TSTP Solution File: SWV590-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV590-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.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 16:26:57 EDT 2022
% Result : Timeout 300.08s 300.61s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV590-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Wed Jun 15 15:27:26 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.05/1.43 *** allocated 10000 integers for termspace/termends
% 1.05/1.43 *** allocated 10000 integers for clauses
% 1.05/1.43 *** allocated 10000 integers for justifications
% 1.05/1.43 *** allocated 15000 integers for termspace/termends
% 1.05/1.43 *** allocated 22500 integers for termspace/termends
% 1.05/1.43 Bliksem 1.12
% 1.05/1.43
% 1.05/1.43
% 1.05/1.43 Automatic Strategy Selection
% 1.05/1.43
% 1.05/1.43 Clauses:
% 1.05/1.43 [
% 1.05/1.43 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.05/1.43 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.05/1.43 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.05/1.43 X ), Z, X ) ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.05/1.43 , Y, X ) ) ],
% 1.05/1.43 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.05/1.43 , X ) ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.05/1.43 , Y, X ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.43 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.05/1.43 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 1.05/1.43 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.05/1.43 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.05/1.43 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.43 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.05/1.43 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.05/1.43 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.05/1.43 , U ) ), hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z
% 1.05/1.43 ), T ), U ) ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.05/1.43 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.05/1.43 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.05/1.43 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.05/1.43 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.05/1.43 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.05/1.43 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.05/1.43 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.43 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.05/1.43 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.05/1.43 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.05/1.43 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.43 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.05/1.43 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.05/1.43 Z, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.05/1.43 , T, X ), X ), T, X ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.05/1.43 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.05/1.43 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.05/1.43 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.05/1.43 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.05/1.43 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.05/1.43 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.05/1.43 , V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.05/1.43 T, X, U, W, Y, V0 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.05/1.43 T, X, U, Y, W, V0 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.05/1.43 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.05/1.43 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.05/1.43 , V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.05/1.43 X, T, U, Y, W, V0 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.05/1.43 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.05/1.43 , V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.05/1.43 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.05/1.43 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.05/1.43 , V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.05/1.43 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.05/1.43 W, V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.05/1.43 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.05/1.43 W, V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.05/1.43 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.05/1.43 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.05/1.43 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.05/1.43 W, V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.05/1.43 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.05/1.43 , V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.05/1.43 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.05/1.43 W, V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.05/1.43 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.05/1.43 , V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.05/1.43 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.05/1.43 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.05/1.43 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.05/1.43 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.05/1.43 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.05/1.43 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.05/1.43 T, X, U, W, Z, V0 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.05/1.43 T, X, U, W, Y, V0 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.05/1.43 T, X, U, Z, W, V0 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.05/1.43 T, X, U, Y, W, V0 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.05/1.43 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.05/1.43 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.05/1.43 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.05/1.43 X, T, U, Z, W, V0 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.05/1.43 X, T, U, Y, W, V0 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.05/1.43 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.05/1.43 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.05/1.43 , V0, U, V1 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.05/1.43 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.05/1.43 , V0, U, V1 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.05/1.43 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.05/1.43 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.43 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.05/1.43 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.05/1.43 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 1.05/1.43 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.05/1.43 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.05/1.43 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.43 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.05/1.43 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.43 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.05/1.43 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.05/1.43 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.05/1.43 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.05/1.43 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.05/1.43 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.05/1.43 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.05/1.43 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.05/1.43 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.05/1.43 V0, V1 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.05/1.43 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.05/1.43 V0, V1 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.05/1.43 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.05/1.43 , V0, V1 ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.05/1.43 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.05/1.43 , V0, V1 ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.05/1.43 ), =( Z, Y ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.05/1.43 ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.05/1.43 , X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.43 , X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.05/1.43 , T ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.43 , 'tc_nat' ), 'tc_nat' ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.05/1.43 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.05/1.43 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.05/1.43 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.05/1.43 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.05/1.43 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.05/1.43 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.05/1.43 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( 'c_Suc', Y )
% 1.05/1.43 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastAtMost'( X, Y, 'tc_nat'
% 1.05/1.43 ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.43 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.05/1.43 , hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.05/1.43 'c_Suc', T ), Z, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.05/1.43 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.05/1.43 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.05/1.43 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.05/1.43 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.43 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.05/1.43 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.43 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.05/1.43 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.05/1.43 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.43 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.05/1.43 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.43 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.05/1.43 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z,
