/11.41 Done
% 11.01/11.41
% 11.01/11.41 Resimplifying inuse:
% 11.01/11.41 Done
% 11.01/11.41
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 18090
% 39.13/39.54 Kept: 6316
% 39.13/39.54 Inuse: 324
% 39.13/39.54 Deleted: 9
% 39.13/39.54 Deletedinuse: 0
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 24878
% 39.13/39.54 Kept: 8360
% 39.13/39.54 Inuse: 404
% 39.13/39.54 Deleted: 13
% 39.13/39.54 Deletedinuse: 1
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 31699
% 39.13/39.54 Kept: 10361
% 39.13/39.54 Inuse: 444
% 39.13/39.54 Deleted: 15
% 39.13/39.54 Deletedinuse: 3
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 38022
% 39.13/39.54 Kept: 12378
% 39.13/39.54 Inuse: 494
% 39.13/39.54 Deleted: 16
% 39.13/39.54 Deletedinuse: 4
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 47672
% 39.13/39.54 Kept: 15043
% 39.13/39.54 Inuse: 524
% 39.13/39.54 Deleted: 16
% 39.13/39.54 Deletedinuse: 4
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 54271
% 39.13/39.54 Kept: 17122
% 39.13/39.54 Inuse: 593
% 39.13/39.54 Deleted: 17
% 39.13/39.54 Deletedinuse: 4
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 67306
% 39.13/39.54 Kept: 20358
% 39.13/39.54 Inuse: 613
% 39.13/39.54 Deleted: 17
% 39.13/39.54 Deletedinuse: 4
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying clauses:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 76595
% 39.13/39.54 Kept: 23085
% 39.13/39.54 Inuse: 643
% 39.13/39.54 Deleted: 541
% 39.13/39.54 Deletedinuse: 4
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 87841
% 39.13/39.54 Kept: 25485
% 39.13/39.54 Inuse: 673
% 39.13/39.54 Deleted: 541
% 39.13/39.54 Deletedinuse: 4
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 98498
% 39.13/39.54 Kept: 27498
% 39.13/39.54 Inuse: 698
% 39.13/39.54 Deleted: 541
% 39.13/39.54 Deletedinuse: 4
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 109734
% 39.13/39.54 Kept: 29507
% 39.13/39.54 Inuse: 760
% 39.13/39.54 Deleted: 543
% 39.13/39.54 Deletedinuse: 5
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 118203
% 39.13/39.54 Kept: 31532
% 39.13/39.54 Inuse: 792
% 39.13/39.54 Deleted: 543
% 39.13/39.54 Deletedinuse: 5
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 127719
% 39.13/39.54 Kept: 33638
% 39.13/39.54 Inuse: 862
% 39.13/39.54 Deleted: 545
% 39.13/39.54 Deletedinuse: 7
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 148227
% 39.13/39.54 Kept: 36274
% 39.13/39.54 Inuse: 882
% 39.13/39.54 Deleted: 545
% 39.13/39.54 Deletedinuse: 7
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 165784
% 39.13/39.54 Kept: 39320
% 39.13/39.54 Inuse: 892
% 39.13/39.54 Deleted: 546
% 39.13/39.54 Deletedinuse: 8
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying clauses:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 176381
% 39.13/39.54 Kept: 41495
% 39.13/39.54 Inuse: 942
% 39.13/39.54 Deleted: 1131
% 39.13/39.54 Deletedinuse: 10
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 190438
% 39.13/39.54 Kept: 44544
% 39.13/39.54 Inuse: 1002
% 39.13/39.54 Deleted: 1133
% 39.13/39.54 Deletedinuse: 12
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 200670
% 39.13/39.54 Kept: 46554
% 39.13/39.54 Inuse: 1029
% 39.13/39.54 Deleted: 1138
% 39.13/39.54 Deletedinuse: 17
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 211507
% 39.13/39.54 Kept: 48667
% 39.13/39.54 Inuse: 1062
% 39.13/39.54 Deleted: 1138
% 39.13/39.54 Deletedinuse: 17
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 220601
% 39.13/39.54 Kept: 50728
% 39.13/39.54 Inuse: 1102
% 39.13/39.54 Deleted: 1138
% 39.13/39.54 Deletedinuse: 17
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 231257
% 39.13/39.54 Kept: 53745
% 39.13/39.54 Inuse: 1132
% 39.13/39.54 Deleted: 1138
% 39.13/39.54 Deletedinuse: 17
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 237046
