TSTP Solution File: SWV678-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV678-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:27:43 EDT 2022
% Result : Unsatisfiable 133.06s 133.47s
% Output : Refutation 133.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SWV678-1 : TPTP v8.1.0. Released v4.1.0.
% 0.05/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Wed Jun 15 17:30:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.94/1.30 *** allocated 10000 integers for termspace/termends
% 0.94/1.30 *** allocated 10000 integers for clauses
% 0.94/1.30 *** allocated 10000 integers for justifications
% 0.94/1.30 *** allocated 15000 integers for termspace/termends
% 0.94/1.30 Bliksem 1.12
% 0.94/1.30
% 0.94/1.30
% 0.94/1.30 Automatic Strategy Selection
% 0.94/1.30
% 0.94/1.30 Clauses:
% 0.94/1.30 [
% 0.94/1.30 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.94/1.30 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.30 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.30 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.30 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.94/1.30 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.94/1.30 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.30 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.94/1.30 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.30 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.94/1.30 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.30 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.30 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 0.94/1.30 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.94/1.30 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.30 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 0.94/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.30 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.30 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.94/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.30 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.30 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.30 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.30 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.94/1.30 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.30 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.94/1.30 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.30 'c_Suc'( X ), 'tc_nat' ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.30 'c_Suc'( X ), 'tc_nat' ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.30 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.30 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.30 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.94/1.30 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.94/1.30 , Y, X ) ) ],
% 0.94/1.30 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.30 'tc_nat' ), Y, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 0.94/1.30 ,
% 0.94/1.30 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.30 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 0.94/1.30 ,
% 0.94/1.30 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.94/1.30 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 0.94/1.30 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.94/1.30 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.30 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.30 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.94/1.30 ,
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.30 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.30 , X ) ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.94/1.30 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.94/1.30 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.30 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 0.94/1.30 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 0.94/1.30 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.30 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.30 ,
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.30 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.30 ,
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.30 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.94/1.30 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.30 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.30 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.30 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.94/1.30 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.30 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 0.94/1.30 ,
% 0.94/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.30 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.30 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.94/1.30 , T, X ), X ), T, X ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.94/1.30 ,
% 0.94/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.94/1.30 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.94/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.94/1.30 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.94/1.30 ,
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.30 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 0.94/1.30 ), X ), Y ) ],
% 0.94/1.30 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.94/1.30 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 0.94/1.30 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 0.94/1.30 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.30 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.30 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.94/1.30 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.30 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.94/1.30 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.94/1.30 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.30 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.94/1.30 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.30 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.94/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.30 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 0.94/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.30 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.30 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.94/1.30 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.94/1.30 ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.94/1.30 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.94/1.30 ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.94/1.30 Y, 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.94/1.30 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.94/1.30 ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.94/1.30 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.94/1.30 ],
% 0.94/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.94/1.30 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.94/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.94/1.30 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.94/1.30 ,
% 0.94/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.94/1.30 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.94/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.94/1.30 , T, X ), X ) ) ],
% 0.94/1.30 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 0.94/1.30 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.30 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.30 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.94/1.30 'c_GCD_Ogcd__class_Ogcd'( Y, 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 0.94/1.30 ), 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.94/1.30 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.94/1.30 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.94/1.30 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.30 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.94/1.30 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.30 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.94/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.94/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.30 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.30 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.30 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.30 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.94/1.30 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 0.94/1.30 ,
% 0.94/1.30 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 0.94/1.30 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.30 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.94/1.30 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.30 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.94/1.30 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.94/1.30 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 0.94/1.30 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.30 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.94/1.30 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.30 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.94/1.30 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.30 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.94/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.94/1.30 ) ],
% 0.94/1.30 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.30 ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.94/1.30 ), =( Z, Y ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 0.94/1.30 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 0.94/1.30 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 0.94/1.30 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 0.94/1.30 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.94/1.30 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.94/1.30 , Z, 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.94/1.30 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 0.94/1.30 , Z, 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 0.94/1.30 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 0.94/1.30 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.30 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) )
% 0.94/1.30 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 0.94/1.30 , 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.94/1.30 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.30 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.30 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.94/1.30 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.94/1.30 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.94/1.30 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.30 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.94/1.30 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.94/1.30 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.94/1.30 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.30 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 0.94/1.30 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.30 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.30 , X ) ) ],
% 0.94/1.30 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.94/1.30 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.30 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.94/1.30 ],
% 0.94/1.30 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.94/1.30 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.30 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.30 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.30 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.30 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.94/1.30 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.30 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.94/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.94/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.30 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 0.94/1.30 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 0.94/1.30 'class_RealVector_Oreal__normed__field'( X ) ), ~( =(
% 0.94/1.30 'c_Transcendental_Oexp'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 0.94/1.30 ,
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.94/1.30 , X ), X ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.94/1.30 , X ), X ) ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.94/1.30 ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.94/1.30 ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.94/1.30 ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.30 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.30 ), X ) ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.94/1.30 ],
% 0.94/1.30 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.94/1.30 ],
% 0.94/1.30 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.30 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.94/1.30 ), 'tc_nat' ), X ) ],
% 0.94/1.30 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.94/1.30 , X, 'tc_nat' ), X ) ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.94/1.30 ],
% 0.94/1.30 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.30 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.94/1.30 ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 0.94/1.30 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.94/1.30 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.94/1.30 'tc_nat' ) ) ],
% 0.94/1.30 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 0.94/1.30 Y, Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.94/1.30 , Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat'
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 0.94/1.30 Y, Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.94/1.30 , Y, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 0.94/1.30 ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 0.94/1.30 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.94/1.30 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.94/1.30 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 0.94/1.30 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.94/1.30 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.94/1.30 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.94/1.30 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.94/1.30 , 'tc_nat' ), X, 'tc_nat' ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.94/1.30 , 'tc_nat' ), X, 'tc_nat' ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.94/1.30 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.94/1.30 , 'tc_nat' ), X, 'tc_nat' ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.94/1.30 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 0.94/1.30 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.94/1.30 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.94/1.30 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 0.94/1.30 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.94/1.30 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.94/1.30 'tc_nat' ) ) ],
% 0.94/1.30 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 0.94/1.31 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.94/1.31 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.94/1.31 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.31 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.94/1.31 ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.31 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.94/1.31 ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.31 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 0.94/1.31 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.31 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.94/1.31 , X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.94/1.31 , X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.31 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.94/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.94/1.31 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.31 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.31 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.94/1.31 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.31 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.31 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.94/1.31 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.31 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.31 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.94/1.31 X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.31 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.31 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.94/1.31 X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.94/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.94/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.94/1.31 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.31 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.94/1.31 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.94/1.31 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.94/1.31 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.31 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.94/1.31 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.31 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.31 X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.31 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 0.94/1.31 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.94/1.31 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 0.94/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.94/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 Z, T, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 0.94/1.31 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 0.94/1.31 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.94/1.31 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.94/1.31 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 0.94/1.31 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 0.94/1.31 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 0.94/1.31 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.31 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 0.94/1.31 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.31 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 0.94/1.31 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 0.94/1.31 ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 0.94/1.31 X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.94/1.31 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.94/1.31 X ), T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 0.94/1.31 X ), T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.94/1.31 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.94/1.31 ) ) ],
% 0.94/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.94/1.31 ) ) ],
% 0.94/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.31 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.94/1.31 , X ), X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 0.94/1.31 , X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 0.94/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 0.94/1.31 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.94/1.31 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 0.94/1.31 , X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 0.94/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.94/1.31 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ 'c_lessequals'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y,
% 0.94/1.31 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X,
% 0.94/1.31 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.94/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.94/1.31 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.94/1.31 X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.94/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 0.94/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.94/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.31 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.94/1.31 X ) ) ), =( Z, T ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.94/1.31 X ) ) ), =( Z, T ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.94/1.31 X ) ) ), =( Y, T ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.94/1.31 , X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 0.94/1.31 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.31 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.94/1.31 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.31 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.94/1.31 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 0.94/1.31 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 0.94/1.31 , X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.31 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.94/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.94/1.31 ), 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.94/1.31 ), 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 0.94/1.31 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.94/1.31 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 0.94/1.31 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.94/1.31 'c_Transcendental_Oexp'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.94/1.31 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.94/1.31 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 0.94/1.31 'c_Suc'( X ), 'tc_nat' ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 0.94/1.31 , X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 0.94/1.31 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.31 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.94/1.31 , 'tc_nat' ), X ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.94/1.31 , 'tc_nat' ), X ) ],
% 0.94/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.94/1.31 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.31 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.94/1.31 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, X, 'tc_nat' ), X ) ],
% 0.94/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.94/1.31 X ) ) ],
% 0.94/1.31 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 X, T, 'tc_nat' ) ],
% 0.94/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.94/1.31 X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.94/1.31 X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 0.94/1.31 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.94/1.31 'c_lessequals'( Z, Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 0.94/1.31 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.31 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.94/1.31 'c_lessequals'( Z, Y, X ) ) ],
