TSTP Solution File: SWV591-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV591-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 : Wed Jul 20 16:26:58 EDT 2022
% Result : Timeout 300.07s 300.62s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : SWV591-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.11 % Command : bliksem %s
% 0.10/0.31 % Computer : n025.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.31 % CPULimit : 300
% 0.16/0.31 % DateTime : Thu Jun 16 06:50:56 EDT 2022
% 0.16/0.31 % CPUTime :
% 0.81/1.21 *** allocated 10000 integers for termspace/termends
% 0.81/1.21 *** allocated 10000 integers for clauses
% 0.81/1.21 *** allocated 10000 integers for justifications
% 0.81/1.21 *** allocated 15000 integers for termspace/termends
% 0.81/1.21 *** allocated 22500 integers for termspace/termends
% 0.81/1.21 Bliksem 1.12
% 0.81/1.21
% 0.81/1.21
% 0.81/1.21 Automatic Strategy Selection
% 0.81/1.21
% 0.81/1.21 Clauses:
% 0.81/1.21 [
% 0.81/1.21 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.81/1.21 , X ) ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.81/1.21 , Y, X ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.21 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 0.81/1.21 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 0.81/1.21 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.81/1.21 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 0.81/1.21 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.21 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 0.81/1.21 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.81/1.21 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 0.81/1.21 , U ) ), hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z
% 0.81/1.21 ), T ), U ) ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 0.81/1.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.81/1.21 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 0.81/1.21 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 0.81/1.21 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.81/1.21 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.81/1.21 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 0.81/1.21 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.21 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.81/1.21 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 0.81/1.21 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.81/1.21 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.81/1.21 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.81/1.21 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 0.81/1.21 Z, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.81/1.21 , T, X ), X ), T, X ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 0.81/1.21 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 0.81/1.21 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 0.81/1.21 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 0.81/1.21 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.81/1.21 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.81/1.21 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 0.81/1.21 , V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.81/1.21 T, X, U, W, Y, V0 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.81/1.21 T, X, U, Y, W, V0 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.81/1.21 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.81/1.21 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 0.81/1.21 , V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.81/1.21 X, T, U, Y, W, V0 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.81/1.21 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 0.81/1.21 , V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.81/1.21 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 0.81/1.21 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 0.81/1.21 , V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 0.81/1.21 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 0.81/1.21 W, V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.81/1.21 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 0.81/1.21 W, V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.81/1.21 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 0.81/1.21 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 0.81/1.21 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 0.81/1.21 W, V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.81/1.21 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 0.81/1.21 , V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.81/1.21 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 0.81/1.21 W, V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 0.81/1.21 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 0.81/1.21 , V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.81/1.21 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 0.81/1.21 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.81/1.21 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 0.81/1.21 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.81/1.21 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 0.81/1.21 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.81/1.21 T, X, U, W, Z, V0 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.81/1.21 T, X, U, W, Y, V0 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.81/1.21 T, X, U, Z, W, V0 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.81/1.21 T, X, U, Y, W, V0 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 0.81/1.21 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 0.81/1.21 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.81/1.21 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.81/1.21 X, T, U, Z, W, V0 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.81/1.21 X, T, U, Y, W, V0 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 0.81/1.21 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 0.81/1.21 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 0.81/1.21 , V0, U, V1 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 0.81/1.21 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 0.81/1.21 , V0, U, V1 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 0.81/1.21 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 0.81/1.21 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.81/1.21 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 0.81/1.21 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 0.81/1.21 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 0.81/1.21 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.81/1.21 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 0.81/1.21 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.21 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 0.81/1.21 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.21 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 0.81/1.21 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 0.81/1.21 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Z ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.81/1.21 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.81/1.21 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.81/1.21 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 0.81/1.21 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 0.81/1.21 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 0.81/1.21 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 0.81/1.21 V0, V1 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 0.81/1.21 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 0.81/1.21 V0, V1 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 0.81/1.21 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 0.81/1.21 , V0, V1 ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 0.81/1.21 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 0.81/1.21 , V0, V1 ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 0.81/1.21 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.81/1.21 , Y, X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.81/1.21 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.81/1.21 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.81/1.21 X ), Z, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.81/1.21 , X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.81/1.21 , X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 0.81/1.21 , T ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 0.81/1.21 , 'tc_nat' ), 'tc_nat' ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 0.81/1.21 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.81/1.21 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 0.81/1.21 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 0.81/1.21 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.81/1.21 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 0.81/1.21 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 0.81/1.21 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.81/1.21 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.81/1.21 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.81/1.21 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.81/1.21 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.21 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.81/1.21 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.21 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 0.81/1.21 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 0.81/1.21 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.21 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 0.81/1.21 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.81/1.21 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.81/1.21 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z,
% 0.81/1.21 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.81/1.21 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.81/1.21 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 0.81/1.21 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 0.81/1.21 , X ) ), hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.81/1.21 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.81/1.21 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.21 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 0.81/1.21 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), T,
% 0.81/1.21 'tc_nat' ), 'tc_nat', X ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T,
% 0.81/1.21 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 0.81/1.21 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 0.81/1.21 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 0.81/1.21 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.81/1.21 ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 0.81/1.21 ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.21 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.81/1.21 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.81/1.21 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.81/1.21 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.81/1.21 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.81/1.21 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.81/1.21 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 0.81/1.21 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.21 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.81/1.21 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 0.81/1.21 ), T ) ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.21 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.81/1.21 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.81/1.21 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.21 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 0.81/1.21 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.21 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 0.81/1.21 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.81/1.21 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 0.81/1.21 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ),
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X
% 0.81/1.21 ) ), U ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 0.81/1.21 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 0.81/1.21 ) ), Z ) ), T ), W ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 0.81/1.21 ) ), Z ) ), W ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.81/1.21 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.81/1.21 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.81/1.21 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.81/1.21 ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.81/1.21 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.81/1.21 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.81/1.21 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.81/1.21 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.81/1.21 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 0.81/1.21 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 0.81/1.21 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 0.81/1.21 , X ) ), T ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 0.81/1.21 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( T, X ) ),