% 1.05/1.43 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.43 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.05/1.43 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.05/1.43 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.05/1.43 , X ) ), hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.43 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.05/1.43 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.43 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.05/1.43 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), T,
% 1.05/1.43 'tc_nat' ), 'tc_nat', X ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T,
% 1.05/1.43 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.05/1.43 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.05/1.43 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.05/1.43 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.05/1.43 ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.05/1.43 ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.43 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.05/1.43 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.05/1.43 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.05/1.43 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.05/1.43 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.05/1.43 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.05/1.43 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.05/1.43 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.43 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.05/1.43 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.05/1.43 ), T ) ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.43 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.05/1.43 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.43 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.43 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.43 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.05/1.43 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.43 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.05/1.43 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.05/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 1.05/1.43 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ),
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X
% 1.05/1.43 ) ), U ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 1.05/1.43 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 1.05/1.43 ) ), Z ) ), T ), W ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.05/1.43 ) ), Z ) ), W ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.05/1.43 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.05/1.43 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.05/1.43 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.43 ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.05/1.43 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.05/1.43 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.05/1.43 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.05/1.43 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.05/1.43 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.05/1.43 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.05/1.43 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.05/1.43 , X ) ), T ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.05/1.43 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( T, X ) ),
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.05/1.43 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.05/1.43 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.05/1.43 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ), T ) )
% 1.05/1.43 ],
% 1.05/1.43 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.05/1.43 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.43 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.05/1.43 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.05/1.43 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.05/1.43 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.43 ) ) ],
% 1.05/1.43 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.05/1.43 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.05/1.43 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.05/1.43 ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.05/1.43 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.05/1.43 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.05/1.43 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.05/1.43 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Set_Oimage'( 'c_Suc', 'c_SetInterval_Oord__class_OatLeastAtMost'(
% 1.05/1.43 X, Y, 'tc_nat' ), 'tc_nat', 'tc_nat' ),
% 1.05/1.43 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( 'c_Suc', X ), hAPP(
% 1.05/1.43 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.05/1.43 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.43 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.05/1.43 , hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.05/1.43 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.05/1.43 ) ), hAPP( Y, hAPP( 'c_Suc', T ) ) ) ), 'c_HOL_Oord__class_Oless'( hAPP(
% 1.05/1.43 'c_Suc', T ), Z, 'tc_nat' ) ],
% 1.05/1.43 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.05/1.43 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.05/1.43 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.05/1.43 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.05/1.43 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.43 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.05/1.43 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.05/1.43 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.05/1.43 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.05/1.43 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.05/1.43 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.05/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.05/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.05/1.43 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.43 , 'tc_nat' ), 'tc_nat' ) ],
% 1.05/1.43 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Z ) ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.05/1.43 , T, X ) ) ), =( Z, T ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.05/1.43 , T, X ) ) ), =( Y, Z ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.05/1.43 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.43 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.05/1.43 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.05/1.43 ), 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.43 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.43 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.05/1.43 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.05/1.43 , Y, X ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 1.05/1.43 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 1.05/1.43 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 1.05/1.43 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.43 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.43 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.05/1.43 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.05/1.43 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.05/1.43 , Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.05/1.43 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.05/1.43 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.05/1.43 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.43 ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.05/1.43 ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.05/1.43 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.43 ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.05/1.43 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.05/1.43 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.05/1.43 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.43 ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.43 ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.43 ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.05/1.43 ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.43 ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.43 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.43 ) ), =( Y, Z ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.43 ) ), =( Y, Z ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.43 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.05/1.43 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.05/1.43 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.05/1.43 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.05/1.43 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.05/1.43 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.05/1.43 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), T ), Z, X ) ) ],
% 1.05/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.05/1.43 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.05/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.05/1.43 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.05/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.05/1.43 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.05/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.05/1.43 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.05/1.43 T, X ) ), T, X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.43 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.05/1.43 ) ), Z ), T, X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.05/1.43 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.43 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.43 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.05/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ), W, X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.43 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.05/1.43 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.05/1.43 ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.43 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ) ), X ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.05/1.43 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.05/1.43 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.05/1.43 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.05/1.43 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.05/1.43 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.05/1.43 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.05/1.43 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.43 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.05/1.43 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.05/1.43 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.05/1.43 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.05/1.43 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.43 T, X ) ) ],