% 39.13/39.54 Kept: 55763
% 39.13/39.54 Inuse: 1141
% 39.13/39.54 Deleted: 1138
% 39.13/39.54 Deletedinuse: 17
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 248454
% 39.13/39.54 Kept: 58997
% 39.13/39.54 Inuse: 1142
% 39.13/39.54 Deleted: 1138
% 39.13/39.54 Deletedinuse: 17
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying clauses:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 257119
% 39.13/39.54 Kept: 61466
% 39.13/39.54 Inuse: 1162
% 39.13/39.54 Deleted: 1471
% 39.13/39.54 Deletedinuse: 17
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54 Resimplifying inuse:
% 39.13/39.54 Done
% 39.13/39.54
% 39.13/39.54
% 39.13/39.54 Intermediate Status:
% 39.13/39.54 Generated: 292346
% 90.39/90.80 Kept: 65822
% 90.39/90.80 Inuse: 1182
% 90.39/90.80 Deleted: 1471
% 90.39/90.80 Deletedinuse: 17
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80
% 90.39/90.80 Intermediate Status:
% 90.39/90.80 Generated: 324553
% 90.39/90.80 Kept: 68835
% 90.39/90.80 Inuse: 1187
% 90.39/90.80 Deleted: 1471
% 90.39/90.80 Deletedinuse: 17
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80
% 90.39/90.80 Intermediate Status:
% 90.39/90.80 Generated: 340562
% 90.39/90.80 Kept: 73905
% 90.39/90.80 Inuse: 1212
% 90.39/90.80 Deleted: 1471
% 90.39/90.80 Deletedinuse: 17
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80
% 90.39/90.80 Intermediate Status:
% 90.39/90.80 Generated: 355912
% 90.39/90.80 Kept: 76887
% 90.39/90.80 Inuse: 1242
% 90.39/90.80 Deleted: 1479
% 90.39/90.80 Deletedinuse: 25
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80
% 90.39/90.80 Intermediate Status:
% 90.39/90.80 Generated: 368027
% 90.39/90.80 Kept: 79062
% 90.39/90.80 Inuse: 1282
% 90.39/90.80 Deleted: 1479
% 90.39/90.80 Deletedinuse: 25
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80
% 90.39/90.80 Intermediate Status:
% 90.39/90.80 Generated: 384897
% 90.39/90.80 Kept: 81411
% 90.39/90.80 Inuse: 1302
% 90.39/90.80 Deleted: 1479
% 90.39/90.80 Deletedinuse: 25
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80 Resimplifying clauses:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80
% 90.39/90.80 Intermediate Status:
% 90.39/90.80 Generated: 409444
% 90.39/90.80 Kept: 85352
% 90.39/90.80 Inuse: 1312
% 90.39/90.80 Deleted: 1949
% 90.39/90.80 Deletedinuse: 25
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80
% 90.39/90.80 Intermediate Status:
% 90.39/90.80 Generated: 433971
% 90.39/90.80 Kept: 88352
% 90.39/90.80 Inuse: 1322
% 90.39/90.80 Deleted: 1949
% 90.39/90.80 Deletedinuse: 25
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80
% 90.39/90.80 Intermediate Status:
% 90.39/90.80 Generated: 450574
% 90.39/90.80 Kept: 90372
% 90.39/90.80 Inuse: 1346
% 90.39/90.80 Deleted: 1949
% 90.39/90.80 Deletedinuse: 25
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80
% 90.39/90.80 Intermediate Status:
% 90.39/90.80 Generated: 474702
% 90.39/90.80 Kept: 93129
% 90.39/90.80 Inuse: 1352
% 90.39/90.80 Deleted: 1949
% 90.39/90.80 Deletedinuse: 25
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80
% 90.39/90.80 Intermediate Status:
% 90.39/90.80 Generated: 495163
% 90.39/90.80 Kept: 95740
% 90.39/90.80 Inuse: 1377
% 90.39/90.80 Deleted: 1949
% 90.39/90.80 Deletedinuse: 25
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80
% 90.39/90.80 Intermediate Status:
% 90.39/90.80 Generated: 512864
% 90.39/90.80 Kept: 97814
% 90.39/90.80 Inuse: 1397
% 90.39/90.80 Deleted: 1949
% 90.39/90.80 Deletedinuse: 25
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80 Resimplifying inuse:
% 90.39/90.80 Done
% 90.39/90.80
% 90.39/90.80
% 90.39/90.80 Intermediate Status:
% 90.39/90.80 Generated: 524154
% 90.39/90.81 Kept: 99932
% 90.39/90.81 Inuse: 1427
% 90.39/90.81 Deleted: 1949
% 90.39/90.81 Deletedinuse: 25