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 0.81/1.21 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 0.81/1.21 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 0.81/1.21 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ), T ) )
% 0.81/1.21 ],
% 0.81/1.21 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 0.81/1.21 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.21 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.81/1.21 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.81/1.21 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.81/1.21 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.81/1.21 ) ) ],
% 0.81/1.21 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.81/1.21 ), =( Z, Y ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.81/1.21 ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.81/1.21 ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.81/1.21 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.81/1.21 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 0.81/1.21 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.81/1.21 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.81/1.21 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.81/1.21 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 0.81/1.21 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.81/1.21 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.81/1.21 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.21 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 0.81/1.21 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 0.81/1.21 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 0.81/1.21 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 0.81/1.21 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.81/1.21 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.81/1.21 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.81/1.21 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.81/1.21 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 0.81/1.21 , 'tc_nat' ), 'tc_nat' ) ],
% 0.81/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Z ) ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.81/1.21 , T, X ) ) ), =( Z, T ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.81/1.21 , T, X ) ) ), =( Y, Z ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.81/1.21 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.81/1.21 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 0.81/1.21 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.81/1.21 ), 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.21 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.21 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.81/1.21 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.81/1.21 , Y, X ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 0.81/1.21 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 0.81/1.21 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 0.81/1.21 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.81/1.21 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.81/1.21 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 0.81/1.21 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 0.81/1.21 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.81/1.21 , Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 0.81/1.21 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 0.81/1.21 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 0.81/1.21 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.81/1.21 ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.81/1.21 ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 0.81/1.21 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.81/1.21 ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.81/1.21 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.81/1.21 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.81/1.21 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.81/1.21 ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.81/1.21 ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.81/1.21 ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.81/1.21 ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.81/1.21 ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.81/1.21 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.81/1.21 ) ), =( Y, Z ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.81/1.21 ) ), =( Y, Z ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.81/1.21 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 0.81/1.21 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 0.81/1.21 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.81/1.21 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 0.81/1.21 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.81/1.21 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.81/1.21 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), T ), Z, X ) ) ],
% 0.81/1.21 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 0.81/1.21 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 0.81/1.21 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 0.81/1.21 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 0.81/1.21 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 0.81/1.21 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 0.81/1.21 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 0.81/1.21 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 0.81/1.21 T, X ) ), T, X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.81/1.21 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 0.81/1.21 ) ), Z ), T, X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 0.81/1.21 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.21 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.21 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.81/1.21 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ), W, X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.21 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 0.81/1.21 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 0.81/1.21 ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.21 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ) ), X ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 0.81/1.21 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.81/1.21 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.81/1.21 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 0.81/1.21 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.81/1.21 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.81/1.21 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.81/1.21 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.21 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 0.81/1.21 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.81/1.21 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.81/1.21 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 0.81/1.21 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 0.81/1.21 'c_Int_OBit0'( X ) ), 'c_Int_OBit1'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 0.81/1.21 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 0.81/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.81/1.21 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 0.81/1.21 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.81/1.21 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.81/1.21 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.81/1.21 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.81/1.21 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 0.81/1.21 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 0.81/1.21 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 0.81/1.21 , 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.81/1.21 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.81/1.21 , 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 0.81/1.21 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.81/1.21 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 0.81/1.21 ],
% 0.81/1.21 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 0.81/1.21 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 0.81/1.21 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.81/1.21 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ) ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.81/1.21 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 0.81/1.21 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 0.81/1.21 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 0.81/1.21 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 0.81/1.21 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 0.81/1.21 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.21 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 0.81/1.21 ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 0.81/1.21 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.81/1.21 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.81/1.21 , Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 0.81/1.21 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 0.81/1.21 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.81/1.21 , X, 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 0.81/1.21 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 0.81/1.21 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 0.81/1.21 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 0.81/1.21 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 0.81/1.21 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.81/1.21 , X, 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.81/1.21 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 0.81/1.21 ), 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.81/1.21 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 0.81/1.21 ), 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.81/1.21 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.81/1.21 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.81/1.21 'tc_nat' ) ), =( Y, Z ) ],
% 0.81/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 0.81/1.21 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 0.81/1.21 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.81/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 0.81/1.21 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 0.81/1.21 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.81/1.21 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 0.81/1.21 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.81/1.21 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 0.81/1.21 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 0.81/1.21 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 0.81/1.21 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 0.81/1.21 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 0.81/1.21 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 0.81/1.21 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 0.81/1.21 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.21 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 0.81/1.21 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 0.81/1.21 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.21 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 0.81/1.21 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 0.81/1.21 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.21 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 0.81/1.21 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.81/1.21 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.81/1.21 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 0.81/1.21 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 0.81/1.21 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 0.81/1.21 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 0.81/1.21 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 0.81/1.21 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.81/1.21 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 0.81/1.21 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.21 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 0.81/1.21 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.21 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 0.81/1.21 [ 'c_Fun_Oinj__on'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.81/1.21 , 'tc_nat', 'tc_nat', 'tc_nat' ), Y, 'tc_nat', 'tc_nat' ) ],
% 0.81/1.21 [ =( 'c_Set_Oimage'( 'c_Suc',
% 0.81/1.21 'c_SetInterval_Oord__class_OatLeastLessThan'( X, Y, 'tc_nat' ), 'tc_nat'
% 0.81/1.21 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc'
% 0.81/1.21 , X ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.81/1.21 ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.81/1.21 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.81/1.21 ,