% 1.05/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.05/1.43 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.43 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.05/1.43 'c_Int_OBit0'( X ) ), 'c_Int_OBit1'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.05/1.43 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.05/1.43 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.05/1.43 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.05/1.43 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.05/1.43 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.43 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.05/1.43 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.05/1.43 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.05/1.43 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.05/1.43 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.05/1.43 , 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.05/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.05/1.43 , 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.05/1.43 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.05/1.43 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.05/1.43 ],
% 1.05/1.43 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.05/1.43 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.05/1.43 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.05/1.43 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ) ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.05/1.43 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.05/1.43 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.05/1.43 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.05/1.43 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.05/1.43 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.05/1.43 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.43 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.05/1.43 ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.05/1.43 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.05/1.43 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.05/1.43 , Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.05/1.43 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.05/1.43 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.05/1.43 , X, 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.05/1.43 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.05/1.43 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.05/1.43 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.43 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.05/1.43 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.05/1.43 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.05/1.43 , X, 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.43 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.05/1.43 ), 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.43 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.05/1.43 ), 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.43 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.43 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.05/1.43 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.43 'tc_nat' ) ), =( Y, Z ) ],
% 1.05/1.43 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.05/1.43 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.05/1.43 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.05/1.43 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.05/1.43 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.05/1.43 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.05/1.43 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.05/1.43 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.05/1.43 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.43 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.05/1.43 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.05/1.43 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.05/1.43 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.05/1.43 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.05/1.43 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.05/1.43 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.05/1.43 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.43 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.05/1.43 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.05/1.43 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.43 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.05/1.43 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.05/1.43 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.05/1.43 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.43 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.05/1.43 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.43 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.05/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.05/1.43 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.05/1.43 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.05/1.43 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.05/1.43 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.05/1.43 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.05/1.43 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.05/1.43 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.05/1.43 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.05/1.43 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.43 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.05/1.43 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.43 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.05/1.43 [ 'c_Fun_Oinj__on'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.05/1.43 , 'tc_nat', 'tc_nat', 'tc_nat' ), Y, 'tc_nat', 'tc_nat' ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.43 ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.43 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.05/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.05/1.43 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.05/1.43 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.05/1.43 ,
% 1.05/1.43 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.05/1.43 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.43 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.43 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.43 [ =( 'c_Set_Oimage'( 'c_Suc',
% 1.05/1.43 'c_SetInterval_Oord__class_OatLeastLessThan'( X, Y, 'tc_nat' ), 'tc_nat'
% 1.05/1.43 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc'
% 1.05/1.43 , X ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.05/1.43 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.05/1.43 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.43 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.05/1.44 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.05/1.44 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.05/1.44 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.05/1.44 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.05/1.44 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 X ), X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.05/1.44 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.05/1.44 ) ) ],
% 1.05/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.05/1.44 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.05/1.44 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.05/1.44 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.05/1.44 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.05/1.44 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.05/1.44 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.05/1.44 ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.05/1.44 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.05/1.44 ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.05/1.44 ), Z ) ), T ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.05/1.44 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.05/1.44 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.05/1.44 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.05/1.44 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.05/1.44 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.05/1.44 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.05/1.44 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.05/1.44 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.05/1.44 'tc_nat' ) ), Y ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.05/1.44 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.05/1.44 ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.05/1.44 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.05/1.44 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.05/1.44 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.05/1.44 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.05/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.05/1.44 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.05/1.44 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.05/1.44 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.44 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.05/1.44 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.05/1.44 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.05/1.44 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.05/1.44 , X ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.05/1.44 X ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ), X ) )