% 0.94/1.31 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.94/1.31 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 0.94/1.31 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 0.94/1.31 ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.94/1.31 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.94/1.31 ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 0.94/1.31 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 0.94/1.31 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.31 X ) ) ],
% 0.94/1.31 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.94/1.31 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.94/1.31 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.94/1.31 X ), Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.94/1.31 , T, X ), X ), T, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.31 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.31 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 0.94/1.31 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.31 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.94/1.31 ), Y ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 ) ), =( Y, Z ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 ) ), =( Y, Z ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.94/1.31 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.94/1.31 , U, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.94/1.31 ), Y ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.94/1.31 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 0.94/1.31 Y, X ), Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 0.94/1.31 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.31 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.94/1.31 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.31 ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 0.94/1.31 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 0.94/1.31 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.94/1.31 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.94/1.31 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.94/1.31 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.94/1.31 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 0.94/1.31 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 0.94/1.31 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 0.94/1.31 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 0.94/1.31 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 0.94/1.31 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.94/1.31 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 0.94/1.31 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'tc_nat' ) ],
% 0.94/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.94/1.31 'tc_nat' ) ],
% 0.94/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'tc_nat' ) ],
% 0.94/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'tc_nat' ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.31 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 0.94/1.31 ],
% 0.94/1.31 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.94/1.31 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.94/1.31 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.31 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.31 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.31 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.94/1.31 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.94/1.31 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.94/1.31 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.94/1.31 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 0.94/1.31 ],
% 0.94/1.31 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 0.94/1.31 'tc_nat' ) ],
% 0.94/1.31 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 0.94/1.31 , X, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 0.94/1.31 'tc_nat' ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.94/1.31 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.31 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.94/1.31 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.94/1.31 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.94/1.31 ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 0.94/1.31 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.31 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.31 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.31 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 0.94/1.31 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.94/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.31 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.94/1.31 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.31 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.94/1.31 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.31 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.31 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ), ~( =( 'v_a',
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.94/1.31 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.31 X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.31 X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.31 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.31 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 , X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.31 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.94/1.31 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.94/1.31 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.94/1.31 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.31 ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.94/1.31 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.94/1.31 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.94/1.31 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 0.94/1.31 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.94/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.94/1.31 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 0.94/1.31 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 0.94/1.31 Z, X ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.94/1.31 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ), =( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ), =( X,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.94/1.31 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 0.94/1.31 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z,
% 0.94/1.31 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( Y,
% 0.94/1.31 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 0.94/1.31 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 0.94/1.31 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 0.94/1.31 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 0.94/1.31 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.94/1.31 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.94/1.31 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.94/1.31 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.94/1.31 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.31 'tc_nat' ), 'tc_nat' ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 , X ) ],
% 0.94/1.31 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.31 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.94/1.31 , Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.94/1.31 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.94/1.31 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.94/1.31 , X ) ) ],
% 0.94/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.94/1.31 , Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.94/1.31 , Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.94/1.31 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.31 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.31 , X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 , X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.94/1.31 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.94/1.31 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.94/1.31 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 0.94/1.31 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.31 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.94/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.94/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.31 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.31 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.94/1.31 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.94/1.31 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 0.94/1.31 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 0.94/1.31 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.94/1.31 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.94/1.31 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.94/1.31 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.31 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.94/1.31 X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.31 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 Z, T, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 Z, T, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.31 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.94/1.31 X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.94/1.31 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 Y, T, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 Y, T, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.94/1.31 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.94/1.31 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.94/1.31 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_GCD_Ogcd__class_Ogcd'( Y, 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 0.94/1.31 ), 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.94/1.31 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 0.94/1.31 ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 0.94/1.31 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'( X, Y,
% 0.94/1.31 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.94/1.31 , 'tc_nat' ), Z, 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X
% 0.94/1.31 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' )
% 0.94/1.31 ) ],
% 0.94/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.94/1.31 , 'tc_nat' ), Z, 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y
% 0.94/1.31 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' )
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.94/1.31 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.94/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.94/1.31 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.94/1.31 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.94/1.31 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.31 ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.31 ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.31 ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.31 ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 0.94/1.31 ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.31 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 0.94/1.31 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.94/1.31 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.94/1.31 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 0.94/1.31 ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.94/1.31 ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 0.94/1.31 ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.94/1.31 ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 0.94/1.31 ), Y, X ) ), =( Z, T ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.94/1.31 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 0.94/1.31 ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 0.94/1.31 ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 0.94/1.31 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.94/1.31 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 0.94/1.31 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 0.94/1.31 , X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 0.94/1.31 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 0.94/1.31 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 0.94/1.31 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 0.94/1.31 Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.31 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 0.94/1.31 Y, X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 0.94/1.31 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.94/1.31 'c_Transcendental_Oexp'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_Transcendental_Oexp'( Y, X ),
% 0.94/1.31 'c_Transcendental_Oexp'( Z, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.94/1.31 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.94/1.31 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 0.94/1.31 , Z, X ), T, X ), ~( 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 0.94/1.31 , U, X ), T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 0.94/1.31 , Z, X ), 'c_Power_Opower__class_Opower'( T, U, X ), X ), ~(
% 0.94/1.31 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 0.94/1.31 , Z, X ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 0.94/1.31 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.94/1.31 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 0.94/1.31 , 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_nat' ), X ),
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'( Y, T, X
% 0.94/1.31 ), 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ), ~( 'c_lessequals'(
% 0.94/1.31 T, Z, 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 0.94/1.31 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.94/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.94/1.31 ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.31 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.94/1.31 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.94/1.31 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 0.94/1.31 ), X, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 0.94/1.31 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 0.94/1.31 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.31 Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.94/1.31 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 0.94/1.31 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 0.94/1.31 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 0.94/1.31 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.94/1.31 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 0.94/1.31 , Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.94/1.31 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Z
% 0.94/1.31 , Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 0.94/1.31 'tc_nat' ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 0.94/1.31 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), Y, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ),
% 0.94/1.31 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), X, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ),
% 0.94/1.31 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.94/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.94/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.94/1.31 , X, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z,
% 0.94/1.31 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 0.94/1.31 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 0.94/1.31 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 0.94/1.31 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.31 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 0.94/1.31 , 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.31 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.31 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.94/1.31 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.94/1.31 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 0.94/1.31 , Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 Y, T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 0.94/1.31 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.94/1.31 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 Y, T, X ), X ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.31 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 0.94/1.31 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.31 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 0.94/1.31 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~(
% 0.94/1.31 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 0.94/1.31 'tc_nat' ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 Y, T, X ), X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.94/1.31 'c_lessequals'( Z, Y, X ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.31 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.31 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.94/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 0.94/1.31 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 0.94/1.31 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.94/1.31 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 Y, T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 0.94/1.31 ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 0.94/1.31 ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.94/1.31 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.31 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.31 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.94/1.31 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.94/1.31 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 0.94/1.31 , Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.94/1.31 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.94/1.31 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.31 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.94/1.31 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 Z, T, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 0.94/1.31 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 0.94/1.31 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ],
% 0.94/1.31 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.94/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.94/1.31 ],
% 0.94/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.31 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 0.94/1.31 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.31 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.94/1.31 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.94/1.31 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.94/1.31 , T, X ) ) ), =( Z, T ) ],
% 0.94/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.31 , T, X ) ) ), =( Y, Z ) ],
% 0.94/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 0.94/1.31 'tc_nat' ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.94/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.31 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.94/1.31 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.94/1.31 [ 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ), ~( =( 'v_a',
% 0.94/1.31 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ) ],
% 0.94/1.31 [ 'class_Ring__and__Field_Ofield'( 't_a' ) ],
% 0.94/1.31 [ ~( =( 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'(
% 0.94/1.31 'v_a', 'v_m', 't_a' ), 'c_Power_Opower__class_Opower'( 'v_a', 'v_n',
% 0.94/1.31 't_a' ), 't_a' ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( 't_a' ), 'v_a'
% 0.94/1.31 , 't_a' ), 'c_HOL_Ominus__class_Ominus'( 'v_n', 'v_m', 'tc_nat' ), 't_a'
% 0.94/1.31 ) ) ), 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ],
% 0.94/1.31 [ ~( =( 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'(
% 0.94/1.31 'v_a', 'v_m', 't_a' ), 'c_Power_Opower__class_Opower'( 'v_a', 'v_n',
% 0.94/1.31 't_a' ), 't_a' ), 'c_Power_Opower__class_Opower'( 'v_a',
% 0.94/1.31 'c_HOL_Ominus__class_Ominus'( 'v_m', 'v_n', 'tc_nat' ), 't_a' ) ) ), ~(
% 0.94/1.31 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ) ],
% 0.94/1.31 [ ~( =( 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'(
% 0.94/1.31 'v_a', 'v_m', 't_a' ), 'c_Power_Opower__class_Opower'( 'v_a', 'v_n',
% 0.94/1.31 't_a' ), 't_a' ), 'c_Power_Opower__class_Opower'(
% 0.94/1.31 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( 't_a' ), 'v_a'
% 0.94/1.31 , 't_a' ), 'c_HOL_Ominus__class_Ominus'( 'v_n', 'v_m', 'tc_nat' ), 't_a'
% 0.94/1.31 ) ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'(
% 0.94/1.31 'c_Power_Opower__class_Opower'( 'v_a', 'v_m', 't_a' ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ), 't_a' ),
% 0.94/1.31 'c_Power_Opower__class_Opower'( 'v_a', 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.31 'v_m', 'v_n', 'tc_nat' ), 't_a' ) ) ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_Ring__and__Field_Ono__zero__divisors'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_OrderedGroup_Oab__semigroup__add'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_Ring__and__Field_Odivision__ring'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_OrderedGroup_Ocomm__monoid__add'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_Ring__and__Field_Ozero__neq__one'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_Ring__and__Field_Ocomm__ring__1'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_Ring__and__Field_Osemiring__1'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_Ring__and__Field_Osemiring__0'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_OrderedGroup_Oab__group__add'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_Ring__and__Field_Omult__zero'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_OrderedGroup_Omonoid__mult'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_OrderedGroup_Omonoid__add'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_OrderedGroup_Ogroup__add'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_Ring__and__Field_Oring__1'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.94/1.31 'class_Ring__and__Field_Oidom'( X ) ],
% 0.94/1.31 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), 'class_Power_Opower'( X ) ]
% 0.94/1.31 ,
% 0.94/1.31 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.94/1.31 ],
% 0.94/1.31 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.94/1.31 ) ],
% 0.94/1.31 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.94/1.31 [ 'class_Power_Opower'( 'tc_nat' ) ]
% 0.94/1.31 ] .