% 0.81/1.21 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 0.81/1.21 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.21 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 0.81/1.21 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 0.81/1.21 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 0.81/1.21 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 0.81/1.21 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 0.81/1.21 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 0.81/1.21 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.81/1.21 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 X ), X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.21 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.81/1.21 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 0.81/1.21 ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.21 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 0.81/1.21 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.21 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 0.81/1.21 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.21 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 0.81/1.21 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.21 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.81/1.21 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 0.81/1.21 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.81/1.21 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.81/1.21 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.81/1.21 ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.81/1.21 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.81/1.21 ), T ) ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.81/1.21 ), Z ) ), T ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.81/1.21 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.21 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.81/1.21 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.81/1.21 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.81/1.21 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 0.81/1.21 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.81/1.21 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.81/1.21 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.81/1.21 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Z ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 0.81/1.21 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.81/1.21 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.81/1.21 'tc_nat' ) ), Y ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 0.81/1.21 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.81/1.21 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Z ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.81/1.21 ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Z ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.21 X ) ) ],
% 0.81/1.21 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.21 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.21 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.21 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.21 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 0.81/1.21 'c_Power_Opower__class_Opower'( X ), Z ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.22 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 0.81/1.22 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.81/1.22 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 0.81/1.22 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 0.81/1.22 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 0.81/1.22 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 0.81/1.22 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 0.81/1.22 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 0.81/1.22 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 0.81/1.22 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 0.81/1.22 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.81/1.22 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.81/1.22 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 0.81/1.22 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 0.81/1.22 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 0.81/1.22 , X ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.81/1.22 X ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Z ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ), X ) )
% 0.81/1.22 ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 0.81/1.22 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.22 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.81/1.22 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 0.81/1.22 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 0.81/1.22 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 0.81/1.22 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 0.81/1.22 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 0.81/1.22 , X, Z, U, W, V0 ) ) ],
% 0.81/1.22 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.81/1.22 ) ), =( 'c_Finite__Set_Osetsum'( Y,
% 0.81/1.22 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc',
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 0.81/1.22 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.81/1.22 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.81/1.22 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.81/1.22 T, X ) ) ],
% 0.81/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.81/1.22 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.22 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 0.81/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.22 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.22 , Y ), T ), Z, X ) ) ],
% 0.81/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.22 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.22 , Y ), Z ), T, X ) ) ],
% 0.81/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.22 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.81/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.22 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 0.81/1.22 ), Z ), Y ) ],
% 0.81/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.22 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 0.81/1.22 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 0.81/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.22 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 0.81/1.22 , X ) ), T, X ) ) ],
% 0.81/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.22 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 0.81/1.22 ), Z ), T, X ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.81/1.22 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.22 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'(
% 0.81/1.22 Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.81/1.22 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.81/1.22 , Y ), Z ), Z, X ), Y ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 0.81/1.22 ) ), 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( Z
% 0.81/1.22 , X ), T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ), T, X ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.22 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.81/1.22 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 0.81/1.22 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.81/1.22 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 0.81/1.22 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.22 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.81/1.22 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 0.81/1.22 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.81/1.22 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.81/1.22 ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 0.81/1.22 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.81/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 0.81/1.22 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 0.81/1.22 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 0.81/1.22 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 0.81/1.22 , Y ) ) ],
% 0.81/1.22 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.22 'tc_nat' ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.81/1.22 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.81/1.22 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 0.81/1.22 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ), 'tc_nat' ) ) ) ],
% 0.81/1.22 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.81/1.22 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ), 'tc_nat' ) ],
% 0.81/1.22 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.81/1.22 ), 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.81/1.22 ), 'tc_nat' ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 0.81/1.22 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 0.81/1.22 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 0.81/1.22 'c_Int_OPls' ), X ), X ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ),
% 0.81/1.22 'c_Int_OPls' ), X ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 0.81/1.22 'c_Int_OBit0'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit0'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 0.81/1.22 [ =( 'c_Int_OBit0'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_Int_Oint' ), X ), X ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.81/1.22 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.81/1.22 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 0.81/1.22 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 0.81/1.22 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 0.81/1.22 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 0.81/1.22 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.81/1.22 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 0.81/1.22 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 0.81/1.22 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 0.81/1.22 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.81/1.22 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 0.81/1.22 ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.81/1.22 , Z ), Y ), 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.81/1.22 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.81/1.22 ],
% 0.81/1.22 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.81/1.22 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 0.81/1.22 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 0.81/1.22 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.81/1.22 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 0.81/1.22 ) ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.81/1.22 X, T, 'tc_nat' ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 0.81/1.22 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), X ), Y ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 0.81/1.22 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), X ), Y ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 0.81/1.22 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 0.81/1.22 'c_Suc', Y ) ) ) ],
% 0.81/1.22 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 0.81/1.22 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.81/1.22 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 0.81/1.22 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 0.81/1.22 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.81/1.22 'tc_nat' ) ) ) ],
% 0.81/1.22 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 0.81/1.22 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 0.81/1.22 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 0.81/1.22 'tc_nat' ) ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.81/1.22 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 0.81/1.22 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 0.81/1.22 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 0.81/1.22 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 0.81/1.22 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 0.81/1.22 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 0.81/1.22 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 0.81/1.22 ), Z ), Y ), 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 0.81/1.22 ), Y ), Z ), 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 0.81/1.22 ), Y ), Z ), 'tc_nat' ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 0.81/1.22 ), X ), Z ), 'tc_nat' ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 0.81/1.22 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.81/1.22 'tc_nat' ) ), Y ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.81/1.22 'tc_nat' ) ), Y ) ],
% 0.81/1.22 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 0.81/1.22 'tc_nat' ), 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.81/1.22 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.81/1.22 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 0.81/1.22 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.81/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 0.81/1.22 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Z ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_Int_OPls'
% 0.81/1.22 ) ), Y ), X ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 0.81/1.22 ) ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ),
% 0.81/1.22 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.81/1.22 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), Y ), Y ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.81/1.22 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.81/1.22 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 0.81/1.22 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 0.81/1.22 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 0.81/1.22 ) ],