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81
% 90.39/90.81 Intermediate Status:
% 90.39/90.81 Generated: 537434
% 90.39/90.81 Kept: 102435
% 90.39/90.81 Inuse: 1447
% 90.39/90.81 Deleted: 1949
% 90.39/90.81 Deletedinuse: 25
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81 Resimplifying clauses:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81
% 90.39/90.81 Intermediate Status:
% 90.39/90.81 Generated: 556695
% 90.39/90.81 Kept: 105565
% 90.39/90.81 Inuse: 1462
% 90.39/90.81 Deleted: 2207
% 90.39/90.81 Deletedinuse: 25
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81
% 90.39/90.81 Intermediate Status:
% 90.39/90.81 Generated: 583988
% 90.39/90.81 Kept: 108550
% 90.39/90.81 Inuse: 1472
% 90.39/90.81 Deleted: 2207
% 90.39/90.81 Deletedinuse: 25
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81
% 90.39/90.81 Intermediate Status:
% 90.39/90.81 Generated: 611420
% 90.39/90.81 Kept: 111236
% 90.39/90.81 Inuse: 1482
% 90.39/90.81 Deleted: 2207
% 90.39/90.81 Deletedinuse: 25
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81
% 90.39/90.81 Intermediate Status:
% 90.39/90.81 Generated: 630269
% 90.39/90.81 Kept: 113679
% 90.39/90.81 Inuse: 1497
% 90.39/90.81 Deleted: 2207
% 90.39/90.81 Deletedinuse: 25
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81
% 90.39/90.81 Intermediate Status:
% 90.39/90.81 Generated: 641150
% 90.39/90.81 Kept: 115827
% 90.39/90.81 Inuse: 1522
% 90.39/90.81 Deleted: 2207
% 90.39/90.81 Deletedinuse: 25
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81
% 90.39/90.81 Intermediate Status:
% 90.39/90.81 Generated: 654574
% 90.39/90.81 Kept: 118080
% 90.39/90.81 Inuse: 1547
% 90.39/90.81 Deleted: 2207
% 90.39/90.81 Deletedinuse: 25
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81
% 90.39/90.81 Intermediate Status:
% 90.39/90.81 Generated: 669954
% 90.39/90.81 Kept: 120489
% 90.39/90.81 Inuse: 1567
% 90.39/90.81 Deleted: 2207
% 90.39/90.81 Deletedinuse: 25
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81
% 90.39/90.81 Intermediate Status:
% 90.39/90.81 Generated: 685584
% 90.39/90.81 Kept: 123755
% 90.39/90.81 Inuse: 1575
% 90.39/90.81 Deleted: 2207
% 90.39/90.81 Deletedinuse: 25
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81 Resimplifying clauses:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81
% 90.39/90.81 Intermediate Status:
% 90.39/90.81 Generated: 709000
% 90.39/90.81 Kept: 130206
% 90.39/90.81 Inuse: 1583
% 90.39/90.81 Deleted: 2712
% 90.39/90.81 Deletedinuse: 25
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 90.39/90.81 Done
% 90.39/90.81
% 90.39/90.81
% 90.39/90.81 Intermediate Status:
% 90.39/90.81 Generated: 719304
% 90.39/90.81 Kept: 133031
% 90.39/90.81 Inuse: 1597
% 90.39/90.81 Deleted: 2712
% 90.39/90.81 Deletedinuse: 25
% 90.39/90.81
% 90.39/90.81 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 738880
% 167.34/167.80 Kept: 135794
% 167.34/167.80 Inuse: 1607
% 167.34/167.80 Deleted: 2712
% 167.34/167.80 Deletedinuse: 25
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 753380
% 167.34/167.80 Kept: 138665
% 167.34/167.80 Inuse: 1622
% 167.34/167.80 Deleted: 2713
% 167.34/167.80 Deletedinuse: 26
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 763988
% 167.34/167.80 Kept: 140689
% 167.34/167.80 Inuse: 1630
% 167.34/167.80 Deleted: 2713
% 167.34/167.80 Deletedinuse: 26
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 793306
% 167.34/167.80 Kept: 143781
% 167.34/167.80 Inuse: 1657
% 167.34/167.80 Deleted: 2713
% 167.34/167.80 Deletedinuse: 26
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying clauses:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 804810
% 167.34/167.80 Kept: 145781
% 167.34/167.80 Inuse: 1685
% 167.34/167.80 Deleted: 3010
% 167.34/167.80 Deletedinuse: 27