% 0.94/1.31
% 0.94/1.31
% 0.94/1.31 percentage equality = 0.196507, percentage horn = 0.868966
% 0.94/1.31 This is a problem with some equality
% 0.94/1.31
% 0.94/1.31
% 0.94/1.31
% 0.94/1.31 Options Used:
% 0.94/1.31
% 0.94/1.31 useres = 1
% 0.94/1.31 useparamod = 1
% 0.94/1.31 useeqrefl = 1
% 0.94/1.31 useeqfact = 1
% 0.94/1.31 usefactor = 1
% 0.94/1.31 usesimpsplitting = 0
% 0.94/1.31 usesimpdemod = 5
% 0.94/1.31 usesimpres = 3
% 0.94/1.31
% 0.94/1.31 resimpinuse = 1000
% 0.94/1.31 resimpclauses = 20000
% 0.94/1.31 substype = eqrewr
% 0.94/1.31 backwardsubs = 1
% 0.94/1.31 selectoldest = 5
% 0.94/1.31
% 0.94/1.31 litorderings [0] = split
% 0.94/1.31 litorderings [1] = extend the termordering, first sorting on arguments
% 0.94/1.31
% 0.94/1.31 termordering = kbo
% 0.94/1.31
% 0.94/1.31 litapriori = 0
% 0.94/1.31 termapriori = 1
% 0.94/1.31 litaposteriori = 0
% 0.94/1.31 termaposteriori = 0
% 0.94/1.31 demodaposteriori = 0
% 0.94/1.31 ordereqreflfact = 0
% 0.94/1.31
% 0.94/1.31 litselect = negord
% 0.94/1.31
% 0.94/1.31 maxweight = 15
% 0.94/1.31 maxdepth = 30000
% 0.94/1.31 maxlength = 115
% 0.94/1.31 maxnrvars = 195
% 0.94/1.31 excuselevel = 1
% 0.94/1.31 increasemaxweight = 1
% 0.94/1.31
% 0.94/1.31 maxselected = 10000000
% 0.94/1.31 maxnrclauses = 10000000
% 0.94/1.31
% 0.94/1.31 showgenerated = 0
% 0.94/1.31 showkept = 0
% 0.94/1.31 showselected = 0
% 0.94/1.31 showdeleted = 0
% 0.94/1.31 showresimp = 1
% 7.18/7.60 showstatus = 2000
% 7.18/7.60
% 7.18/7.60 prologoutput = 1
% 7.18/7.60 nrgoals = 5000000
% 7.18/7.60 totalproof = 1
% 7.18/7.60
% 7.18/7.60 Symbols occurring in the translation:
% 7.18/7.60
% 7.18/7.60 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 7.18/7.60 . [1, 2] (w:1, o:91, a:1, s:1, b:0),
% 7.18/7.60 ! [4, 1] (w:0, o:43, a:1, s:1, b:0),
% 7.18/7.60 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 7.18/7.60 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 7.18/7.60 'class_OrderedGroup_Ocomm__monoid__add' [40, 1] (w:1, o:49, a:1, s:1
% 7.18/7.60 , b:0),
% 7.18/7.60 'c_HOL_Oplus__class_Oplus' [43, 3] (w:1, o:121, a:1, s:1, b:0),
% 7.18/7.60 'class_Ring__and__Field_Ocomm__semiring__1' [45, 1] (w:1, o:51, a:1
% 7.18/7.60 , s:1, b:0),
% 7.18/7.60 'class_OrderedGroup_Oab__group__add' [49, 1] (w:1, o:52, a:1, s:1, b:
% 7.18/7.60 0),
% 7.18/7.60 'tc_nat' [52, 0] (w:1, o:26, a:1, s:1, b:0),
% 7.18/7.60 'class_OrderedGroup_Oab__semigroup__add' [54, 1] (w:1, o:53, a:1, s:1
% 7.18/7.60 , b:0),
% 7.18/7.60 'c_HOL_Ozero__class_Ozero' [56, 1] (w:1, o:54, a:1, s:1, b:0),
% 7.18/7.60 'c_HOL_Oord__class_Oless' [57, 3] (w:1, o:120, a:1, s:1, b:0),
% 7.18/7.60 'class_Ring__and__Field_Ozero__neq__one' [58, 1] (w:1, o:55, a:1, s:1
% 7.18/7.60 , b:0),
% 7.18/7.60 'class_Ring__and__Field_Ono__zero__divisors' [59, 1] (w:1, o:57, a:1
% 7.18/7.60 , s:1, b:0),
% 7.18/7.60 'class_Ring__and__Field_Omult__zero' [60, 1] (w:1, o:56, a:1, s:1, b:
% 7.18/7.60 0),
% 7.18/7.60 'class_Power_Opower' [61, 1] (w:1, o:72, a:1, s:1, b:0),
% 7.18/7.60 'c_Power_Opower__class_Opower' [62, 3] (w:1, o:122, a:1, s:1, b:0),
% 7.18/7.60 'c_Suc' [63, 1] (w:1, o:73, a:1, s:1, b:0),
% 7.18/7.60 'c_Ring__and__Field_Odvd__class_Odvd' [64, 3] (w:1, o:123, a:1, s:1
% 7.18/7.60 , b:0),
% 7.18/7.60 'class_Divides_Osemiring__div' [65, 1] (w:1, o:75, a:1, s:1, b:0),
% 7.18/7.60 'c_Divides_Odiv__class_Omod' [66, 3] (w:1, o:124, a:1, s:1, b:0),
% 7.18/7.60 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [67, 1]
% 7.18/7.60 (w:1, o:58, a:1, s:1, b:0),
% 7.18/7.60 'c_lessequals' [68, 3] (w:1, o:125, a:1, s:1, b:0),
% 7.18/7.60 'c_HOL_Ominus__class_Ominus' [69, 3] (w:1, o:126, a:1, s:1, b:0),
% 7.18/7.60 'class_Ring__and__Field_Oordered__idom' [70, 1] (w:1, o:76, a:1, s:1
% 7.18/7.60 , b:0),
% 7.18/7.60 'class_Ring__and__Field_Oordered__field' [71, 1] (w:1, o:77, a:1, s:1
% 7.18/7.60 , b:0),
% 7.18/7.60 'class_Ring__and__Field_Odivision__by__zero' [72, 1] (w:1, o:78, a:1
% 7.18/7.60 , s:1, b:0),
% 7.18/7.60 'c_HOL_Oone__class_Oone' [73, 1] (w:1, o:79, a:1, s:1, b:0),
% 7.18/7.60 'c_HOL_Oinverse__class_Oinverse' [74, 2] (w:1, o:116, a:1, s:1, b:0)
% 7.18/7.60 ,
% 7.18/7.60 'class_Ring__and__Field_Oordered__semidom' [75, 1] (w:1, o:80, a:1
% 7.18/7.60 , s:1, b:0),
% 7.18/7.60 'c_GCD_Ogcd__class_Ogcd' [76, 3] (w:1, o:119, a:1, s:1, b:0),
% 7.18/7.60 'class_OrderedGroup_Opordered__comm__monoid__add' [77, 1] (w:1, o:59
% 7.18/7.60 , a:1, s:1, b:0),
% 7.18/7.60 'c_Nat_Osemiring__1__class_Oof__nat' [78, 2] (w:1, o:117, a:1, s:1
% 7.18/7.60 , b:0),
% 7.18/7.60 'class_Orderings_Opreorder' [79, 1] (w:1, o:61, a:1, s:1, b:0),
% 7.18/7.60 'class_Orderings_Oorder' [80, 1] (w:1, o:60, a:1, s:1, b:0),
% 7.18/7.60 'class_OrderedGroup_Olordered__ab__group__add' [81, 1] (w:1, o:62, a:
% 7.18/7.60 1, s:1, b:0),
% 7.18/7.60 'class_Ring__and__Field_Odivision__ring' [82, 1] (w:1, o:81, a:1, s:1
% 7.18/7.60 , b:0),
% 7.18/7.60 'class_Ring__and__Field_Osemiring__0' [83, 1] (w:1, o:84, a:1, s:1
% 7.18/7.60 , b:0),
% 7.18/7.60 'class_Nat_Osemiring__char__0' [87, 1] (w:1, o:48, a:1, s:1, b:0),
% 7.18/7.60 'class_Ring__and__Field_Oidom' [88, 1] (w:1, o:85, a:1, s:1, b:0),
% 7.18/7.60 'class_Int_Onumber__ring' [89, 1] (w:1, o:86, a:1, s:1, b:0),
% 7.18/7.60 'class_Orderings_Olinorder' [90, 1] (w:1, o:63, a:1, s:1, b:0),
% 7.18/7.60 'c_HOL_Oinverse__class_Odivide' [91, 3] (w:1, o:127, a:1, s:1, b:0),
% 7.18/7.60
% 7.18/7.60 'class_SEQ_Obanach' [92, 1] (w:1, o:90, a:1, s:1, b:0),
% 7.18/7.60 'class_RealVector_Oreal__normed__field' [93, 1] (w:1, o:87, a:1, s:1
% 7.18/7.60 , b:0),
% 7.18/7.60 'c_Transcendental_Oexp' [94, 2] (w:1, o:118, a:1, s:1, b:0),
% 7.18/7.60 'class_OrderedGroup_Omonoid__add' [95, 1] (w:1, o:64, a:1, s:1, b:0)
% 7.18/7.60 ,
% 7.18/7.60 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [97, 1]
% 7.18/7.60 (w:1, o:65, a:1, s:1, b:0),
% 7.18/7.60 'class_OrderedGroup_Opordered__ab__group__add' [98, 1] (w:1, o:66, a:
% 7.18/7.60 1, s:1, b:0),
% 7.18/7.60 'class_OrderedGroup_Opordered__ab__semigroup__add' [99, 1] (w:1, o:67
% 7.18/7.60 , a:1, s:1, b:0),
% 7.18/7.60 'class_Ring__and__Field_Ofield' [101, 1] (w:1, o:88, a:1, s:1, b:0),
% 7.18/7.60
% 7.18/7.60 'class_Ring__and__Field_Osemiring__1' [103, 1] (w:1, o:89, a:1, s:1
% 31.96/32.34 , b:0),
% 31.96/32.34 'class_OrderedGroup_Ocancel__ab__semigroup__add' [104, 1] (w:1, o:68
% 31.96/32.34 , a:1, s:1, b:0),
% 31.96/32.34 'class_OrderedGroup_Ocancel__semigroup__add' [105, 1] (w:1, o:69, a:1
% 31.96/32.34 , s:1, b:0),
% 31.96/32.34 'class_Divides_Oring__div' [109, 1] (w:1, o:74, a:1, s:1, b:0),
% 31.96/32.34 'class_Ring__and__Field_Ocomm__ring__1' [114, 1] (w:1, o:50, a:1, s:1
% 31.96/32.34 , b:0),
% 31.96/32.34 'class_OrderedGroup_Ogroup__add' [115, 1] (w:1, o:70, a:1, s:1, b:0)
% 31.96/32.34 ,
% 31.96/32.34 'class_Ring__and__Field_Oring__1__no__zero__divisors' [116, 1] (w:1
% 31.96/32.34 , o:82, a:1, s:1, b:0),
% 31.96/32.34 't_a' [118, 0] (w:1, o:36, a:1, s:1, b:0),
% 31.96/32.34 'v_a' [119, 0] (w:1, o:37, a:1, s:1, b:0),
% 31.96/32.34 'class_Ring__and__Field_Oring__1' [122, 1] (w:1, o:83, a:1, s:1, b:0)
% 31.96/32.34 ,
% 31.96/32.34 'v_n' [123, 0] (w:1, o:41, a:1, s:1, b:0),
% 31.96/32.34 'v_m' [124, 0] (w:1, o:40, a:1, s:1, b:0),
% 31.96/32.34 'class_OrderedGroup_Omonoid__mult' [125, 1] (w:1, o:71, a:1, s:1, b:0
% 31.96/32.34 ).