% 1.05/1.44 ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.05/1.44 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ =( 'c_Set_Oimage'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.44 X, 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.05/1.44 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, 'tc_nat' ), 'tc_nat',
% 1.05/1.44 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.05/1.44 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.05/1.44 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.05/1.44 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.05/1.44 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.05/1.44 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.05/1.44 , X, Z, U, W, V0 ) ) ],
% 1.05/1.44 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.44 ) ), =( 'c_Finite__Set_Osetsum'( Y,
% 1.05/1.44 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc',
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 1.05/1.44 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), T ), Z, X ) ) ],
% 1.05/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), Z ), T, X ) ) ],
% 1.05/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.05/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.05/1.44 ), Z ), Y ) ],
% 1.05/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.05/1.44 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.05/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.05/1.44 , X ) ), T, X ) ) ],
% 1.05/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.05/1.44 ), Z ), T, X ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.05/1.44 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'(
% 1.05/1.44 Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.05/1.44 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.05/1.44 , Y ), Z ), Z, X ), Y ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.05/1.44 ) ), 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.44 , X ), T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ), T, X ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.05/1.44 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.05/1.44 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.05/1.44 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.05/1.44 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.05/1.44 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.05/1.44 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.05/1.44 ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.05/1.44 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.44 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.05/1.44 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.05/1.44 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.05/1.44 , Y ) ) ],
% 1.05/1.44 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.44 'tc_nat' ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.05/1.44 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.05/1.44 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.05/1.44 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.05/1.44 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.44 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ), 'tc_nat' ) ],
% 1.05/1.44 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.05/1.44 ), 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.05/1.44 ), 'tc_nat' ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.05/1.44 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.05/1.44 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.05/1.44 'c_Int_OPls' ), X ), X ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ),
% 1.05/1.44 'c_Int_OPls' ), X ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.05/1.44 'c_Int_OBit0'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit0'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.05/1.44 [ =( 'c_Int_OBit0'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_Int_Oint' ), X ), X ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.05/1.44 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.05/1.44 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.05/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.05/1.44 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.05/1.44 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.05/1.44 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.05/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.05/1.44 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.05/1.44 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.05/1.44 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.05/1.44 ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.05/1.44 , Z ), Y ), 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.05/1.44 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.05/1.44 ],
% 1.05/1.44 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.05/1.44 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.05/1.44 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.05/1.44 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.05/1.44 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.05/1.44 ) ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.44 X, T, 'tc_nat' ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.05/1.44 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), X ), Y ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.05/1.44 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), X ), Y ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.05/1.44 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.05/1.44 'c_Suc', Y ) ) ) ],
% 1.05/1.44 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.05/1.44 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.44 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.05/1.44 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.05/1.44 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.05/1.44 'tc_nat' ) ) ) ],
% 1.05/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.05/1.44 'tc_nat' ) ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.05/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.05/1.44 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.05/1.44 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.05/1.44 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.05/1.44 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.05/1.44 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.05/1.44 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.05/1.44 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.05/1.44 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.05/1.44 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.05/1.44 ), X ), Z ), 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.44 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.05/1.44 , hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'(
% 1.05/1.44 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.05/1.44 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.05/1.44 ) ) ), 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', T ), Z, 'tc_nat' ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.05/1.44 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.05/1.44 'tc_nat' ) ), Y ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.05/1.44 'tc_nat' ) ), Y ) ],
% 1.05/1.44 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.05/1.44 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.44 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'(
% 1.05/1.44 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.05/1.44 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.05/1.44 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.05/1.44 ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.05/1.44 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.05/1.44 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.05/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.44 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'(
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ), 'tc_nat', X
% 1.05/1.44 ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.05/1.44 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.05/1.44 , U, 'tc_nat' ), 'tc_nat', X ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_Int_OPls'
% 1.05/1.44 ) ), Y ), X ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.05/1.44 ) ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ),
% 1.05/1.44 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.05/1.44 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), Y ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.05/1.44 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.05/1.44 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.05/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.05/1.44 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.05/1.44 ) ],