% 0.81/1.22 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.81/1.22 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 0.81/1.22 [ 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), X, 'tc_nat', 'tc_nat' ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 0.81/1.22 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 0.81/1.22 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 0.81/1.22 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.81/1.22 ), Y ), Y ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Z ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.81/1.22 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Z ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.81/1.22 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 0.81/1.22 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 0.81/1.22 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 0.81/1.22 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 0.81/1.22 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 0.81/1.22 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 0.81/1.22 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 0.81/1.22 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 0.81/1.22 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.81/1.22 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z, 'tc_nat', 'tc_nat', 'tc_nat' )
% 0.81/1.22 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ),
% 0.81/1.22 'c_HOL_Ominus__class_Ominus'( 'c_Finite__Set_Osetsum'( Y,
% 0.81/1.22 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), Z )
% 0.81/1.22 , 'tc_nat' ), 'tc_nat', X ), 'c_Finite__Set_Osetsum'( Y,
% 0.81/1.22 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ), X ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.81/1.22 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower__class_Opower'( X ), Z ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.81/1.22 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 0.81/1.22 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 0.81/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 0.81/1.22 ) ) ],
% 0.81/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 0.81/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 0.81/1.22 ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 0.81/1.22 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.81/1.22 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.22 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 0.81/1.22 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 0.81/1.22 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.81/1.22 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 0.81/1.22 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 0.81/1.22 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.81/1.22 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 0.81/1.22 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.81/1.22 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 0.81/1.22 ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.81/1.22 ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.81/1.22 ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.81/1.22 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.81/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 0.81/1.22 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 0.81/1.22 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.81/1.22 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 0.81/1.22 [ =( 'c_Set_Oimage'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.22 X, 'tc_nat', 'tc_nat', 'tc_nat' ),
% 0.81/1.22 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, 'tc_nat' ), 'tc_nat'
% 0.81/1.22 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.81/1.22 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 0.81/1.22 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 0.81/1.22 Y ) ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 0.81/1.22 , Z ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 0.81/1.22 , Z ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.81/1.22 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 0.81/1.22 ) ) ), =( Z, U ), =( Y, T ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.81/1.22 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 0.81/1.22 ) ) ), =( Z, U ), =( Y, T ) ],
% 0.81/1.22 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 0.81/1.22 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.81/1.22 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.81/1.22 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 0.81/1.22 ) ), Z ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 0.81/1.22 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.22 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 0.81/1.22 [ =( 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W ),
% 0.81/1.22 'c_Set_Oimage'( 'c_COMBB'( X, Y, U, W, T ), Z, T, W ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 0.81/1.22 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.81/1.22 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ), 'tc_nat', X
% 0.81/1.22 ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 0.81/1.22 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.81/1.22 Z, U, 'tc_nat' ), 'tc_nat', X ) ) ],
% 0.81/1.22 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 0.81/1.22 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.81/1.22 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 0.81/1.22 ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 0.81/1.22 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 0.81/1.22 ) ],
% 0.81/1.22 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OPls', X ) ), Y ), Y ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OPls', X ) ), Y ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 0.81/1.22 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 0.81/1.22 X ), Z, T, X ) ) ],
% 0.81/1.22 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 0.81/1.22 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 0.81/1.22 X ), Z, T, X ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.81/1.22 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ) ), Y ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ) ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.81/1.22 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), 'tc_nat', X
% 0.81/1.22 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'(
% 0.81/1.22 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T,
% 0.81/1.22 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', X, 'tc_nat' ),
% 0.81/1.22 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ), 'c_Finite__Set_Osetsum'( Y,
% 0.81/1.22 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ) ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.81/1.22 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.81/1.22 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.81/1.22 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.81/1.22 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.81/1.22 ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.81/1.22 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.81/1.22 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.81/1.22 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.81/1.22 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 0.81/1.22 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 0.81/1.22 , Y ) ],
% 0.81/1.22 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 0.81/1.22 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 0.81/1.22 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 0.81/1.22 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), =(
% 0.81/1.22 'c_Finite__Set_Osetsum'( 'v_f',
% 0.81/1.22 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_n' ), 'tc_nat' ), 'tc_nat', 't_a' ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ), 'c_Finite__Set_Osetsum'(
% 0.81/1.22 'v_f', 'c_Set_Oimage'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 0.81/1.22 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'tc_nat', 't_a' ) )
% 0.81/1.22 , 'c_Finite__Set_Osetsum'( 'v_f', 'c_Set_Oimage'( 'c_COMBC'( 'c_COMBB'(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 0.81/1.22 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 0.81/1.22 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat',
% 0.81/1.22 'tc_nat' ), 'tc_nat', 't_a' ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.81/1.22 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 0.81/1.22 ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.81/1.22 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 0.81/1.22 ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 0.81/1.22 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.81/1.22 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), Y ), Z ) ), T ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), Y ), Z ) ), T ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.81/1.22 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.81/1.22 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.81/1.22 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 0.81/1.22 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.81/1.22 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 0.81/1.22 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 0.81/1.22 , X ) ), T ) ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 0.81/1.22 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.81/1.22 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 0.81/1.22 ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.81/1.22 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 0.81/1.22 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat', X )
% 0.81/1.22 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( Y,
% 0.81/1.22 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( Y,
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( Y,
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 'tc_nat' ), X ), X ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 0.81/1.22 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 0.81/1.22 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 0.81/1.22 , Y ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 0.81/1.22 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 0.81/1.22 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.81/1.22 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.81/1.22 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.81/1.22 Y ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ],
% 0.81/1.22 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ),
% 0.81/1.22 'c_Finite__Set_Osetsum'( 'v_f', 'c_Set_Oimage'( hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 0.81/1.22 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'tc_nat', 't_a' ) )
% 0.81/1.22 , 'c_Finite__Set_Osetsum'( 'v_f', 'c_Set_Oimage'( 'c_COMBC'( 'c_COMBB'(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 0.81/1.22 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 0.81/1.22 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 0.81/1.22 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat',
% 0.81/1.22 'tc_nat' ), 'tc_nat', 't_a' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.81/1.22 't_a' ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'v_f', hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 't_a', 'tc_nat' ),
% 0.81/1.22 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat', 't_a' ) ),
% 0.81/1.22 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'v_f', 'c_COMBC'( 'c_COMBB'(
% 0.81/1.22 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 0.81/1.22 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 0.81/1.22 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 0.81/1.22 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 0.81/1.22 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 0.81/1.22 'tc_nat' ), 'tc_nat', 't_a', 'tc_nat' ),
% 0.81/1.22 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 0.81/1.22 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat', 't_a' ) ) ) ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.81/1.22 'class_OrderedGroup_Oab__semigroup__add'( X ) ],
% 0.81/1.22 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.81/1.22 'class_OrderedGroup_Omonoid__add'( X ) ],
% 0.81/1.22 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.81/1.22 'class_Orderings_Opreorder'( Y ) ) ],
% 0.81/1.22 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.81/1.22 'class_Orderings_Oorder'( Y ) ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.81/1.22 ],
% 0.81/1.22 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.81/1.22 ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.81/1.22 ],
% 0.81/1.22 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 0.81/1.22 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 0.81/1.22 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.81/1.22 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 0.81/1.22 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.81/1.22 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 0.81/1.22 ],
% 0.81/1.22 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 0.81/1.22 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 0.81/1.22 ,
% 0.81/1.22 [ 'c_fequal'( X, X, Y ) ],
% 0.81/1.22 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 0.81/1.22 ] .