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Starting Search:
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 6861
% 31.96/32.34 Kept: 2207
% 31.96/32.34 Inuse: 161
% 31.96/32.34 Deleted: 5
% 31.96/32.34 Deletedinuse: 0
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 16186
% 31.96/32.34 Kept: 4212
% 31.96/32.34 Inuse: 275
% 31.96/32.34 Deleted: 9
% 31.96/32.34 Deletedinuse: 0
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 25862
% 31.96/32.34 Kept: 6512
% 31.96/32.34 Inuse: 306
% 31.96/32.34 Deleted: 16
% 31.96/32.34 Deletedinuse: 6
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 37950
% 31.96/32.34 Kept: 8514
% 31.96/32.34 Inuse: 366
% 31.96/32.34 Deleted: 16
% 31.96/32.34 Deletedinuse: 6
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 52197
% 31.96/32.34 Kept: 10654
% 31.96/32.34 Inuse: 386
% 31.96/32.34 Deleted: 17
% 31.96/32.34 Deletedinuse: 7
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 68195
% 31.96/32.34 Kept: 12663
% 31.96/32.34 Inuse: 447
% 31.96/32.34 Deleted: 20
% 31.96/32.34 Deletedinuse: 9
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 83164
% 31.96/32.34 Kept: 14688
% 31.96/32.34 Inuse: 505
% 31.96/32.34 Deleted: 23
% 31.96/32.34 Deletedinuse: 12
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 95514
% 31.96/32.34 Kept: 16696
% 31.96/32.34 Inuse: 535
% 31.96/32.34 Deleted: 46
% 31.96/32.34 Deletedinuse: 35
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 107812
% 31.96/32.34 Kept: 18710
% 31.96/32.34 Inuse: 604
% 31.96/32.34 Deleted: 46
% 31.96/32.34 Deletedinuse: 35
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying clauses:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 122241
% 31.96/32.34 Kept: 21332
% 31.96/32.34 Inuse: 635
% 31.96/32.34 Deleted: 4048
% 31.96/32.34 Deletedinuse: 35
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 134667
% 31.96/32.34 Kept: 23369
% 31.96/32.34 Inuse: 670
% 31.96/32.34 Deleted: 4048
% 31.96/32.34 Deletedinuse: 35
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 152264
% 31.96/32.34 Kept: 25392
% 31.96/32.34 Inuse: 725
% 31.96/32.34 Deleted: 4048
% 31.96/32.34 Deletedinuse: 35
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 167183
% 31.96/32.34 Kept: 27396
% 31.96/32.34 Inuse: 776
% 31.96/32.34 Deleted: 4048
% 31.96/32.34 Deletedinuse: 35
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 179635
% 31.96/32.34 Kept: 29486
% 31.96/32.34 Inuse: 798
% 31.96/32.34 Deleted: 4050
% 31.96/32.34 Deletedinuse: 35
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 199235
% 31.96/32.34 Kept: 31515
% 31.96/32.34 Inuse: 816
% 31.96/32.34 Deleted: 4052
% 31.96/32.34 Deletedinuse: 35
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 235287
% 31.96/32.34 Kept: 33774
% 31.96/32.34 Inuse: 842
% 31.96/32.34 Deleted: 4061
% 31.96/32.34 Deletedinuse: 37
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 252777
% 31.96/32.34 Kept: 36182
% 31.96/32.34 Inuse: 874
% 31.96/32.34 Deleted: 4061
% 31.96/32.34 Deletedinuse: 37
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 266280
% 31.96/32.34 Kept: 38186
% 31.96/32.34 Inuse: 899
% 31.96/32.34 Deleted: 4061
% 31.96/32.34 Deletedinuse: 37
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34 Resimplifying inuse:
% 31.96/32.34 Done
% 31.96/32.34
% 31.96/32.34
% 31.96/32.34 Intermediate Status:
% 31.96/32.34 Generated: 283691
% 31.96/32.34 Kept: 40196
% 31.96/32.34 Inuse: 923
% 84.28/84.77 Deleted: 4061
% 84.28/84.77 Deletedinuse: 37
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying clauses:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 321564
% 84.28/84.77 Kept: 42755
% 84.28/84.77 Inuse: 939
% 84.28/84.77 Deleted: 4629
% 84.28/84.77 Deletedinuse: 37
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 346134
% 84.28/84.77 Kept: 45297
% 84.28/84.77 Inuse: 969
% 84.28/84.77 Deleted: 4629
% 84.28/84.77 Deletedinuse: 37
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 365056
% 84.28/84.77 Kept: 47653
% 84.28/84.77 Inuse: 993
% 84.28/84.77 Deleted: 4630
% 84.28/84.77 Deletedinuse: 37
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 381502
% 84.28/84.77 Kept: 49674
% 84.28/84.77 Inuse: 1016
% 84.28/84.77 Deleted: 4631
% 84.28/84.77 Deletedinuse: 38
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 395680
% 84.28/84.77 Kept: 52631
% 84.28/84.77 Inuse: 1037
% 84.28/84.77 Deleted: 4635
% 84.28/84.77 Deletedinuse: 38
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 417392
% 84.28/84.77 Kept: 54959
% 84.28/84.77 Inuse: 1084
% 84.28/84.77 Deleted: 4635
% 84.28/84.77 Deletedinuse: 38
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 431179
% 84.28/84.77 Kept: 57173
% 84.28/84.77 Inuse: 1119
% 84.28/84.77 Deleted: 4641
% 84.28/84.77 Deletedinuse: 44
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 448191
% 84.28/84.77 Kept: 59986
% 84.28/84.77 Inuse: 1144
% 84.28/84.77 Deleted: 4648
% 84.28/84.77 Deletedinuse: 50
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying clauses:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 472530
% 84.28/84.77 Kept: 63567
% 84.28/84.77 Inuse: 1182
% 84.28/84.77 Deleted: 5538
% 84.28/84.77 Deletedinuse: 50
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 500867
% 84.28/84.77 Kept: 66759
% 84.28/84.77 Inuse: 1192
% 84.28/84.77 Deleted: 5540
% 84.28/84.77 Deletedinuse: 52
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 521470
% 84.28/84.77 Kept: 69539
% 84.28/84.77 Inuse: 1217
% 84.28/84.77 Deleted: 5541
% 84.28/84.77 Deletedinuse: 53
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 529072
% 84.28/84.77 Kept: 71597
% 84.28/84.77 Inuse: 1223
% 84.28/84.77 Deleted: 5541
% 84.28/84.77 Deletedinuse: 53
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 543297
% 84.28/84.77 Kept: 73598
% 84.28/84.77 Inuse: 1263
% 84.28/84.77 Deleted: 5541
% 84.28/84.77 Deletedinuse: 53
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 567285
% 84.28/84.77 Kept: 77722
% 84.28/84.77 Inuse: 1277
% 84.28/84.77 Deleted: 5541
% 84.28/84.77 Deletedinuse: 53
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 582182
% 84.28/84.77 Kept: 79785
% 84.28/84.77 Inuse: 1296
% 84.28/84.77 Deleted: 5542
% 84.28/84.77 Deletedinuse: 53
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying clauses:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 597635
% 84.28/84.77 Kept: 81796
% 84.28/84.77 Inuse: 1326
% 84.28/84.77 Deleted: 6202
% 84.28/84.77 Deletedinuse: 53
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 621799
% 84.28/84.77 Kept: 83864
% 84.28/84.77 Inuse: 1350
% 84.28/84.77 Deleted: 6203
% 84.28/84.77 Deletedinuse: 54
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 642200
% 84.28/84.77 Kept: 86045
% 84.28/84.77 Inuse: 1390
% 84.28/84.77 Deleted: 6203
% 84.28/84.77 Deletedinuse: 54
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 665002
% 84.28/84.77 Kept: 88194
% 84.28/84.77 Inuse: 1410
% 84.28/84.77 Deleted: 6205
% 84.28/84.77 Deletedinuse: 56
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 683842
% 84.28/84.77 Kept: 90820
% 84.28/84.77 Inuse: 1430
% 84.28/84.77 Deleted: 6225
% 84.28/84.77 Deletedinuse: 76
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 701686
% 84.28/84.77 Kept: 93187
% 84.28/84.77 Inuse: 1436
% 84.28/84.77 Deleted: 6229
% 84.28/84.77 Deletedinuse: 76
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 719189
% 84.28/84.77 Kept: 95224
% 84.28/84.77 Inuse: 1446
% 84.28/84.77 Deleted: 6229
% 84.28/84.77 Deletedinuse: 76
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 736824
% 84.28/84.77 Kept: 97372
% 84.28/84.77 Inuse: 1481
% 84.28/84.77 Deleted: 6229
% 84.28/84.77 Deletedinuse: 76
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77 Resimplifying inuse:
% 84.28/84.77 Done
% 84.28/84.77
% 84.28/84.77
% 84.28/84.77 Intermediate Status:
% 84.28/84.77 Generated: 752723
% 84.28/84.77 Kept: 99479
% 84.28/84.77 Inuse: 1506
% 84.28/84.77 Deleted: 6230
% 84.28/84.77 Deletedinuse: 77
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 763249
% 133.06/133.47 Kept: 101522
% 133.06/133.47 Inuse: 1526
% 133.06/133.47 Deleted: 6230
% 133.06/133.47 Deletedinuse: 77
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying clauses:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 774071
% 133.06/133.47 Kept: 103539
% 133.06/133.47 Inuse: 1533
% 133.06/133.47 Deleted: 7125
% 133.06/133.47 Deletedinuse: 78
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 787510
% 133.06/133.47 Kept: 105543
% 133.06/133.47 Inuse: 1546
% 133.06/133.47 Deleted: 7125
% 133.06/133.47 Deletedinuse: 78
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 808756
% 133.06/133.47 Kept: 108142
% 133.06/133.47 Inuse: 1560
% 133.06/133.47 Deleted: 7125
% 133.06/133.47 Deletedinuse: 78
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 826100
% 133.06/133.47 Kept: 110265
% 133.06/133.47 Inuse: 1591
% 133.06/133.47 Deleted: 7125
% 133.06/133.47 Deletedinuse: 78
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 838400
% 133.06/133.47 Kept: 112477
% 133.06/133.47 Inuse: 1616
% 133.06/133.47 Deleted: 7126
% 133.06/133.47 Deletedinuse: 79
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 856669
% 133.06/133.47 Kept: 115879
% 133.06/133.47 Inuse: 1639
% 133.06/133.47 Deleted: 7126
% 133.06/133.47 Deletedinuse: 79
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 881072
% 133.06/133.47 Kept: 118639
% 133.06/133.47 Inuse: 1656
% 133.06/133.47 Deleted: 7126
% 133.06/133.47 Deletedinuse: 79
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 905467
% 133.06/133.47 Kept: 121899
% 133.06/133.47 Inuse: 1681
% 133.06/133.47 Deleted: 7128
% 133.06/133.47 Deletedinuse: 81
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying clauses:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 919949
% 133.06/133.47 Kept: 123900
% 133.06/133.47 Inuse: 1692
% 133.06/133.47 Deleted: 8163
% 133.06/133.47 Deletedinuse: 82
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 937885
% 133.06/133.47 Kept: 125966
% 133.06/133.47 Inuse: 1721
% 133.06/133.47 Deleted: 8163
% 133.06/133.47 Deletedinuse: 82
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 954599
% 133.06/133.47 Kept: 128094
% 133.06/133.47 Inuse: 1746
% 133.06/133.47 Deleted: 8163
% 133.06/133.47 Deletedinuse: 82
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 983425
% 133.06/133.47 Kept: 130441
% 133.06/133.47 Inuse: 1766
% 133.06/133.47 Deleted: 8163
% 133.06/133.47 Deletedinuse: 82
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1020739
% 133.06/133.47 Kept: 133924
% 133.06/133.47 Inuse: 1781
% 133.06/133.47 Deleted: 8163
% 133.06/133.47 Deletedinuse: 82
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1044881
% 133.06/133.47 Kept: 137854
% 133.06/133.47 Inuse: 1793
% 133.06/133.47 Deleted: 8163
% 133.06/133.47 Deletedinuse: 82
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1063413
% 133.06/133.47 Kept: 140508
% 133.06/133.47 Inuse: 1811
% 133.06/133.47 Deleted: 8163
% 133.06/133.47 Deletedinuse: 82
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1077708
% 133.06/133.47 Kept: 142582
% 133.06/133.47 Inuse: 1836
% 133.06/133.47 Deleted: 8163
% 133.06/133.47 Deletedinuse: 82
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying clauses:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1095337
% 133.06/133.47 Kept: 144799
% 133.06/133.47 Inuse: 1866
% 133.06/133.47 Deleted: 8547
% 133.06/133.47 Deletedinuse: 83
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1116308
% 133.06/133.47 Kept: 146967
% 133.06/133.47 Inuse: 1896
% 133.06/133.47 Deleted: 8547
% 133.06/133.47 Deletedinuse: 83
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1137671
% 133.06/133.47 Kept: 149048
% 133.06/133.47 Inuse: 1921
% 133.06/133.47 Deleted: 8549
% 133.06/133.47 Deletedinuse: 85
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1155696
% 133.06/133.47 Kept: 151311
% 133.06/133.47 Inuse: 1946
% 133.06/133.47 Deleted: 8549
% 133.06/133.47 Deletedinuse: 85
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1173392
% 133.06/133.47 Kept: 153332
% 133.06/133.47 Inuse: 1965
% 133.06/133.47 Deleted: 8549
% 133.06/133.47 Deletedinuse: 85
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1194227
% 133.06/133.47 Kept: 155766
% 133.06/133.47 Inuse: 1976
% 133.06/133.47 Deleted: 8549
% 133.06/133.47 Deletedinuse: 85
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1217914
% 133.06/133.47 Kept: 157783
% 133.06/133.47 Inuse: 2005
% 133.06/133.47 Deleted: 8549
% 133.06/133.47 Deletedinuse: 85
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1267647
% 133.06/133.47 Kept: 161202
% 133.06/133.47 Inuse: 2021
% 133.06/133.47 Deleted: 8551
% 133.06/133.47 Deletedinuse: 87
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1284860
% 133.06/133.47 Kept: 163246
% 133.06/133.47 Inuse: 2042
% 133.06/133.47 Deleted: 8551
% 133.06/133.47 Deletedinuse: 87
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying clauses:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1303806
% 133.06/133.47 Kept: 166467
% 133.06/133.47 Inuse: 2051
% 133.06/133.47 Deleted: 9894
% 133.06/133.47 Deletedinuse: 87
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1331642
% 133.06/133.47 Kept: 168558
% 133.06/133.47 Inuse: 2065
% 133.06/133.47 Deleted: 9901
% 133.06/133.47 Deletedinuse: 94
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1353094
% 133.06/133.47 Kept: 170565
% 133.06/133.47 Inuse: 2089
% 133.06/133.47 Deleted: 9916
% 133.06/133.47 Deletedinuse: 109
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1372770
% 133.06/133.47 Kept: 172609
% 133.06/133.47 Inuse: 2123
% 133.06/133.47 Deleted: 9916
% 133.06/133.47 Deletedinuse: 109
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1410541
% 133.06/133.47 Kept: 174624
% 133.06/133.47 Inuse: 2187
% 133.06/133.47 Deleted: 9916
% 133.06/133.47 Deletedinuse: 109
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1470697
% 133.06/133.47 Kept: 176628
% 133.06/133.47 Inuse: 2236
% 133.06/133.47 Deleted: 9920
% 133.06/133.47 Deletedinuse: 113
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1509920
% 133.06/133.47 Kept: 178630
% 133.06/133.47 Inuse: 2288
% 133.06/133.47 Deleted: 9920
% 133.06/133.47 Deletedinuse: 113
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1556913
% 133.06/133.47 Kept: 180635
% 133.06/133.47 Inuse: 2348
% 133.06/133.47 Deleted: 9920
% 133.06/133.47 Deletedinuse: 113
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Intermediate Status:
% 133.06/133.47 Generated: 1629171
% 133.06/133.47 Kept: 182636
% 133.06/133.47 Inuse: 2403
% 133.06/133.47 Deleted: 9920
% 133.06/133.47 Deletedinuse: 113
% 133.06/133.47
% 133.06/133.47 Resimplifying inuse:
% 133.06/133.47 Done
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 Bliksems!, er is een bewijs:
% 133.06/133.47 % SZS status Unsatisfiable
% 133.06/133.47 % SZS output start Refutation
% 133.06/133.47
% 133.06/133.47 clause( 334, [ ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ), ~( =(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ) ] )
% 133.06/133.47 .
% 133.06/133.47 clause( 474, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 133.06/133.47 ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 133.06/133.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 133.06/133.47 'tc_nat' ), X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 .
% 133.06/133.47 clause( 483, [ 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ] )
% 133.06/133.47 .
% 133.06/133.47 clause( 502, [ 'class_Ring__and__Field_Ofield'( 't_a' ) ] )
% 133.06/133.47 .
% 133.06/133.47 clause( 503, [ ~( =( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.47 'c_Power_Opower__class_Opower'( 'v_a', 'v_m', 't_a' ),
% 133.06/133.47 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ), 't_a' ),
% 133.06/133.47 'c_Power_Opower__class_Opower'( 'v_a', 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 'v_m', 'v_n', 'tc_nat' ), 't_a' ) ) ) ] )
% 133.06/133.47 .
% 133.06/133.47 clause( 915, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ) ] )
% 133.06/133.47 .
% 133.06/133.47 clause( 168626, [ ~( 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ), =(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ] )
% 133.06/133.47 .
% 133.06/133.47 clause( 182890, [] )
% 133.06/133.47 .
% 133.06/133.47
% 133.06/133.47
% 133.06/133.47 % SZS output end Refutation
% 133.06/133.47 found a proof!
% 133.06/133.47
% 133.06/133.47 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 133.06/133.47
% 133.06/133.47 initialclauses(
% 133.06/133.47 [ clause( 182892, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 133.06/133.47 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 133.06/133.47 ) ) ] )
% 133.06/133.47 , clause( 182893, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 133.06/133.47 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 182894, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 133.06/133.47 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 133.06/133.47 ) ) ] )
% 133.06/133.47 , clause( 182895, [ =( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat'
% 133.06/133.47 ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182896, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 133.06/133.47 ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182897, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 133.06/133.47 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 133.06/133.47 ) ) ] )
% 133.06/133.47 , clause( 182898, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 133.06/133.47 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 182899, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 133.06/133.47 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 182900, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 133.06/133.47 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 182901, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 133.06/133.47 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 182902, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182903, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 133.06/133.47 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 133.06/133.47 , clause( 182904, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ] )
% 133.06/133.47 , clause( 182905, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 133.06/133.47 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 133.06/133.47 , clause( 182906, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 133.06/133.47 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 133.06/133.47 , clause( 182907, [ ~(
% 133.06/133.47 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 133.06/133.47 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 133.06/133.47 , clause( 182908, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182909, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 182910, [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 133.06/133.47 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182911, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 182912, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 182913, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 133.06/133.47 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 182914, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.47 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 133.06/133.47 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 133.06/133.47 , Y, X ) ) ] )
% 133.06/133.47 , clause( 182915, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 X, Y, 'tc_nat' ), Y, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 133.06/133.47 ) ) ] )
% 133.06/133.47 , clause( 182916, [ =( 'c_GCD_Ogcd__class_Ogcd'( X,
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182917, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 133.06/133.47 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 182918, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 133.06/133.47 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 133.06/133.47 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 133.06/133.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 133.06/133.47 , clause( 182919, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 182920, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 182921, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' )