% 1.05/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.05/1.44 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.05/1.44 [ 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), X, 'tc_nat', 'tc_nat' ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.05/1.44 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.05/1.44 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.05/1.44 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.05/1.44 ), Y ), Y ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.05/1.44 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.05/1.44 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.05/1.44 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.05/1.44 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.05/1.44 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.05/1.44 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.05/1.44 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.05/1.44 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.05/1.44 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.05/1.44 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.05/1.44 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.05/1.44 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ),
% 1.05/1.44 'c_HOL_Ominus__class_Ominus'( 'c_Finite__Set_Osetsum'( Y,
% 1.05/1.44 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), Z )
% 1.05/1.44 , 'tc_nat' ), 'tc_nat', X ), 'c_Finite__Set_Osetsum'( Y,
% 1.05/1.44 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ), X ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.05/1.44 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.05/1.44 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.05/1.44 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.05/1.44 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.05/1.44 ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.05/1.44 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.05/1.44 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.05/1.44 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.05/1.44 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.05/1.44 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.05/1.44 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.05/1.44 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.05/1.44 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.05/1.44 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.05/1.44 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.05/1.44 ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.05/1.44 ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.05/1.44 ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.44 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.05/1.44 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.05/1.44 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.05/1.44 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.05/1.44 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.05/1.44 [ =( 'c_Set_Oimage'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.44 X, 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.05/1.44 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, 'tc_nat' ), 'tc_nat'
% 1.05/1.44 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.05/1.44 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.05/1.44 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.05/1.44 Y ) ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.05/1.44 , Z ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.05/1.44 , Z ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.44 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.05/1.44 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.44 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.05/1.44 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.05/1.44 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.05/1.44 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.05/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.44 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.05/1.44 ) ), Z ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.05/1.44 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.05/1.44 [ =( 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W ),
% 1.05/1.44 'c_Set_Oimage'( 'c_COMBB'( X, Y, U, W, T ), Z, T, W ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.44 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.44 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ), 'tc_nat', X
% 1.05/1.44 ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.05/1.44 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.05/1.44 Z, U, 'tc_nat' ), 'tc_nat', X ) ) ],
% 1.05/1.44 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.05/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.05/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.05/1.44 ) ) ],
% 1.05/1.44 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.05/1.44 ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.05/1.44 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.05/1.44 ) ],
% 1.05/1.44 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OPls', X ) ), Y ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.05/1.44 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.05/1.44 X ), Z, T, X ) ) ],
% 1.05/1.44 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.05/1.44 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.05/1.44 X ), Z, T, X ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.44 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ) ), Y ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ) ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.44 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), 'tc_nat', X
% 1.05/1.44 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'(
% 1.05/1.44 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T,
% 1.05/1.44 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', X, 'tc_nat' ),
% 1.05/1.44 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.05/1.44 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ) ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.05/1.44 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.44 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.44 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.44 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.44 ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.44 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.05/1.44 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.44 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.05/1.44 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.05/1.44 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.05/1.44 , Y ) ],
% 1.05/1.44 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.05/1.44 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.05/1.44 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.05/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.44 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.05/1.44 ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.44 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.05/1.44 ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.05/1.44 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.05/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), Y ), Z ) ), T ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), Y ), Z ) ), T ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.05/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.05/1.44 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.05/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.05/1.44 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.05/1.44 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.05/1.44 , X ) ), T ) ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.05/1.44 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.44 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.05/1.44 ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.44 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.05/1.44 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat', X )
% 1.05/1.44 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( Y,
% 1.05/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( Y,
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( Y,
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.44 'tc_nat' ), X ), X ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.44 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.05/1.44 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.05/1.44 , Y ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.05/1.44 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.05/1.44 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.44 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.05/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.05/1.44 Y ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ],
% 1.05/1.44 [ ~( =( 'c_Finite__Set_Osetsum'( 'v_f',
% 1.05/1.44 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_n' ), 'tc_nat' ), 'tc_nat', 't_a' ),
% 1.05/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ), 'c_Finite__Set_Osetsum'(
% 1.05/1.44 'v_f', 'c_Set_Oimage'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.05/1.44 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.44 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'tc_nat', 't_a' ) )
% 1.05/1.44 , 'c_Finite__Set_Osetsum'( 'v_f', 'c_Set_Oimage'( 'c_COMBC'( 'c_COMBB'(
% 1.05/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.05/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.05/1.44 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.05/1.44 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.05/1.44 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.05/1.44 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.05/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat',
% 1.05/1.44 'tc_nat' ), 'tc_nat', 't_a' ) ) ) ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.05/1.44 'class_OrderedGroup_Oab__semigroup__add'( X ) ],
% 1.05/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.05/1.44 'class_OrderedGroup_Omonoid__add'( X ) ],
% 1.05/1.44 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.05/1.44 'class_Orderings_Opreorder'( Y ) ) ],
% 1.05/1.44 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.05/1.44 'class_Orderings_Oorder'( Y ) ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.05/1.44 ],