% 0.81/1.22
% 0.81/1.22
% 0.81/1.22 percentage equality = 0.385424, percentage horn = 0.893491
% 0.81/1.22 This is a problem with some equality
% 0.81/1.22
% 0.81/1.22
% 0.81/1.22
% 0.81/1.22 Options Used:
% 0.81/1.22
% 0.81/1.22 useres = 1
% 0.81/1.22 useparamod = 1
% 0.81/1.22 useeqrefl = 1
% 0.81/1.22 useeqfact = 1
% 0.81/1.22 usefactor = 1
% 0.81/1.22 usesimpsplitting = 0
% 0.81/1.22 usesimpdemod = 5
% 0.81/1.22 usesimpres = 3
% 0.81/1.22
% 0.81/1.22 resimpinuse = 1000
% 0.81/1.22 resimpclauses = 20000
% 0.81/1.22 substype = eqrewr
% 0.81/1.22 backwardsubs = 1
% 0.81/1.22 selectoldest = 5
% 0.81/1.22
% 0.81/1.22 litorderings [0] = split
% 0.81/1.22 litorderings [1] = extend the termordering, first sorting on arguments
% 1.74/2.21
% 1.74/2.21 termordering = kbo
% 1.74/2.21
% 1.74/2.21 litapriori = 0
% 1.74/2.21 termapriori = 1
% 1.74/2.21 litaposteriori = 0
% 1.74/2.21 termaposteriori = 0
% 1.74/2.21 demodaposteriori = 0
% 1.74/2.21 ordereqreflfact = 0
% 1.74/2.21
% 1.74/2.21 litselect = negord
% 1.74/2.21
% 1.74/2.21 maxweight = 15
% 1.74/2.21 maxdepth = 30000
% 1.74/2.21 maxlength = 115
% 1.74/2.21 maxnrvars = 195
% 1.74/2.21 excuselevel = 1
% 1.74/2.21 increasemaxweight = 1
% 1.74/2.21
% 1.74/2.21 maxselected = 10000000
% 1.74/2.21 maxnrclauses = 10000000
% 1.74/2.21
% 1.74/2.21 showgenerated = 0
% 1.74/2.21 showkept = 0
% 1.74/2.21 showselected = 0
% 1.74/2.21 showdeleted = 0
% 1.74/2.21 showresimp = 1
% 1.74/2.21 showstatus = 2000
% 1.74/2.21
% 1.74/2.21 prologoutput = 1
% 1.74/2.21 nrgoals = 5000000
% 1.74/2.21 totalproof = 1
% 1.74/2.21
% 1.74/2.21 Symbols occurring in the translation:
% 1.74/2.21
% 1.74/2.21 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.74/2.21 . [1, 2] (w:1, o:132, a:1, s:1, b:0),
% 1.74/2.21 ! [4, 1] (w:0, o:75, a:1, s:1, b:0),
% 1.74/2.21 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.74/2.21 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.74/2.21 'tc_nat' [40, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.74/2.21 'c_HOL_Oord__class_Oless' [41, 3] (w:1, o:161, a:1, s:1, b:0),
% 1.74/2.21 'class_Orderings_Oorder' [43, 1] (w:1, o:80, a:1, s:1, b:0),
% 1.74/2.21 'class_Orderings_Olinorder' [45, 1] (w:1, o:81, a:1, s:1, b:0),
% 1.74/2.21 'c_Suc' [47, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.74/2.21 'c_HOL_Ozero__class_Ozero' [48, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.74/2.21 hAPP [49, 2] (w:1, o:157, a:1, s:1, b:0),
% 1.74/2.21 'c_Divides_Odiv__class_Omod' [50, 3] (w:1, o:162, a:1, s:1, b:0),
% 1.74/2.21 'class_Ring__and__Field_Oordered__semidom' [51, 1] (w:1, o:86, a:1
% 1.74/2.21 , s:1, b:0),
% 1.74/2.21 'c_Power_Opower__class_Opower' [52, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.74/2.21 'class_Divides_Osemiring__div' [57, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.74/2.21 'c_Divides_Odiv__class_Odiv' [59, 3] (w:1, o:163, a:1, s:1, b:0),
% 1.74/2.21 'c_Power_Opower_Opower' [62, 3] (w:1, o:164, a:1, s:1, b:0),
% 1.74/2.21 'tc_Int_Oint' [63, 0] (w:1, o:34, a:1, s:1, b:0),
% 1.74/2.21 'c_HOL_Oplus__class_Oplus' [64, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.74/2.21 'c_HOL_Otimes__class_Otimes' [67, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.74/2.21 'c_HOL_Oone__class_Oone' [69, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.74/2.21 'c_Parity_Oeven__odd__class_Oeven' [72, 2] (w:1, o:158, a:1, s:1, b:0
% 1.74/2.21 ),
% 1.74/2.21 'class_Divides_Oring__div' [73, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.74/2.21 'c_HOL_Ominus__class_Ominus' [74, 3] (w:1, o:165, a:1, s:1, b:0),
% 1.74/2.21 'class_Ring__and__Field_Oordered__idom' [75, 1] (w:1, o:93, a:1, s:1
% 1.74/2.21 , b:0),
% 1.74/2.21 'c_Groebner__Basis_Ogb__semiring' [82, 6] (w:1, o:173, a:1, s:1, b:0)
% 1.74/2.21 ,
% 1.74/2.21 'c_Int_Onumber__class_Onumber__of' [88, 2] (w:1, o:159, a:1, s:1, b:0
% 1.74/2.21 ),
% 1.74/2.21 'class_OrderedGroup_Opordered__ab__group__add' [89, 1] (w:1, o:94, a:
% 1.74/2.21 1, s:1, b:0),
% 1.74/2.21 'class_Orderings_Opreorder' [92, 1] (w:1, o:95, a:1, s:1, b:0),
% 1.74/2.21 'class_Ring__and__Field_Ocomm__semiring__1' [95, 1] (w:1, o:96, a:1
% 1.74/2.21 , s:1, b:0),
% 1.74/2.21 hBOOL [100, 1] (w:1, o:97, a:1, s:1, b:0),
% 1.74/2.21 'class_OrderedGroup_Ocomm__monoid__add' [101, 1] (w:1, o:98, a:1, s:1
% 1.74/2.21 , b:0),
% 1.74/2.21 'c_SetInterval_Oord__class_OatLeastLessThan' [103, 3] (w:1, o:166, a:
% 1.74/2.21 1, s:1, b:0),