% 133.06/133.47 , =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 182922, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 133.06/133.47 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), X ) ) ] )
% 133.06/133.47 , clause( 182923, [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 133.06/133.47 'tc_nat' ) ), Y ) ), =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 133.06/133.47 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182924, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 182925, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 182926, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 182927, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 133.06/133.47 , clause( 182928, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182929, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 ~( 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X
% 133.06/133.47 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 182930, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 133.06/133.47 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 133.06/133.47 ) ) ] )
% 133.06/133.47 , clause( 182931, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 133.06/133.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 133.06/133.47 , clause( 182932, [ ~( 'class_Orderings_Oorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 133.06/133.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 133.06/133.47 , clause( 182933, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y
% 133.06/133.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 182934, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 133.06/133.47 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 133.06/133.47 , T, X ), X ), T, X ) ) ] )
% 133.06/133.47 , clause( 182935, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 133.06/133.47 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 182936, [ =( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182937, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 133.06/133.47 ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 133.06/133.47 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 182938, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 133.06/133.47 ), X ), Y ) ] )
% 133.06/133.47 , clause( 182939, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 133.06/133.47 'tc_nat' ), 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ),
% 133.06/133.47 =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ] )
% 133.06/133.47 , clause( 182940, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182941, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 182942, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 182943, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 133.06/133.47 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 182944, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 133.06/133.47 X ) ) ) ] )
% 133.06/133.47 , clause( 182945, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 133.06/133.47 X ) ) ) ] )
% 133.06/133.47 , clause( 182946, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 182947, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 182948, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 182949, [ ~(
% 133.06/133.47 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 133.06/133.47 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 133.06/133.47 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 133.06/133.47 , clause( 182950, [ ~(
% 133.06/133.47 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 133.06/133.47 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 133.06/133.47 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 133.06/133.47 , clause( 182951, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182952, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182953, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182954, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182955, [ 'c_HOL_Oord__class_Oless'( X,
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182956, [ 'c_HOL_Oord__class_Oless'( X,
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182957, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 133.06/133.47 Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182958, [ 'c_HOL_Oord__class_Oless'( X,
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182959, [ 'c_HOL_Oord__class_Oless'( X,
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182960, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 133.06/133.47 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 182961, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 133.06/133.47 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 182962, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 133.06/133.47 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 133.06/133.47 , clause( 182963, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 133.06/133.47 , T, X ), X ) ) ] )
% 133.06/133.47 , clause( 182964, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 133.06/133.47 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182965, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( Y, 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 133.06/133.47 ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182966, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 133.06/133.47 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 133.06/133.47 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 133.06/133.47 , clause( 182967, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X )
% 133.06/133.47 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182968, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) )
% 133.06/133.47 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182969, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 133.06/133.47 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 133.06/133.47 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 182970, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 133.06/133.47 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 133.06/133.47 ) ) ] )
% 133.06/133.47 , clause( 182971, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182972, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182973, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 133.06/133.47 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 182974, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 133.06/133.47 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 182975, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 182976, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 182977, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 133.06/133.47 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 133.06/133.47 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 182978, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 133.06/133.47 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 182979, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 133.06/133.47 , clause( 182980, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 182981, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 133.06/133.47 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 182982, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 133.06/133.47 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 182983, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 182984, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X )
% 133.06/133.47 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182985, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 133.06/133.47 ), =( Z, Y ) ] )
% 133.06/133.47 , clause( 182986, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 133.06/133.47 , clause( 182987, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 133.06/133.47 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 133.06/133.47 ), =( Y, X ) ] )
% 133.06/133.47 , clause( 182988, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 133.06/133.47 'tc_nat' ) ), =( Y, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X,
% 133.06/133.47 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182989, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 133.06/133.47 , Y, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X,
% 133.06/133.47 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182990, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 133.06/133.47 , clause( 182991, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 133.06/133.47 , X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 133.06/133.47 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182992, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 133.06/133.47 'tc_nat' ) ), =( Y, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X,
% 133.06/133.47 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182993, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 133.06/133.47 , X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 133.06/133.47 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182994, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 133.06/133.47 , X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 133.06/133.47 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 182995, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 133.06/133.47 , clause( 182996, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 182997, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 182998, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 133.06/133.47 ), =( Z, Y ) ] )
% 133.06/133.47 , clause( 182999, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.47 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 133.06/133.47 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183000, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.47 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 133.06/133.47 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183001, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.47 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 133.06/133.47 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183002, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.47 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 133.06/133.47 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183003, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183004, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183005, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.47 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 133.06/133.47 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183006, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.47 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 133.06/133.47 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183007, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.47 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183008, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.47 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183009, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), X, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y
% 133.06/133.47 , 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183010, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183011, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ] )
% 133.06/133.47 , clause( 183012, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 133.06/133.47 , clause( 183013, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' )
% 133.06/133.47 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183014, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183015, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183016, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 133.06/133.47 , clause( 183017, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 183018, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 133.06/133.47 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 133.06/133.47 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183019, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 133.06/133.47 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183020, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 133.06/133.47 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 133.06/133.47 , clause( 183021, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 133.06/133.47 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 183022, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 133.06/133.47 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 133.06/133.47 , clause( 183023, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 133.06/133.47 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 183024, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 133.06/133.47 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183025, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 133.06/133.47 , clause( 183026, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183027, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ] )
% 133.06/133.47 , clause( 183028, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 183029, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ] )
% 133.06/133.47 , clause( 183030, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183031, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183032, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183033, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183034, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 133.06/133.47 'c_Power_Opower__class_Opower'( T, Z, X ) ) ), =( Y, T ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 133.06/133.47 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 133.06/133.47 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183035, [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 133.06/133.47 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183036, [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 133.06/133.47 'class_RealVector_Oreal__normed__field'( X ) ), ~( =(
% 133.06/133.47 'c_Transcendental_Oexp'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 133.06/133.47 , clause( 183037, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 133.06/133.47 , clause( 183038, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 133.06/133.47 , clause( 183039, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183040, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183041, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183042, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 133.06/133.47 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183043, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183044, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183045, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183046, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 133.06/133.47 , clause( 183047, [ =( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 133.06/133.47 , clause( 183048, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183049, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183050, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183051, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183052, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183053, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183054, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183055, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y, 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183056, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X, 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183057, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X, 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183058, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y, 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183059, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X, 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183060, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y, 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183061, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183062, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183063, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 133.06/133.47 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183064, [ ~(
% 133.06/133.47 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 133.06/133.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 133.06/133.47 , clause( 183065, [ ~(
% 133.06/133.47 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 133.06/133.47 , clause( 183066, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 133.06/133.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183067, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183068, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 133.06/133.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183069, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 133.06/133.47 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ),
% 133.06/133.47 ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183070, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 133.06/133.47 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' )
% 133.06/133.47 ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183071, [ ~( 'class_Orderings_Oorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 133.06/133.47 , clause( 183072, [ ~( 'class_Orderings_Oorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 133.06/133.47 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 133.06/133.47 , clause( 183073, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 133.06/133.47 ), 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 133.06/133.47 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ] )
% 133.06/133.47 , clause( 183074, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 133.06/133.47 , clause( 183075, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 133.06/133.47 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 133.06/133.47 , clause( 183076, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 133.06/133.47 Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 183077, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 133.06/133.47 Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 183078, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 133.06/133.47 'c_lessequals'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 183079, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 133.06/133.47 X ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 133.06/133.47 ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 133.06/133.47 , clause( 183080, [ ~( 'class_Orderings_Oorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 183081, [ ~( 'class_Orderings_Oorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 133.06/133.47 Z, Y ) ] )
% 133.06/133.47 , clause( 183082, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 183083, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 133.06/133.47 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 133.06/133.47 , clause( 183084, [ ~( 'class_Orderings_Oorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 133.06/133.47 Y, Z ) ] )
% 133.06/133.47 , clause( 183085, [ ~( 'class_Orderings_Oorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 183086, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 183087, [ ~( 'class_Orderings_Oorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 183088, [ ~(
% 133.06/133.47 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 133.06/133.47 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183089, [ ~(
% 133.06/133.47 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 133.06/133.47 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 133.06/133.47 , clause( 183090, [ ~(
% 133.06/133.47 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 133.06/133.47 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183091, [ ~(