% 1.05/1.44 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.05/1.44 ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.05/1.44 ],
% 1.05/1.44 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.05/1.44 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.05/1.44 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.05/1.44 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.05/1.44 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.05/1.44 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.05/1.44 ],
% 1.05/1.44 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.05/1.44 ,
% 1.05/1.44 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.05/1.44 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.33/1.72 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.33/1.72 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.33/1.72 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.33/1.72 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.33/1.72 ,
% 1.33/1.72 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.33/1.72 ,
% 1.33/1.72 [ 'c_fequal'( X, X, Y ) ],
% 1.33/1.72 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.33/1.72 ] .
% 1.33/1.72
% 1.33/1.72
% 1.33/1.72 percentage equality = 0.386537, percentage horn = 0.891654
% 1.33/1.72 This is a problem with some equality
% 1.33/1.72
% 1.33/1.72
% 1.33/1.72
% 1.33/1.72 Options Used:
% 1.33/1.72
% 1.33/1.72 useres = 1
% 1.33/1.72 useparamod = 1
% 1.33/1.72 useeqrefl = 1
% 1.33/1.72 useeqfact = 1
% 1.33/1.72 usefactor = 1
% 1.33/1.72 usesimpsplitting = 0
% 1.33/1.72 usesimpdemod = 5
% 1.33/1.72 usesimpres = 3
% 1.33/1.72
% 1.33/1.72 resimpinuse = 1000
% 1.33/1.72 resimpclauses = 20000
% 1.33/1.72 substype = eqrewr
% 1.33/1.72 backwardsubs = 1
% 1.33/1.72 selectoldest = 5
% 1.33/1.72
% 1.33/1.72 litorderings [0] = split
% 1.33/1.72 litorderings [1] = extend the termordering, first sorting on arguments
% 1.33/1.72
% 1.33/1.72 termordering = kbo
% 1.33/1.72
% 1.33/1.72 litapriori = 0
% 1.33/1.72 termapriori = 1
% 1.33/1.72 litaposteriori = 0
% 1.33/1.72 termaposteriori = 0
% 1.33/1.72 demodaposteriori = 0
% 1.33/1.72 ordereqreflfact = 0
% 1.33/1.72
% 1.33/1.72 litselect = negord
% 1.33/1.72
% 1.33/1.72 maxweight = 15
% 1.33/1.72 maxdepth = 30000
% 1.33/1.72 maxlength = 115
% 1.33/1.72 maxnrvars = 195
% 1.33/1.72 excuselevel = 1
% 1.33/1.72 increasemaxweight = 1
% 1.33/1.72
% 1.33/1.72 maxselected = 10000000
% 1.33/1.72 maxnrclauses = 10000000
% 1.33/1.72
% 1.33/1.72 showgenerated = 0
% 1.33/1.72 showkept = 0
% 1.33/1.72 showselected = 0
% 1.33/1.72 showdeleted = 0
% 1.33/1.72 showresimp = 1
% 1.33/1.72 showstatus = 2000
% 1.33/1.72
% 1.33/1.72 prologoutput = 1
% 1.33/1.72 nrgoals = 5000000
% 1.33/1.72 totalproof = 1
% 1.33/1.72
% 1.33/1.72 Symbols occurring in the translation:
% 1.33/1.72
% 1.33/1.72 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.33/1.72 . [1, 2] (w:1, o:132, a:1, s:1, b:0),
% 1.33/1.72 ! [4, 1] (w:0, o:75, a:1, s:1, b:0),
% 1.33/1.72 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.33/1.72 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.33/1.72 'class_Divides_Oring__div' [40, 1] (w:1, o:80, a:1, s:1, b:0),
% 1.33/1.72 'c_Divides_Odiv__class_Omod' [43, 3] (w:1, o:161, a:1, s:1, b:0),
% 1.33/1.72 'c_HOL_Ominus__class_Ominus' [47, 3] (w:1, o:162, a:1, s:1, b:0),
% 1.33/1.72 'class_Orderings_Opreorder' [48, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.33/1.72 'c_HOL_Oord__class_Oless' [50, 3] (w:1, o:163, a:1, s:1, b:0),
% 1.33/1.72 'tc_nat' [51, 0] (w:1, o:19, a:1, s:1, b:0),
% 1.33/1.72 'class_Orderings_Oorder' [53, 1] (w:1, o:81, a:1, s:1, b:0),
% 1.33/1.72 'class_Orderings_Olinorder' [54, 1] (w:1, o:83, a:1, s:1, b:0),
% 1.33/1.72 'c_Suc' [56, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.33/1.72 'c_HOL_Ozero__class_Ozero' [57, 1] (w:1, o:84, a:1, s:1, b:0),
% 1.33/1.72 hAPP [58, 2] (w:1, o:157, a:1, s:1, b:0),
% 1.33/1.72 'class_Ring__and__Field_Oordered__semidom' [59, 1] (w:1, o:88, a:1
% 1.33/1.72 , s:1, b:0),
% 1.33/1.72 'c_Power_Opower__class_Opower' [60, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.33/1.72 'class_Divides_Osemiring__div' [64, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.33/1.72 'c_Divides_Odiv__class_Odiv' [65, 3] (w:1, o:164, a:1, s:1, b:0),
% 1.33/1.72 'c_Power_Opower_Opower' [68, 3] (w:1, o:165, a:1, s:1, b:0),
% 1.33/1.72 'tc_Int_Oint' [69, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.33/1.72 'c_HOL_Oplus__class_Oplus' [70, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.33/1.72 'c_HOL_Otimes__class_Otimes' [73, 1] (w:1, o:93, a:1, s:1, b:0),
% 1.33/1.72 'c_HOL_Oone__class_Oone' [75, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.33/1.72 'c_Parity_Oeven__odd__class_Oeven' [77, 2] (w:1, o:158, a:1, s:1, b:0
% 1.33/1.72 ),
% 1.33/1.72 'class_Ring__and__Field_Oordered__idom' [78, 1] (w:1, o:94, a:1, s:1
% 1.33/1.72 , b:0),
% 1.33/1.72 'c_Groebner__Basis_Ogb__semiring' [85, 6] (w:1, o:174, a:1, s:1, b:0)
% 1.33/1.72 ,
% 1.33/1.72 'c_Int_Onumber__class_Onumber__of' [91, 2] (w:1, o:159, a:1, s:1, b:0
% 1.33/1.72 ),
% 1.33/1.72 'class_OrderedGroup_Opordered__ab__group__add' [92, 1] (w:1, o:95, a:
% 1.33/1.72 1, s:1, b:0),
% 1.33/1.72 'class_Ring__and__Field_Ocomm__semiring__1' [97, 1] (w:1, o:96, a:1
% 1.33/1.72 , s:1, b:0),
% 1.33/1.72 'c_SetInterval_Oord__class_OatLeastLessThan' [100, 3] (w:1, o:166, a:
% 1.33/1.72 1, s:1, b:0),
% 1.33/1.72 'c_SetInterval_Oord__class_OatLeastAtMost' [101, 3] (w:1, o:167, a:1
% 1.33/1.72 , s:1, b:0),
% 1.33/1.72 'class_OrderedGroup_Ocomm__monoid__add' [102, 1] (w:1, o:97, a:1, s:1
% 1.33/1.72 , b:0),
% 1.33/1.72 'c_Finite__Set_Osetsum' [104, 4] (w:1, o:169, a:1, s:1, b:0),
% 1.33/1.72 hBOOL [107, 1] (w:1, o:98, a:1, s:1, b:0),
% 1.33/1.72 'class_Ring__and__Field_Oordered__ring__strict' [108, 1] (w:1, o:87
% 8.66/9.02 , a:1, s:1, b:0),
% 8.66/9.02 'class_Ring__and__Field_Oordered__semiring__strict' [109, 1] (w:1, o:
% 8.66/9.02 99, a:1, s:1, b:0),
% 8.66/9.02 'class_Ring__and__Field_Oordered__comm__semiring__strict' [110, 1]
% 8.66/9.02 (w:1, o:100, a:1, s:1, b:0),
% 8.66/9.02 'class_OrderedGroup_Opordered__comm__monoid__add' [111, 1] (w:1, o:
% 8.66/9.02 101, a:1, s:1, b:0),
% 8.66/9.02 'class_OrderedGroup_Olordered__ab__group__add' [112, 1] (w:1, o:102
% 8.66/9.02 , a:1, s:1, b:0),
% 8.66/9.02 'class_RealVector_Oreal__normed__algebra' [113, 1] (w:1, o:103, a:1
% 8.66/9.02 , s:1, b:0),
% 8.66/9.02 'class_Ring__and__Field_Oring' [114, 1] (w:1, o:104, a:1, s:1, b:0),
% 8.66/9.02
% 8.66/9.02 'class_Ring__and__Field_Ozero__neq__one' [116, 1] (w:1, o:105, a:1
% 8.66/9.02 , s:1, b:0),
% 8.66/9.02 'class_Ring__and__Field_Ono__zero__divisors' [117, 1] (w:1, o:86, a:1
% 8.66/9.02 , s:1, b:0),
% 8.66/9.02 'class_Ring__and__Field_Omult__zero' [118, 1] (w:1, o:85, a:1, s:1
% 8.66/9.02 , b:0),
% 8.66/9.02 'class_Power_Opower' [119, 1] (w:1, o:118, a:1, s:1, b:0),
% 8.66/9.02 'class_Ring__and__Field_Osemiring__0' [120, 1] (w:1, o:121, a:1, s:1
% 8.66/9.02 , b:0),
% 8.66/9.02 'class_Int_Onumber' [121, 1] (w:1, o:122, a:1, s:1, b:0),
% 8.66/9.02 'class_Int_Onumber__ring' [123, 1] (w:1, o:123, a:1, s:1, b:0),
% 8.66/9.02 'class_OrderedGroup_Omonoid__mult' [124, 1] (w:1, o:106, a:1, s:1, b:
% 8.66/9.02 0),
% 8.66/9.02 'c_Int_OPls' [126, 0] (w:1, o:56, a:1, s:1, b:0),
% 8.66/9.02 'c_Int_OBit1' [127, 1] (w:1, o:125, a:1, s:1, b:0),
% 8.66/9.02 'c_Int_OBit0' [128, 1] (w:1, o:124, a:1, s:1, b:0),
% 8.66/9.02 'c_Set_Oimage' [129, 4] (w:1, o:170, a:1, s:1, b:0),
% 8.66/9.02 'c_Fun_Oinj__on' [130, 4] (w:1, o:171, a:1, s:1, b:0),
% 8.66/9.02 'class_OrderedGroup_Oab__group__add' [134, 1] (w:1, o:107, a:1, s:1
% 8.66/9.02 , b:0),
% 8.66/9.02 'class_Ring__and__Field_Oring__1__no__zero__divisors' [136, 1] (w:1
% 8.66/9.02 , o:119, a:1, s:1, b:0),
% 8.66/9.02 'class_OrderedGroup_Ogroup__add' [137, 1] (w:1, o:108, a:1, s:1, b:0)
% 8.66/9.02 ,
% 8.66/9.02 'class_Ring__and__Field_Oidom' [138, 1] (w:1, o:126, a:1, s:1, b:0),
% 8.66/9.02
% 8.66/9.02 'class_OrderedGroup_Ocomm__monoid__mult' [139, 1] (w:1, o:109, a:1
% 8.66/9.02 , s:1, b:0),
% 8.66/9.02 'class_Ring__and__Field_Opordered__ring' [141, 1] (w:1, o:127, a:1
% 8.66/9.02 , s:1, b:0),
% 8.66/9.02 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [142, 1]
% 8.66/9.02 (w:1, o:110, a:1, s:1, b:0),
% 8.66/9.02 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [143, 1]
% 8.66/9.02 (w:1, o:111, a:1, s:1, b:0),
% 8.66/9.02 'c_COMBC' [145, 5] (w:1, o:173, a:1, s:1, b:0),
% 8.66/9.02 'c_COMBB' [146, 5] (w:1, o:172, a:1, s:1, b:0),
% 8.66/9.02 'class_Ring__and__Field_Osemiring__1' [147, 1] (w:1, o:128, a:1, s:1
% 8.66/9.02 , b:0),
% 8.66/9.02 'class_Ring__and__Field_Ocomm__semiring' [149, 1] (w:1, o:129, a:1
% 8.66/9.02 , s:1, b:0),
% 8.66/9.02 'class_OrderedGroup_Ocancel__ab__semigroup__add' [150, 1] (w:1, o:112
% 8.66/9.02 , a:1, s:1, b:0),
% 8.66/9.02 'class_OrderedGroup_Ocancel__semigroup__add' [151, 1] (w:1, o:113, a:
% 8.66/9.02 1, s:1, b:0),
% 8.66/9.02 'class_Ring__and__Field_Oring__no__zero__divisors' [154, 1] (w:1, o:
% 8.66/9.02 120, a:1, s:1, b:0),
% 8.66/9.02 'class_Ring__and__Field_Osemiring' [155, 1] (w:1, o:130, a:1, s:1, b:
% 8.66/9.02 0),
% 8.66/9.02 'class_OrderedGroup_Oab__semigroup__mult' [157, 1] (w:1, o:114, a:1
% 8.66/9.02 , s:1, b:0),
% 8.66/9.02 'tc_fun' [158, 2] (w:1, o:160, a:1, s:1, b:0),
% 8.66/9.02 'class_OrderedGroup_Oab__semigroup__idem__mult' [159, 1] (w:1, o:115
% 8.66/9.02 , a:1, s:1, b:0),
% 8.66/9.02 'class_OrderedGroup_Oab__semigroup__add' [160, 1] (w:1, o:116, a:1
% 8.66/9.02 , s:1, b:0),
% 8.66/9.02 'class_Int_Oring__char__0' [163, 1] (w:1, o:131, a:1, s:1, b:0),
% 8.66/9.02 'class_OrderedGroup_Omonoid__add' [164, 1] (w:1, o:117, a:1, s:1, b:0
% 8.66/9.02 ),
% 8.66/9.02 't_a' [165, 0] (w:1, o:66, a:1, s:1, b:0),
% 8.66/9.02 'v_f' [166, 0] (w:1, o:67, a:1, s:1, b:0),
% 8.66/9.02 'v_n' [167, 0] (w:1, o:68, a:1, s:1, b:0),
% 8.66/9.02 'tc_bool' [171, 0] (w:1, o:72, a:1, s:1, b:0),
% 8.66/9.02 'c_fequal' [172, 3] (w:1, o:168, a:1, s:1, b:0).