% 1.74/2.21 'c_Finite__Set_Osetsum' [104, 4] (w:1, o:168, a:1, s:1, b:0),
% 1.74/2.21 'class_Ring__and__Field_Oordered__ring__strict' [105, 1] (w:1, o:85
% 1.74/2.21 , a:1, s:1, b:0),
% 1.74/2.21 'class_Ring__and__Field_Oordered__semiring__strict' [106, 1] (w:1, o:
% 1.74/2.21 99, a:1, s:1, b:0),
% 1.74/2.21 'class_Ring__and__Field_Oordered__comm__semiring__strict' [107, 1]
% 1.74/2.21 (w:1, o:100, a:1, s:1, b:0),
% 1.74/2.21 'class_OrderedGroup_Opordered__comm__monoid__add' [108, 1] (w:1, o:
% 1.74/2.21 101, a:1, s:1, b:0),
% 1.74/2.21 'class_OrderedGroup_Olordered__ab__group__add' [109, 1] (w:1, o:102
% 1.74/2.21 , a:1, s:1, b:0),
% 1.74/2.21 'class_RealVector_Oreal__normed__algebra' [110, 1] (w:1, o:103, a:1
% 1.74/2.21 , s:1, b:0),
% 1.74/2.21 'class_Ring__and__Field_Oring' [111, 1] (w:1, o:104, a:1, s:1, b:0),
% 1.74/2.21
% 1.74/2.21 'class_Ring__and__Field_Ozero__neq__one' [113, 1] (w:1, o:105, a:1
% 1.74/2.21 , s:1, b:0),
% 1.74/2.21 'class_Ring__and__Field_Ono__zero__divisors' [114, 1] (w:1, o:84, a:1
% 1.74/2.21 , s:1, b:0),
% 1.74/2.21 'class_Ring__and__Field_Omult__zero' [115, 1] (w:1, o:83, a:1, s:1
% 1.74/2.21 , b:0),
% 1.74/2.21 'class_Power_Opower' [116, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.74/2.21 'class_Ring__and__Field_Osemiring__0' [117, 1] (w:1, o:121, a:1, s:1
% 10.30/10.73 , b:0),
% 10.30/10.73 'class_Int_Onumber' [118, 1] (w:1, o:122, a:1, s:1, b:0),
% 10.30/10.73 'class_Int_Onumber__ring' [120, 1] (w:1, o:123, a:1, s:1, b:0),
% 10.30/10.73 'class_OrderedGroup_Omonoid__mult' [121, 1] (w:1, o:106, a:1, s:1, b:
% 10.30/10.73 0),
% 10.30/10.73 'c_Fun_Oinj__on' [123, 4] (w:1, o:169, a:1, s:1, b:0),
% 10.30/10.73 'class_OrderedGroup_Oab__group__add' [127, 1] (w:1, o:107, a:1, s:1
% 10.30/10.73 , b:0),
% 10.30/10.73 'class_Ring__and__Field_Oring__1__no__zero__divisors' [129, 1] (w:1
% 10.30/10.73 , o:119, a:1, s:1, b:0),
% 10.30/10.73 'class_OrderedGroup_Ogroup__add' [130, 1] (w:1, o:108, a:1, s:1, b:0)
% 10.30/10.73 ,
% 10.30/10.73 'class_Ring__and__Field_Oidom' [131, 1] (w:1, o:124, a:1, s:1, b:0),
% 10.30/10.73
% 10.30/10.73 'class_OrderedGroup_Ocomm__monoid__mult' [132, 1] (w:1, o:109, a:1
% 10.30/10.73 , s:1, b:0),
% 10.30/10.73 'class_Ring__and__Field_Opordered__ring' [134, 1] (w:1, o:125, a:1
% 10.30/10.73 , s:1, b:0),
% 10.30/10.73 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [135, 1]
% 10.30/10.73 (w:1, o:110, a:1, s:1, b:0),
% 10.30/10.73 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [136, 1]
% 10.30/10.73 (w:1, o:111, a:1, s:1, b:0),
% 10.30/10.73 'c_Int_OPls' [137, 0] (w:1, o:59, a:1, s:1, b:0),
% 10.30/10.73 'c_Int_OBit1' [138, 1] (w:1, o:127, a:1, s:1, b:0),
% 10.30/10.73 'c_Int_OBit0' [139, 1] (w:1, o:126, a:1, s:1, b:0),
% 10.30/10.73 'c_COMBC' [142, 5] (w:1, o:172, a:1, s:1, b:0),
% 10.30/10.73 'c_Set_Oimage' [143, 4] (w:1, o:170, a:1, s:1, b:0),
% 10.30/10.73 'c_COMBB' [144, 5] (w:1, o:171, a:1, s:1, b:0),
% 10.30/10.73 'class_Ring__and__Field_Osemiring__1' [145, 1] (w:1, o:128, a:1, s:1
% 10.30/10.73 , b:0),
% 10.30/10.73 'class_Ring__and__Field_Ocomm__semiring' [147, 1] (w:1, o:129, a:1
% 10.30/10.73 , s:1, b:0),
% 10.30/10.73 'class_OrderedGroup_Ocancel__ab__semigroup__add' [148, 1] (w:1, o:112
% 10.30/10.73 , a:1, s:1, b:0),
% 10.30/10.73 'class_OrderedGroup_Ocancel__semigroup__add' [149, 1] (w:1, o:113, a:
% 10.30/10.73 1, s:1, b:0),
% 10.30/10.73 'class_Ring__and__Field_Oring__no__zero__divisors' [153, 1] (w:1, o:
% 10.30/10.73 120, a:1, s:1, b:0),
% 10.30/10.73 'class_Ring__and__Field_Osemiring' [154, 1] (w:1, o:130, a:1, s:1, b:
% 10.30/10.73 0),
% 10.30/10.73 'class_OrderedGroup_Oab__semigroup__mult' [156, 1] (w:1, o:114, a:1
% 10.30/10.73 , s:1, b:0),
% 10.30/10.73 'tc_fun' [157, 2] (w:1, o:160, a:1, s:1, b:0),
% 10.30/10.73 'class_OrderedGroup_Oab__semigroup__idem__mult' [158, 1] (w:1, o:115
% 10.30/10.73 , a:1, s:1, b:0),
% 10.30/10.73 't_a' [159, 0] (w:1, o:64, a:1, s:1, b:0),
% 10.30/10.73 'v_f' [160, 0] (w:1, o:65, a:1, s:1, b:0),
% 10.30/10.73 'v_n' [161, 0] (w:1, o:66, a:1, s:1, b:0),
% 10.30/10.73 'class_OrderedGroup_Oab__semigroup__add' [162, 1] (w:1, o:116, a:1
% 10.30/10.73 , s:1, b:0),
% 10.30/10.73 'class_Int_Oring__char__0' [165, 1] (w:1, o:131, a:1, s:1, b:0),
% 10.30/10.73 'class_OrderedGroup_Omonoid__add' [166, 1] (w:1, o:117, a:1, s:1, b:0
% 10.30/10.73 ),
% 10.30/10.73 'tc_bool' [170, 0] (w:1, o:72, a:1, s:1, b:0),
% 10.30/10.73 'c_fequal' [171, 3] (w:1, o:167, a:1, s:1, b:0).