% 133.06/133.47 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 133.06/133.47 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ) ) ] )
% 133.06/133.47 , clause( 183092, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 133.06/133.47 X ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183093, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 133.06/133.47 X ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183094, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 133.06/133.47 'c_lessequals'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 183095, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 133.06/133.47 , clause( 183096, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 133.06/133.47 'c_lessequals'( Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 183097, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 133.06/133.47 , clause( 183098, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 183099, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 133.06/133.47 Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 133.06/133.47 , clause( 183100, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 133.06/133.47 , clause( 183101, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 133.06/133.47 'c_lessequals'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 183102, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.47 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183103, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.47 X ) ) ] )
% 133.06/133.47 , clause( 183104, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 X ), Z, X ) ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 133.06/133.47 'c_Suc'( T ), X ), 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ),
% 133.06/133.47 X ) ) ] )
% 133.06/133.47 , clause( 183105, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 133.06/133.47 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 X ), X ) ) ] )
% 133.06/133.47 , clause( 183106, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 133.06/133.47 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 133.06/133.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 133.06/133.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183107, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 133.06/133.47 Z, T, X ), X ) ) ] )
% 133.06/133.47 , clause( 183108, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 133.06/133.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 133.06/133.47 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183109, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 133.06/133.47 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183110, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 133.06/133.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183111, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 133.06/133.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 133.06/133.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183112, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183113, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183114, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 133.06/133.47 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183115, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 133.06/133.47 , clause( 183116, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ] )
% 133.06/133.47 , clause( 183117, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 133.06/133.47 , clause( 183118, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183119, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 133.06/133.47 , clause( 183120, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 133.06/133.47 , clause( 183121, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 133.06/133.47 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 183122, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 133.06/133.47 X ) ] )
% 133.06/133.47 , clause( 183123, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 133.06/133.47 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 183124, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 133.06/133.47 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 133.06/133.47 , clause( 183125, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 133.06/133.47 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183126, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 133.06/133.47 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 133.06/133.47 X ), T, X ) ) ] )
% 133.06/133.47 , clause( 183127, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 133.06/133.47 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183128, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 133.06/133.47 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 133.06/133.47 X ), T, X ) ) ] )
% 133.06/133.47 , clause( 183129, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.47 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183130, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 183131, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.47 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183132, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183133, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' )
% 133.06/133.47 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183134, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183135, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ] )
% 133.06/133.47 , clause( 183136, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 133.06/133.47 =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183137, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 183138, [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) )
% 133.06/133.47 , =( 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X
% 133.06/133.47 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 183139, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 133.06/133.47 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183140, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 133.06/133.47 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 133.06/133.47 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 133.06/133.47 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 133.06/133.47 , clause( 183141, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 133.06/133.47 ) ) ] )
% 133.06/133.47 , clause( 183142, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 133.06/133.47 ) ) ] )
% 133.06/133.47 , clause( 183143, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183144, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 133.06/133.47 , clause( 183145, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 133.06/133.47 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183146, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 133.06/133.47 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183147, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 133.06/133.47 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 133.06/133.47 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 183148, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 133.06/133.47 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183149, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.47 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183150, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 133.06/133.47 , X ), X ) ] )
% 133.06/133.47 , clause( 183151, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 133.06/133.47 , clause( 183152, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 183153, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 133.06/133.47 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 133.06/133.47 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 133.06/133.47 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 133.06/133.47 , clause( 183154, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 183155, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 133.06/133.47 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 133.06/133.47 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 133.06/133.47 , clause( 183156, [ 'c_lessequals'( 'c_GCD_Ogcd__class_Ogcd'( X, Y,
% 133.06/133.47 'tc_nat' ), Y, 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183157, [ 'c_lessequals'( 'c_GCD_Ogcd__class_Ogcd'( X, Y,
% 133.06/133.47 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183158, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183159, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183160, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' )
% 133.06/133.47 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183161, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183162, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183163, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183164, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183165, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 183166, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 133.06/133.47 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 183167, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 133.06/133.47 X ), X ) ) ] )
% 133.06/133.47 , clause( 183168, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 133.06/133.47 , clause( 183169, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 133.06/133.47 , clause( 183170, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 133.06/133.47 , clause( 183171, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 133.06/133.47 , clause( 183172, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 133.06/133.47 , clause( 183173, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 133.06/133.47 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 133.06/133.47 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 133.06/133.47 , clause( 183174, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X
% 133.06/133.47 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 133.06/133.47 , clause( 183175, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) )
% 133.06/133.47 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 Y, T, X ) ) ), =( Z, T ) ] )
% 133.06/133.47 , clause( 183176, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) )
% 133.06/133.47 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 T, Z, X ) ) ), =( Y, T ) ] )
% 133.06/133.47 , clause( 183177, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 133.06/133.47 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183178, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 133.06/133.47 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183179, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 133.06/133.47 , clause( 183180, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ] )
% 133.06/133.47 , clause( 183181, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 183182, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 133.06/133.47 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 183183, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 133.06/133.47 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 183184, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y,
% 133.06/133.47 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 183185, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 133.06/133.47 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.47 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 183186, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 133.06/133.47 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183187, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 133.06/133.47 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 133.06/133.47 , clause( 183188, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 133.06/133.47 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183189, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 133.06/133.47 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ),
% 133.06/133.47 ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183190, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'(
% 133.06/133.47 X, Y, 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183191, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 133.06/133.47 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 183192, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 133.06/133.47 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 133.06/133.47 , clause( 183193, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183194, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183195, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 133.06/133.47 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183196, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 183197, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 133.06/133.47 , clause( 183198, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 183199, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 133.06/133.47 , clause( 183200, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 133.06/133.47 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183201, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 X, Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183202, [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 133.06/133.47 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 133.06/133.47 'c_Transcendental_Oexp'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 133.06/133.47 , clause( 183203, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' )
% 133.06/133.47 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183204, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183205, [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183206, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 133.06/133.47 , X ) ) ] )
% 133.06/133.47 , clause( 183207, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 133.06/133.47 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183208, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 133.06/133.47 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 133.06/133.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 183209, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 133.06/133.47 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.47 , clause( 183210, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 133.06/133.47 , clause( 183211, [ =( 'c_GCD_Ogcd__class_Ogcd'( X,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 133.06/133.47 , clause( 183212, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 133.06/133.47 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 183213, [ ~(
% 133.06/133.47 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 133.06/133.47 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X
% 133.06/133.47 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 133.06/133.47 ) ) ] )
% 133.06/133.47 , clause( 183214, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, X, 'tc_nat' ), X ) ] )
% 133.06/133.47 , clause( 183215, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y,
% 133.06/133.47 'tc_nat' ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 183216, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ),
% 133.06/133.47 'tc_nat' ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 183217, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 133.06/133.47 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183218, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183219, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183220, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 133.06/133.47 Y, X ) ) ] )
% 133.06/133.47 , clause( 183221, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 X, T, 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183222, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183223, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 133.06/133.47 Y, X ) ) ] )
% 133.06/133.47 , clause( 183224, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 133.06/133.47 X ) ) ] )
% 133.06/133.47 , clause( 183225, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 183226, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 133.06/133.47 'c_lessequals'( Z, Y, X ) ) ] )
% 133.06/133.47 , clause( 183227, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 133.06/133.47 , clause( 183228, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 133.06/133.47 'c_lessequals'( Z, Y, X ) ) ] )
% 133.06/133.47 , clause( 183229, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 133.06/133.47 , clause( 183230, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 133.06/133.47 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 133.06/133.47 X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 133.06/133.47 , clause( 183231, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 133.06/133.47 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183232, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 133.06/133.47 ) ) ] )
% 133.06/133.47 , clause( 183233, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 133.06/133.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183234, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 133.06/133.47 ) ) ] )
% 133.06/133.47 , clause( 183235, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 133.06/133.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 183236, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 133.06/133.47 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 183237, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.47 X ) ) ] )
% 133.06/133.47 , clause( 183238, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 133.06/133.47 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 133.06/133.47 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 133.06/133.47 X ), Z, X ) ) ] )
% 133.06/133.47 , clause( 183239, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 133.06/133.47 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 133.06/133.47 , clause( 183240, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 133.06/133.47 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 133.06/133.47 , clause( 183241, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 133.06/133.47 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 133.06/133.47 , T, X ), X ), T, X ) ) ] )
% 133.06/133.47 , clause( 183242, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 133.06/133.47 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 133.06/133.47 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 183243, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 133.06/133.47 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 133.06/133.47 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 133.06/133.47 , clause( 183244, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 133.06/133.47 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 133.06/133.47 , clause( 183245, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183246, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183247, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183248, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 ) ] )
% 133.06/133.47 , clause( 183249, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 133.06/133.47 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 133.06/133.47 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 183250, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 133.06/133.47 ), Y ) ] )
% 133.06/133.47 , clause( 183251, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 ) ), =( Y, Z ) ] )
% 133.06/133.47 , clause( 183252, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.47 ) ), =( Y, Z ) ] )
% 133.06/133.47 , clause( 183253, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 133.06/133.47 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 133.06/133.47 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 133.06/133.47 , clause( 183254, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 133.06/133.47 , U, X ), X ) ) ] )