% 8.66/9.02
% 8.66/9.02
% 8.66/9.02 Starting Search:
% 8.66/9.02
% 8.66/9.02 Resimplifying inuse:
% 8.66/9.02 Done
% 8.66/9.02
% 8.66/9.02
% 8.66/9.02 Intermediate Status:
% 8.66/9.02 Generated: 4691
% 8.66/9.02 Kept: 2001
% 8.66/9.02 Inuse: 152
% 8.66/9.02 Deleted: 4
% 8.66/9.02 Deletedinuse: 0
% 8.66/9.02
% 8.66/9.02 Resimplifying inuse:
% 8.66/9.02 Done
% 8.66/9.02
% 8.66/9.02 Resimplifying inuse:
% 8.66/9.02 Done
% 8.66/9.02
% 8.66/9.02
% 8.66/9.02 Intermediate Status:
% 8.66/9.02 Generated: 11714
% 8.66/9.02 Kept: 4203
% 8.66/9.02 Inuse: 222
% 8.66/9.02 Deleted: 4
% 8.66/9.02 Deletedinuse: 0
% 8.66/9.02
% 8.66/9.02 Resimplifying inuse:
% 8.66/9.02 Done
% 8.66/9.02
% 8.66/9.02 Resimplifying inuse:
% 8.66/9.02 Done
% 8.66/9.02
% 8.66/9.02
% 8.66/9.02 Intermediate Status:
% 8.66/9.02 Generated: 16423
% 27.25/27.63 Kept: 6283
% 27.25/27.63 Inuse: 301
% 27.25/27.63 Deleted: 10
% 27.25/27.63 Deletedinuse: 0
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 24616
% 27.25/27.63 Kept: 8372
% 27.25/27.63 Inuse: 349
% 27.25/27.63 Deleted: 13
% 27.25/27.63 Deletedinuse: 1
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 31493
% 27.25/27.63 Kept: 10448
% 27.25/27.63 Inuse: 422
% 27.25/27.63 Deleted: 16
% 27.25/27.63 Deletedinuse: 2
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 38878
% 27.25/27.63 Kept: 12943
% 27.25/27.63 Inuse: 469
% 27.25/27.63 Deleted: 17
% 27.25/27.63 Deletedinuse: 3
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 45080
% 27.25/27.63 Kept: 14945
% 27.25/27.63 Inuse: 500
% 27.25/27.63 Deleted: 17
% 27.25/27.63 Deletedinuse: 3
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 52000
% 27.25/27.63 Kept: 17094
% 27.25/27.63 Inuse: 527
% 27.25/27.63 Deleted: 17
% 27.25/27.63 Deletedinuse: 3
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 58406
% 27.25/27.63 Kept: 19126
% 27.25/27.63 Inuse: 567
% 27.25/27.63 Deleted: 18
% 27.25/27.63 Deletedinuse: 4
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying clauses:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 66668
% 27.25/27.63 Kept: 21222
% 27.25/27.63 Inuse: 622
% 27.25/27.63 Deleted: 1068
% 27.25/27.63 Deletedinuse: 4
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 74551
% 27.25/27.63 Kept: 23427
% 27.25/27.63 Inuse: 667
% 27.25/27.63 Deleted: 1068
% 27.25/27.63 Deletedinuse: 4
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 82563
% 27.25/27.63 Kept: 25432
% 27.25/27.63 Inuse: 679
% 27.25/27.63 Deleted: 1068
% 27.25/27.63 Deletedinuse: 4
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 90308
% 27.25/27.63 Kept: 27529
% 27.25/27.63 Inuse: 712
% 27.25/27.63 Deleted: 1068
% 27.25/27.63 Deletedinuse: 4
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 100840
% 27.25/27.63 Kept: 30315
% 27.25/27.63 Inuse: 737
% 27.25/27.63 Deleted: 1068
% 27.25/27.63 Deletedinuse: 4
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 108554
% 27.25/27.63 Kept: 32491
% 27.25/27.63 Inuse: 782
% 27.25/27.63 Deleted: 1068
% 27.25/27.63 Deletedinuse: 4
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 116164
% 27.25/27.63 Kept: 34561
% 27.25/27.63 Inuse: 817
% 27.25/27.63 Deleted: 1068
% 27.25/27.63 Deletedinuse: 4
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 124145
% 27.25/27.63 Kept: 36565
% 27.25/27.63 Inuse: 845
% 27.25/27.63 Deleted: 1068
% 27.25/27.63 Deletedinuse: 4
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 132063
% 27.25/27.63 Kept: 38607
% 27.25/27.63 Inuse: 877
% 27.25/27.63 Deleted: 1068
% 27.25/27.63 Deletedinuse: 4
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying clauses:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 147497
% 27.25/27.63 Kept: 43324
% 27.25/27.63 Inuse: 922
% 27.25/27.63 Deleted: 1493
% 27.25/27.63 Deletedinuse: 5
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 154730
% 27.25/27.63 Kept: 46420
% 27.25/27.63 Inuse: 927
% 27.25/27.63 Deleted: 1493
% 27.25/27.63 Deletedinuse: 5
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 162786
% 27.25/27.63 Kept: 48428
% 27.25/27.63 Inuse: 940
% 27.25/27.63 Deleted: 1493
% 27.25/27.63 Deletedinuse: 5
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 171670
% 27.25/27.63 Kept: 50769
% 27.25/27.63 Inuse: 972
% 27.25/27.63 Deleted: 1493
% 27.25/27.63 Deletedinuse: 5
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 177770
% 27.25/27.63 Kept: 52842
% 27.25/27.63 Inuse: 1002
% 27.25/27.63 Deleted: 1493
% 27.25/27.63 Deletedinuse: 5
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 182695
% 27.25/27.63 Kept: 55040
% 27.25/27.63 Inuse: 1017
% 27.25/27.63 Deleted: 1493
% 27.25/27.63 Deletedinuse: 5
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 188119
% 27.25/27.63 Kept: 57106
% 27.25/27.63 Inuse: 1047
% 27.25/27.63 Deleted: 1493
% 27.25/27.63 Deletedinuse: 5
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 197998
% 27.25/27.63 Kept: 59941
% 27.25/27.63 Inuse: 1054
% 27.25/27.63 Deleted: 1493
% 27.25/27.63 Deletedinuse: 5