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 815367
% 167.34/167.80 Kept: 147796
% 167.34/167.80 Inuse: 1710
% 167.34/167.80 Deleted: 3012
% 167.34/167.80 Deletedinuse: 29
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 821421
% 167.34/167.80 Kept: 150204
% 167.34/167.80 Inuse: 1719
% 167.34/167.80 Deleted: 3030
% 167.34/167.80 Deletedinuse: 29
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 827729
% 167.34/167.80 Kept: 152536
% 167.34/167.80 Inuse: 1724
% 167.34/167.80 Deleted: 3050
% 167.34/167.80 Deletedinuse: 29
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 837981
% 167.34/167.80 Kept: 154538
% 167.34/167.80 Inuse: 1745
% 167.34/167.80 Deleted: 3053
% 167.34/167.80 Deletedinuse: 29
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 847894
% 167.34/167.80 Kept: 156557
% 167.34/167.80 Inuse: 1763
% 167.34/167.80 Deleted: 3053
% 167.34/167.80 Deletedinuse: 29
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 859559
% 167.34/167.80 Kept: 158748
% 167.34/167.80 Inuse: 1786
% 167.34/167.80 Deleted: 3053
% 167.34/167.80 Deletedinuse: 29
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 878014
% 167.34/167.80 Kept: 162485
% 167.34/167.80 Inuse: 1801
% 167.34/167.80 Deleted: 3054
% 167.34/167.80 Deletedinuse: 30
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying clauses:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 894978
% 167.34/167.80 Kept: 164576
% 167.34/167.80 Inuse: 1826
% 167.34/167.80 Deleted: 4257
% 167.34/167.80 Deletedinuse: 30
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 911029
% 167.34/167.80 Kept: 166608
% 167.34/167.80 Inuse: 1852
% 167.34/167.80 Deleted: 4257
% 167.34/167.80 Deletedinuse: 30
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 926612
% 167.34/167.80 Kept: 168741
% 167.34/167.80 Inuse: 1871
% 167.34/167.80 Deleted: 4259
% 167.34/167.80 Deletedinuse: 32
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 938573
% 167.34/167.80 Kept: 170784
% 167.34/167.80 Inuse: 1892
% 167.34/167.80 Deleted: 4259
% 167.34/167.80 Deletedinuse: 32
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 952334
% 167.34/167.80 Kept: 172799
% 167.34/167.80 Inuse: 1913
% 167.34/167.80 Deleted: 4259
% 167.34/167.80 Deletedinuse: 32
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 965630
% 167.34/167.80 Kept: 175041
% 167.34/167.80 Inuse: 1931
% 167.34/167.80 Deleted: 4259
% 167.34/167.80 Deletedinuse: 32
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 975986
% 167.34/167.80 Kept: 180257
% 167.34/167.80 Inuse: 1936
% 167.34/167.80 Deleted: 4259
% 167.34/167.80 Deletedinuse: 32
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 986403
% 167.34/167.80 Kept: 185496
% 167.34/167.80 Inuse: 1941
% 167.34/167.80 Deleted: 4259
% 167.34/167.80 Deletedinuse: 32
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying clauses:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 1028592
% 167.34/167.80 Kept: 188969
% 167.34/167.80 Inuse: 1946
% 167.34/167.80 Deleted: 4556
% 167.34/167.80 Deletedinuse: 32
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 1070861
% 167.34/167.80 Kept: 192313
% 167.34/167.80 Inuse: 1951
% 167.34/167.80 Deleted: 4556
% 167.34/167.80 Deletedinuse: 32
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 1083276
% 167.34/167.80 Kept: 194428
% 167.34/167.80 Inuse: 1956
% 167.34/167.80 Deleted: 4556
% 167.34/167.80 Deletedinuse: 32
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 Generated: 1095759
% 167.34/167.80 Kept: 196549
% 167.34/167.80 Inuse: 1961
% 167.34/167.80 Deleted: 4556
% 167.34/167.80 Deletedinuse: 32
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80 Resimplifying inuse:
% 167.34/167.80 Done
% 167.34/167.80
% 167.34/167.80
% 167.34/167.80 Intermediate Status:
% 167.34/167.80 GenerateCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------