% 133.06/133.47 , clause( 183255, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 133.06/133.47 ), Y ) ] )
% 133.06/133.47 , clause( 183256, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 133.06/133.47 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 133.06/133.47 Y, X ), Z, X ) ) ] )
% 133.06/133.47 , clause( 183257, [ ~(
% 133.06/133.47 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~( =(
% 133.06/133.47 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 133.06/133.47 ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 183258, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 133.06/133.47 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 133.06/133.47 ) ) ] )
% 133.06/133.47 , clause( 183259, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 133.06/133.47 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 133.06/133.47 , clause( 183260, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183261, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 183262, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 133.06/133.47 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ] )
% 133.06/133.47 , clause( 183263, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 133.06/133.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 183264, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 133.06/133.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 183265, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 133.06/133.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 183266, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 133.06/133.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.47 , clause( 183267, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 133.06/133.47 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 133.06/133.47 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 133.06/133.47 , clause( 183268, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 133.06/133.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 133.06/133.47 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 133.06/133.47 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 133.06/133.47 , clause( 183269, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 133.06/133.47 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183270, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' )
% 133.06/133.47 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183271, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 133.06/133.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183272, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183273, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 133.06/133.47 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183274, [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 133.06/133.47 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183275, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183276, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183277, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 133.06/133.47 'tc_nat' ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183278, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 133.06/133.47 'tc_nat' ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183279, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 133.06/133.47 'tc_nat' ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183280, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 133.06/133.47 'tc_nat' ), 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183281, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 133.06/133.47 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183282, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' )
% 133.06/133.47 , ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183283, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y )
% 133.06/133.47 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183284, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 133.06/133.47 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183285, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y )
% 133.06/133.47 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183286, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 133.06/133.47 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183287, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183288, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 133.06/133.47 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183289, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 133.06/133.47 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 183290, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 133.06/133.47 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183291, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 133.06/133.47 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183292, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183293, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183294, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 133.06/133.47 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183295, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 133.06/133.47 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183296, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 133.06/133.47 , X, 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183297, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 133.06/133.47 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183298, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_lessequals'( 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183299, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 133.06/133.47 'tc_nat' ), X, 'tc_nat' ) ] )
% 133.06/133.47 , clause( 183300, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' )
% 133.06/133.47 ] )
% 133.06/133.47 , clause( 183301, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 133.06/133.47 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 133.06/133.47 )
% 133.06/133.47 , clause( 183302, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( Y
% 133.06/133.47 , Z, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183303, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 133.06/133.47 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183304, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'(
% 133.06/133.47 Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183305, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 133.06/133.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183306, [ =( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 X, Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 133.06/133.47 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183307, [ =( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.47 Z, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 133.06/133.47 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183308, [ =( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 133.06/133.47 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 133.06/133.47 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183309, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 133.06/133.47 , clause( 183310, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 133.06/133.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183311, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183312, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 133.06/133.47 , clause( 183313, [ =( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 133.06/133.47 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183314, [ =( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.47 , clause( 183315, [ =( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 133.06/133.47 , clause( 183316, [ =( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ) ] )
% 133.06/133.47 , clause( 183317, [ ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ), ~( =(
% 133.06/133.47 'v_a', 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ) ] )
% 133.06/133.47 , clause( 183318, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.47 ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.47 , clause( 183319, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 133.06/133.47 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.48 X ) ) ] )
% 133.06/133.48 , clause( 183320, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'(
% 133.06/133.48 X ), X ) ] )
% 133.06/133.48 , clause( 183321, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.48 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183322, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 133.06/133.48 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.48 , X ) ) ] )
% 133.06/133.48 , clause( 183323, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 133.06/133.48 ), 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 133.06/133.48 , clause( 183324, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183325, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 133.06/133.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183326, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 133.06/133.48 ] )
% 133.06/133.48 , clause( 183327, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y
% 133.06/133.48 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 133.06/133.48 ), X ) ) ] )
% 133.06/133.48 , clause( 183328, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 133.06/133.48 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 133.06/133.48 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183329, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 133.06/133.48 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 133.06/133.48 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183330, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 133.06/133.48 , clause( 183331, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 133.06/133.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 133.06/133.48 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 133.06/133.48 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 133.06/133.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 133.06/133.48 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 133.06/133.48 Z, X ) ) ] )
% 133.06/133.48 , clause( 183332, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.48 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 133.06/133.48 ] )
% 133.06/133.48 , clause( 183333, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 133.06/133.48 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183334, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 133.06/133.48 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 133.06/133.48 , clause( 183335, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183336, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183337, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.48 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ), =( Y
% 133.06/133.48 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183338, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.48 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ), =( X
% 133.06/133.48 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183339, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 133.06/133.48 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 133.06/133.48 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 133.06/133.48 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.48 , clause( 183340, [ =( 'c_GCD_Ogcd__class_Ogcd'( X,
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( Y, 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ),
% 133.06/133.48 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183341, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'(
% 133.06/133.48 X, Y, 'tc_nat' ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X,
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183342, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'(
% 133.06/133.48 X, Y, 'tc_nat' ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X,
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183343, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y
% 133.06/133.48 ), 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183344, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X
% 133.06/133.48 ), 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183345, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 133.06/133.48 , ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183346, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183347, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.48 , X ) ] )
% 133.06/133.48 , clause( 183348, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183349, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.48 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.48 , clause( 183350, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183351, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.48 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.48 Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183352, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 133.06/133.48 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183353, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 133.06/133.48 , clause( 183354, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183355, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183356, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 133.06/133.48 , clause( 183357, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 133.06/133.48 , clause( 183358, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 133.06/133.48 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183359, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183360, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183361, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183362, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 133.06/133.48 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 133.06/133.48 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183363, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.48 X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat'
% 133.06/133.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183364, [ ~(
% 133.06/133.48 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 133.06/133.48 , clause( 183365, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183366, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.48 'tc_nat' ) ) ) ] )
% 133.06/133.48 , clause( 183367, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.48 'tc_nat' ) ) ) ] )
% 133.06/133.48 , clause( 183368, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 133.06/133.48 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 133.06/133.48 , X ) ) ] )
% 133.06/133.48 , clause( 183369, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 133.06/133.48 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.48 , X ) ) ] )
% 133.06/133.48 , clause( 183370, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 133.06/133.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 133.06/133.48 , clause( 183371, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 133.06/133.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183372, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.48 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 133.06/133.48 , clause( 183373, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 133.06/133.48 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.48 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 133.06/133.48 , clause( 183374, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 133.06/133.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 133.06/133.48 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183375, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 133.06/133.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 133.06/133.48 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.48 , clause( 183376, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 133.06/133.48 =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.48 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.48 , clause( 183377, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.48 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 133.06/133.48 ] )
% 133.06/133.48 , clause( 183378, [ ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.48 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183379, [ ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.48 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183380, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 133.06/133.48 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 133.06/133.48 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ] )
% 133.06/133.48 , clause( 183381, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 133.06/133.48 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 133.06/133.48 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183382, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 133.06/133.48 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183383, [ ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183384, [ ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183385, [ 'c_HOL_Oord__class_Oless'( X,
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 133.06/133.48 Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183386, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.48 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183387, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183388, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183389, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ) )
% 133.06/133.48 , 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183390, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.48 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183391, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 133.06/133.48 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 133.06/133.48 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183392, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183393, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183394, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183395, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183396, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 133.06/133.48 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.48 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183397, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.48 X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat'
% 133.06/133.48 ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183398, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183399, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.48 X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat'
% 133.06/133.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183400, [ ~(
% 133.06/133.48 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 133.06/133.48 X ), X ) ) ] )
% 133.06/133.48 , clause( 183401, [ ~(
% 133.06/133.48 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 Z, T, X ) ) ] )
% 133.06/133.48 , clause( 183402, [ ~(
% 133.06/133.48 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 Z, T, X ) ) ] )
% 133.06/133.48 , clause( 183403, [ ~(
% 133.06/133.48 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 133.06/133.48 X ), X ) ) ] )
% 133.06/133.48 , clause( 183404, [ ~(
% 133.06/133.48 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 Y, T, X ) ) ] )
% 133.06/133.48 , clause( 183405, [ ~(
% 133.06/133.48 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 Y, T, X ) ) ] )