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying clauses:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63 Resimplifying inuse:
% 27.25/27.63 Done
% 27.25/27.63
% 27.25/27.63
% 27.25/27.63 Intermediate Status:
% 27.25/27.63 Generated: 215906
% 27.25/27.63 Kept: 64620
% 27.25/27.63 Inuse: 1073
% 27.25/27.63 Deleted: 1592
% 160.40/160.92 Deletedinuse: 5
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 223717
% 160.40/160.92 Kept: 66665
% 160.40/160.92 Inuse: 1102
% 160.40/160.92 Deleted: 1593
% 160.40/160.92 Deletedinuse: 6
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 240006
% 160.40/160.92 Kept: 69120
% 160.40/160.92 Inuse: 1130
% 160.40/160.92 Deleted: 1597
% 160.40/160.92 Deletedinuse: 8
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 247929
% 160.40/160.92 Kept: 71139
% 160.40/160.92 Inuse: 1159
% 160.40/160.92 Deleted: 1597
% 160.40/160.92 Deletedinuse: 8
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 257301
% 160.40/160.92 Kept: 73494
% 160.40/160.92 Inuse: 1180
% 160.40/160.92 Deleted: 1597
% 160.40/160.92 Deletedinuse: 8
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 264324
% 160.40/160.92 Kept: 75503
% 160.40/160.92 Inuse: 1190
% 160.40/160.92 Deleted: 1597
% 160.40/160.92 Deletedinuse: 8
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 276011
% 160.40/160.92 Kept: 78480
% 160.40/160.92 Inuse: 1200
% 160.40/160.92 Deleted: 1597
% 160.40/160.92 Deletedinuse: 8
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 289978
% 160.40/160.92 Kept: 81740
% 160.40/160.92 Inuse: 1210
% 160.40/160.92 Deleted: 1597
% 160.40/160.92 Deletedinuse: 8
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying clauses:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 298223
% 160.40/160.92 Kept: 83791
% 160.40/160.92 Inuse: 1240
% 160.40/160.92 Deleted: 2007
% 160.40/160.92 Deletedinuse: 8
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 308193
% 160.40/160.92 Kept: 85902
% 160.40/160.92 Inuse: 1285
% 160.40/160.92 Deleted: 2007
% 160.40/160.92 Deletedinuse: 8
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 315209
% 160.40/160.92 Kept: 87916
% 160.40/160.92 Inuse: 1313
% 160.40/160.92 Deleted: 2009
% 160.40/160.92 Deletedinuse: 9
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 324740
% 160.40/160.92 Kept: 92245
% 160.40/160.92 Inuse: 1334
% 160.40/160.92 Deleted: 2010
% 160.40/160.92 Deletedinuse: 10
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 332376
% 160.40/160.92 Kept: 94314
% 160.40/160.92 Inuse: 1344
% 160.40/160.92 Deleted: 2010
% 160.40/160.92 Deletedinuse: 10
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 343815
% 160.40/160.92 Kept: 96316
% 160.40/160.92 Inuse: 1383
% 160.40/160.92 Deleted: 2029
% 160.40/160.92 Deletedinuse: 29
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 353501
% 160.40/160.92 Kept: 98330
% 160.40/160.92 Inuse: 1415
% 160.40/160.92 Deleted: 2029
% 160.40/160.92 Deletedinuse: 29
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 361983
% 160.40/160.92 Kept: 100335
% 160.40/160.92 Inuse: 1439
% 160.40/160.92 Deleted: 2029
% 160.40/160.92 Deletedinuse: 29
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 380862
% 160.40/160.92 Kept: 104681
% 160.40/160.92 Inuse: 1458
% 160.40/160.92 Deleted: 2029
% 160.40/160.92 Deletedinuse: 29
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying clauses:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 388084
% 160.40/160.92 Kept: 106683
% 160.40/160.92 Inuse: 1477
% 160.40/160.92 Deleted: 3143
% 160.40/160.92 Deletedinuse: 37
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 394543
% 160.40/160.92 Kept: 108868
% 160.40/160.92 Inuse: 1494
% 160.40/160.92 Deleted: 3143
% 160.40/160.92 Deletedinuse: 37
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 400270
% 160.40/160.92 Kept: 110927
% 160.40/160.92 Inuse: 1509
% 160.40/160.92 Deleted: 3143
% 160.40/160.92 Deletedinuse: 37
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 415727
% 160.40/160.92 Kept: 113138
% 160.40/160.92 Inuse: 1519
% 160.40/160.92 Deleted: 3143
% 160.40/160.92 Deletedinuse: 37
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 422981
% 160.40/160.92 Kept: 115403
% 160.40/160.92 Inuse: 1539
% 160.40/160.92 Deleted: 3143
% 160.40/160.92 Deletedinuse: 37
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 430904
% 160.40/160.92 Kept: 117758
% 160.40/160.92 Inuse: 1564
% 160.40/160.92 Deleted: 3143
% 160.40/160.92 Deletedinuse: 37
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 438450
% 160.40/160.92 Kept: 119973
% 160.40/160.92 Inuse: 1584
% 160.40/160.92 Deleted: 3144
% 160.40/160.92 Deletedinuse: 38
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92
% 160.40/160.92 Intermediate Status:
% 160.40/160.92 Generated: 448556
% 160.40/160.92 Kept: 122004
% 160.40/160.92 Inuse: 1619
% 160.40/160.92 Deleted: 3144
% 160.40/160.92 Deletedinuse: 38
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 Done
% 160.40/160.92
% 160.40/160.92 Resimplifying inuse:
% 160.40/160.92 DCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------