% 10.30/10.73
% 10.30/10.73
% 10.30/10.73 Starting Search:
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73
% 10.30/10.73 Intermediate Status:
% 10.30/10.73 Generated: 4482
% 10.30/10.73 Kept: 2000
% 10.30/10.73 Inuse: 147
% 10.30/10.73 Deleted: 4
% 10.30/10.73 Deletedinuse: 0
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73
% 10.30/10.73 Intermediate Status:
% 10.30/10.73 Generated: 11271
% 10.30/10.73 Kept: 4104
% 10.30/10.73 Inuse: 212
% 10.30/10.73 Deleted: 4
% 10.30/10.73 Deletedinuse: 0
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73
% 10.30/10.73 Intermediate Status:
% 10.30/10.73 Generated: 15965
% 10.30/10.73 Kept: 6191
% 10.30/10.73 Inuse: 291
% 10.30/10.73 Deleted: 10
% 10.30/10.73 Deletedinuse: 0
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73
% 10.30/10.73 Intermediate Status:
% 10.30/10.73 Generated: 23479
% 10.30/10.73 Kept: 8540
% 10.30/10.73 Inuse: 373
% 10.30/10.73 Deleted: 13
% 10.30/10.73 Deletedinuse: 0
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73
% 10.30/10.73 Intermediate Status:
% 10.30/10.73 Generated: 29238
% 10.30/10.73 Kept: 10663
% 10.30/10.73 Inuse: 428
% 10.30/10.73 Deleted: 15
% 10.30/10.73 Deletedinuse: 2
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73
% 10.30/10.73 Intermediate Status:
% 10.30/10.73 Generated: 35840
% 10.30/10.73 Kept: 12741
% 10.30/10.73 Inuse: 468
% 10.30/10.73 Deleted: 15
% 10.30/10.73 Deletedinuse: 2
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73
% 10.30/10.73 Intermediate Status:
% 10.30/10.73 Generated: 40690
% 10.30/10.73 Kept: 14747
% 10.30/10.73 Inuse: 489
% 10.30/10.73 Deleted: 15
% 10.30/10.73 Deletedinuse: 2
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73
% 10.30/10.73 Intermediate Status:
% 10.30/10.73 Generated: 46582
% 10.30/10.73 Kept: 16764
% 10.30/10.73 Inuse: 524
% 10.30/10.73 Deleted: 16
% 10.30/10.73 Deletedinuse: 3
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73 Resimplifying inuse:
% 10.30/10.73 Done
% 10.30/10.73
% 10.30/10.73
% 10.30/10.73 Intermediate Status:
% 37.57/38.06 Generated: 52778
% 37.57/38.06 Kept: 18771
% 37.57/38.06 Inuse: 569
% 37.57/38.06 Deleted: 16
% 37.57/38.06 Deletedinuse: 3
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying clauses:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 59616
% 37.57/38.06 Kept: 20894
% 37.57/38.06 Inuse: 603
% 37.57/38.06 Deleted: 1035
% 37.57/38.06 Deletedinuse: 3
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 67603
% 37.57/38.06 Kept: 23182
% 37.57/38.06 Inuse: 643
% 37.57/38.06 Deleted: 1035
% 37.57/38.06 Deletedinuse: 3
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 75421
% 37.57/38.06 Kept: 25293
% 37.57/38.06 Inuse: 663
% 37.57/38.06 Deleted: 1035
% 37.57/38.06 Deletedinuse: 3
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 81407
% 37.57/38.06 Kept: 27298
% 37.57/38.06 Inuse: 704
% 37.57/38.06 Deleted: 1035
% 37.57/38.06 Deletedinuse: 3
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 101035
% 37.57/38.06 Kept: 30867
% 37.57/38.06 Inuse: 723
% 37.57/38.06 Deleted: 1036
% 37.57/38.06 Deletedinuse: 4
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 108735
% 37.57/38.06 Kept: 33041
% 37.57/38.06 Inuse: 768
% 37.57/38.06 Deleted: 1036
% 37.57/38.06 Deletedinuse: 4
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 119378
% 37.57/38.06 Kept: 35704
% 37.57/38.06 Inuse: 803
% 37.57/38.06 Deleted: 1036
% 37.57/38.06 Deletedinuse: 4
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 130016
% 37.57/38.06 Kept: 38428
% 37.57/38.06 Inuse: 853
% 37.57/38.06 Deleted: 1036
% 37.57/38.06 Deletedinuse: 4
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying clauses:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 138777
% 37.57/38.06 Kept: 40456
% 37.57/38.06 Inuse: 893
% 37.57/38.06 Deleted: 1501
% 37.57/38.06 Deletedinuse: 5
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 145711
% 37.57/38.06 Kept: 43511
% 37.57/38.06 Inuse: 898
% 37.57/38.06 Deleted: 1501
% 37.57/38.06 Deletedinuse: 5
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 152656
% 37.57/38.06 Kept: 46546
% 37.57/38.06 Inuse: 903
% 37.57/38.06 Deleted: 1501
% 37.57/38.06 Deletedinuse: 5
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 161465
% 37.57/38.06 Kept: 48693
% 37.57/38.06 Inuse: 918
% 37.57/38.06 Deleted: 1501
% 37.57/38.06 Deletedinuse: 5
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 169786
% 37.57/38.06 Kept: 50831
% 37.57/38.06 Inuse: 948
% 37.57/38.06 Deleted: 1501
% 37.57/38.06 Deletedinuse: 5
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 175950
% 37.57/38.06 Kept: 52916
% 37.57/38.06 Inuse: 978
% 37.57/38.06 Deleted: 1501
% 37.57/38.06 Deletedinuse: 5
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 180874
% 37.57/38.06 Kept: 55151
% 37.57/38.06 Inuse: 993
% 37.57/38.06 Deleted: 1501
% 37.57/38.06 Deletedinuse: 5
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 186984
% 37.57/38.06 Kept: 57317
% 37.57/38.06 Inuse: 1023
% 37.57/38.06 Deleted: 1501
% 37.57/38.06 Deletedinuse: 5
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 197254
% 37.57/38.06 Kept: 60339
% 37.57/38.06 Inuse: 1055
% 37.57/38.06 Deleted: 1501
% 37.57/38.06 Deletedinuse: 5
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying clauses:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06 Resimplifying inuse:
% 37.57/38.06 Done
% 37.57/38.06
% 37.57/38.06
% 37.57/38.06 Intermediate Status:
% 37.57/38.06 Generated: 205265
% 37.57/38.06 Kept: 62447
% 37.57/38.06 Inuse: 1068
% 37.57/38.07 Deleted: 1625
% 37.57/38.07 Deletedinuse: 6
% 37.57/38.07
% 37.57/38.07 Resimplifying inuse:
% 37.57/38.07 Done
% 37.57/38.07
% 37.57/38.07
% 37.57/38.07 Intermediate Status:
% 37.57/38.07 Generated: 218630
% 37.57/38.07 Kept: 65989
% 37.57/38.07 Inuse: 1075
% 37.57/38.07 Deleted: 1625
% 37.57/38.07 Deletedinuse: 6
% 37.57/38.07
% 37.57/38.07 Resimplifying inuse:
% 37.57/38.07 Done
% 37.57/38.07
% 37.57/38.07
% 37.57/38.07 Intermediate Status:
% 37.57/38.07 Generated: 232375
% 37.57/38.07 Kept: 68038
% 37.57/38.07 Inuse: 1096
% 37.57/38.07 Deleted: 1627
% 37.57/38.07 Deletedinuse: 6
% 37.57/38.07
% 37.57/38.07 Resimplifying inuse:
% 37.57/38.07 Done
% 37.57/38.07
% 37.57/38.07 Resimplifying inuse:
% 37.57/38.07 Done
% 37.57/38.07
% 37.57/38.07
% 37.57/38.07 Intermediate Status:
% 37.57/38.07 Generated: 240226
% 37.57/38.07 Kept: 70046
% 37.57/38.07 Inuse: 1125
% 37.57/38.07 Deleted: 1629
% 37.57/38.07 Deletedinuse: 8
% 37.57/38.07
% 37.57/38.07 Resimplifying inuse:
% 37.57/38.07 Done
% 37.57/38.07
% 37.57/38.07
% 37.57/38.07 Intermediate Status:
% 37.57/38.07 Generated: 249535
% 37.57/38.07 Kept: 72502
% 37.57/38.07 Inuse: 1146
% 37.57/38.07 Deleted: 1629
% 37.57/38.07 Deletedinuse: 8
% 37.57/38.07
% 37.57/38.07 Resimplifying inuse:
% 37.57/38.07 Done
% 37.57/38.07
% 37.57/38.07 Resimplifying inuse:
% 37.57/38.07 Done
% 37.57/38.07
% 37.57/38.07
% 37.57/38.07 Intermediate Status:
% 37.57/38.07 Generated: 256716
% 37.57/38.07 Kept: 74588
% 37.57/38.07 Inuse: 1156
% 37.57/38.07 Deleted: 1629
% 37.57/38.07 Deletedinuse: 8
% 37.57/38.07
% 37.57/38.07 Resimplifying inuse:
% 37.57/38.07 Done
% 37.57/38.07
% 37.57/38.07
% 37.57/38.07 Intermediate Status:
% 37.57/38.07 Generated: 268367
% 37.57/38.07 Kept: 77637
% 37.57/38.07 Inuse: 1166
% 37.57/38.07 Deleted: 1629
% 37.57/38.07 Deletedinuse: 8
% 37.57/38.07
% 37.57/38.07 Resimplifying inuse:
% 37.57/38.07 Done
% 37.57/38.07
% 37.57/38.07 Resimplifying inuse:
% 37.57/38.07 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 282327
% 165.16/165.68 Kept: 80955
% 165.16/165.68 Inuse: 1176
% 165.16/165.68 Deleted: 1629
% 165.16/165.68 Deletedinuse: 8
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying clauses:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 289987
% 165.16/165.68 Kept: 83102
% 165.16/165.68 Inuse: 1206
% 165.16/165.68 Deleted: 2018
% 165.16/165.68 Deletedinuse: 8
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 300976
% 165.16/165.68 Kept: 85113
% 165.16/165.68 Inuse: 1244
% 165.16/165.68 Deleted: 2018
% 165.16/165.68 Deletedinuse: 8
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 308618
% 165.16/165.68 Kept: 87347
% 165.16/165.68 Inuse: 1276
% 165.16/165.68 Deleted: 2019
% 165.16/165.68 Deletedinuse: 9
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 319974
% 165.16/165.68 Kept: 92071
% 165.16/165.68 Inuse: 1305
% 165.16/165.68 Deleted: 2021
% 165.16/165.68 Deletedinuse: 10
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 327485
% 165.16/165.68 Kept: 94132
% 165.16/165.68 Inuse: 1315
% 165.16/165.68 Deleted: 2021
% 165.16/165.68 Deletedinuse: 10
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 338923
% 165.16/165.68 Kept: 96136
% 165.16/165.68 Inuse: 1354
% 165.16/165.68 Deleted: 2040
% 165.16/165.68 Deletedinuse: 29
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 348639
% 165.16/165.68 Kept: 98153
% 165.16/165.68 Inuse: 1386
% 165.16/165.68 Deleted: 2040
% 165.16/165.68 Deletedinuse: 29
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 357202
% 165.16/165.68 Kept: 100159
% 165.16/165.68 Inuse: 1411
% 165.16/165.68 Deleted: 2040
% 165.16/165.68 Deletedinuse: 29
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying clauses:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 366964
% 165.16/165.68 Kept: 102167
% 165.16/165.68 Inuse: 1444
% 165.16/165.68 Deleted: 3171
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 372990
% 165.16/165.68 Kept: 104261
% 165.16/165.68 Inuse: 1460
% 165.16/165.68 Deleted: 3171
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 387873
% 165.16/165.68 Kept: 107774
% 165.16/165.68 Inuse: 1464
% 165.16/165.68 Deleted: 3171
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 393947
% 165.16/165.68 Kept: 110047
% 165.16/165.68 Inuse: 1480
% 165.16/165.68 Deleted: 3171
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 409199
% 165.16/165.68 Kept: 112256
% 165.16/165.68 Inuse: 1490
% 165.16/165.68 Deleted: 3171
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 416418
% 165.16/165.68 Kept: 114519
% 165.16/165.68 Inuse: 1510
% 165.16/165.68 Deleted: 3171
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 422966
% 165.16/165.68 Kept: 116614
% 165.16/165.68 Inuse: 1530
% 165.16/165.68 Deleted: 3171
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 428354
% 165.16/165.68 Kept: 118628
% 165.16/165.68 Inuse: 1545
% 165.16/165.68 Deleted: 3171
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 439076
% 165.16/165.68 Kept: 120908
% 165.16/165.68 Inuse: 1580
% 165.16/165.68 Deleted: 3171
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying clauses:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 445776
% 165.16/165.68 Kept: 123268
% 165.16/165.68 Inuse: 1600
% 165.16/165.68 Deleted: 4416
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 451864
% 165.16/165.68 Kept: 125363
% 165.16/165.68 Inuse: 1620
% 165.16/165.68 Deleted: 4416
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 467528
% 165.16/165.68 Kept: 127383
% 165.16/165.68 Inuse: 1631
% 165.16/165.68 Deleted: 4416
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 496724
% 165.16/165.68 Kept: 130918
% 165.16/165.68 Inuse: 1640
% 165.16/165.68 Deleted: 4416
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 526351
% 165.16/165.68 Kept: 134497
% 165.16/165.68 Inuse: 1650
% 165.16/165.68 Deleted: 4416
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68 Resimplifying inuse:
% 165.16/165.68 Done
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 542390
% 165.16/165.68 Kept: 136551
% 165.16/165.68 Inuse: 1660
% 165.16/165.68 Deleted: 4416
% 165.16/165.68 Deletedinuse: 37
% 165.16/165.68
% 165.16/165.68
% 165.16/165.68 Intermediate Status:
% 165.16/165.68 Generated: 553123
% 165.16/165.68 Kept: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------