% 133.06/133.48 , clause( 183406, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 133.06/133.48 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183407, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 133.06/133.48 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183408, [ =( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 133.06/133.48 , clause( 183409, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183410, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183411, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y
% 133.06/133.48 ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183412, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( Y, 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 133.06/133.48 ), 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183413, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 133.06/133.48 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183414, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ),
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183415, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 X, 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183416, [ =( 'c_GCD_Ogcd__class_Ogcd'( X,
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183417, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 133.06/133.48 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.48 ) ] )
% 133.06/133.48 , clause( 183418, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183419, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183420, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183421, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183422, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183423, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183424, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 133.06/133.48 Y, X ) ) ] )
% 133.06/133.48 , clause( 183425, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.48 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183426, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.48 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183427, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 133.06/133.48 Y, X ) ) ] )
% 133.06/133.48 , clause( 183428, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 133.06/133.48 Y, X ) ) ] )
% 133.06/133.48 , clause( 183429, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 133.06/133.48 Y, X ) ) ] )
% 133.06/133.48 , clause( 183430, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 133.06/133.48 ), X ) ) ] )
% 133.06/133.48 , clause( 183431, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 133.06/133.48 ), X ) ) ] )
% 133.06/133.48 , clause( 183432, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 133.06/133.48 ), X ) ) ] )
% 133.06/133.48 , clause( 183433, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 133.06/133.48 ), X ) ) ] )
% 133.06/133.48 , clause( 183434, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 133.06/133.48 )
% 133.06/133.48 , clause( 183435, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 133.06/133.48 ] )
% 133.06/133.48 , clause( 183436, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 133.06/133.48 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 133.06/133.48 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183437, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 133.06/133.48 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 133.06/133.48 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183438, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 133.06/133.48 ), X ) ) ] )
% 133.06/133.48 , clause( 183439, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 133.06/133.48 ), X ) ) ] )
% 133.06/133.48 , clause( 183440, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 133.06/133.48 ), X ) ) ] )
% 133.06/133.48 , clause( 183441, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 133.06/133.48 ), X ) ) ] )
% 133.06/133.48 , clause( 183442, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 133.06/133.48 , T ) ] )
% 133.06/133.48 , clause( 183443, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.48 =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 133.06/133.48 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 133.06/133.48 , clause( 183444, [ ~( 'class_Power_Opower'( X ) ), =(
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 133.06/133.48 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 133.06/133.48 , clause( 183445, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 133.06/133.48 ) ] )
% 133.06/133.48 , clause( 183446, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 133.06/133.48 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ] )
% 133.06/133.48 , clause( 183447, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183448, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 133.06/133.48 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 133.06/133.48 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 133.06/133.48 , X ) ) ] )
% 133.06/133.48 , clause( 183449, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 133.06/133.48 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 133.06/133.48 , clause( 183450, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 133.06/133.48 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.48 , clause( 183451, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 133.06/133.48 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.48 , clause( 183452, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 133.06/133.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 133.06/133.48 Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183453, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 133.06/133.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 133.06/133.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 133.06/133.48 , clause( 183454, [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 133.06/133.48 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 133.06/133.48 'c_Transcendental_Oexp'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( 'c_Transcendental_Oexp'( Y, X ),
% 133.06/133.48 'c_Transcendental_Oexp'( Z, X ), X ) ) ] )
% 133.06/133.48 , clause( 183455, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 133.06/133.48 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 133.06/133.48 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.48 , clause( 183456, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 133.06/133.48 , Z, X ), T, X ), ~( 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 133.06/133.48 , U, X ), T, X ) ) ] )
% 133.06/133.48 , clause( 183457, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 133.06/133.48 , Z, X ), 'c_Power_Opower__class_Opower'( T, U, X ), X ), ~(
% 133.06/133.48 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 133.06/133.48 , clause( 183458, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 133.06/133.48 , Z, X ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 133.06/133.48 'c_lessequals'( Z, T, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183459, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 133.06/133.48 , 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_nat' ), X ),
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'( Y, T, X
% 133.06/133.48 ), 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ), ~( 'c_lessequals'(
% 133.06/133.48 T, Z, 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.48 , clause( 183460, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 133.06/133.48 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 133.06/133.48 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 133.06/133.48 ] )
% 133.06/133.48 , clause( 183461, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 133.06/133.48 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 133.06/133.48 ] )
% 133.06/133.48 , clause( 183462, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 133.06/133.48 ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183463, [ =( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 133.06/133.48 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183464, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 133.06/133.48 ), X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183465, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 133.06/133.48 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183466, [ =( 'c_HOL_Oplus__class_Oplus'(
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ), ~(
% 133.06/133.48 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183467, [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X
% 133.06/133.48 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 133.06/133.48 , clause( 183468, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 133.06/133.48 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183469, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 133.06/133.48 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183470, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 133.06/133.48 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183471, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.48 , ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 133.06/133.48 , Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183472, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 133.06/133.48 , ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Z
% 133.06/133.48 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183473, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 133.06/133.48 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183474, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 133.06/133.48 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183475, [ =( 'c_GCD_Ogcd__class_Ogcd'(
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ),
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X,
% 133.06/133.48 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183476, [ =( 'c_GCD_Ogcd__class_Ogcd'(
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X, 'tc_nat' ),
% 133.06/133.48 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X,
% 133.06/133.48 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183477, [ =( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 133.06/133.48 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183478, [ =( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat'
% 133.06/133.48 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183479, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 133.06/133.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 133.06/133.48 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183480, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y,
% 133.06/133.48 'tc_nat' ), 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ),
% 133.06/133.48 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183481, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 133.06/133.48 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 133.06/133.48 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183482, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 133.06/133.48 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X
% 133.06/133.48 , Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 133.06/133.48 )
% 133.06/133.48 , clause( 183483, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 133.06/133.48 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183484, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.48 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183485, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183486, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 133.06/133.48 , clause( 183487, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183488, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ] )
% 133.06/133.48 , clause( 183489, [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 133.06/133.48 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 133.06/133.48 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 133.06/133.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 133.06/133.48 , Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183490, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 133.06/133.48 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 133.06/133.48 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183491, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T,
% 133.06/133.48 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 133.06/133.48 , Y, X ) ) ] )
% 133.06/133.48 , clause( 183492, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 133.06/133.48 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 133.06/133.48 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 133.06/133.48 X ), T, X ) ) ] )
% 133.06/133.48 , clause( 183493, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 133.06/133.48 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 133.06/133.48 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 133.06/133.48 X ), T, X ) ) ] )
% 133.06/133.48 , clause( 183494, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 133.06/133.48 'tc_nat' ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 133.06/133.48 Y, T, X ), X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 133.06/133.48 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.48 , clause( 183495, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X
% 133.06/133.48 , 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183496, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 133.06/133.48 Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 133.06/133.48 , clause( 183497, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 133.06/133.48 Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 133.06/133.48 )
% 133.06/133.48 , clause( 183498, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 133.06/133.48 Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 133.06/133.48 ] )
% 133.06/133.48 , clause( 183499, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183500, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z
% 133.06/133.48 , Y, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183501, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183502, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 133.06/133.48 Y, X ) ] )
% 133.06/133.48 , clause( 183503, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 133.06/133.48 Y, Y, X ) ] )
% 133.06/133.48 , clause( 183504, [ 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183505, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 133.06/133.48 , clause( 183506, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 133.06/133.48 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 133.06/133.48 , clause( 183507, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 133.06/133.48 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 133.06/133.48 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183508, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 133.06/133.48 ) ] )
% 133.06/133.48 , clause( 183509, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 133.06/133.48 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183510, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 133.06/133.48 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 133.06/133.48 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 133.06/133.48 , clause( 183511, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 133.06/133.48 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 133.06/133.48 ~( 'c_lessequals'( U, T, X ) ) ] )
% 133.06/133.48 , clause( 183512, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 133.06/133.48 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 133.06/133.48 , clause( 183513, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 133.06/133.48 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183514, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 133.06/133.48 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 133.06/133.48 , clause( 183515, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 133.06/133.48 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 133.06/133.48 , clause( 183516, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 133.06/133.48 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 133.06/133.48 Z, T, X ), X ) ) ] )
% 133.06/133.48 , clause( 183517, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 133.06/133.48 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 133.06/133.48 , clause( 183518, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 133.06/133.48 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 133.06/133.48 , clause( 183519, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 133.06/133.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 133.06/133.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ] )
% 133.06/133.48 , clause( 183520, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 133.06/133.48 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 133.06/133.48 ] )
% 133.06/133.48 , clause( 183521, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 133.06/133.48 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.48 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat'
% 133.06/133.48 ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183522, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 133.06/133.48 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.48 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183523, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 133.06/133.48 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.48 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183524, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 133.06/133.48 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ] )
% 133.06/133.48 , clause( 183525, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 133.06/133.48 , T, X ) ) ), =( Z, T ) ] )
% 133.06/133.48 , clause( 183526, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 133.06/133.48 , T, X ) ) ), =( Y, Z ) ] )
% 133.06/133.48 , clause( 183527, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 133.06/133.48 'tc_nat' ), X, 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183528, [ =( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 133.06/133.48 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183529, [ =( 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 133.06/133.48 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183530, [ 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183531, [ ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ), ~( =(
% 133.06/133.48 'v_a', 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ) ] )
% 133.06/133.48 , clause( 183532, [ 'class_Ring__and__Field_Ofield'( 't_a' ) ] )
% 133.06/133.48 , clause( 183533, [ ~( =( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'v_a', 'v_m', 't_a' ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ), 't_a' ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 'c_HOL_Oone__class_Oone'( 't_a' ), 'v_a', 't_a' ),
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( 'v_n', 'v_m', 'tc_nat' ), 't_a' ) ) ),
% 133.06/133.48 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183534, [ ~( =( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'v_a', 'v_m', 't_a' ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ), 't_a' ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'v_a', 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.48 'v_m', 'v_n', 'tc_nat' ), 't_a' ) ) ), ~( 'c_lessequals'( 'v_n', 'v_m',
% 133.06/133.48 'tc_nat' ) ) ] )
% 133.06/133.48 , clause( 183535, [ ~( =( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'v_a', 'v_m', 't_a' ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ), 't_a' ),
% 133.06/133.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.48 'c_HOL_Oone__class_Oone'( 't_a' ), 'v_a', 't_a' ),
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( 'v_n', 'v_m', 'tc_nat' ), 't_a' ) ) ), ~(
% 133.06/133.48 =( 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'( 'v_a'
% 133.06/133.48 , 'v_m', 't_a' ), 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ),
% 133.06/133.48 't_a' ), 'c_Power_Opower__class_Opower'( 'v_a',
% 133.06/133.48 'c_HOL_Ominus__class_Ominus'( 'v_m', 'v_n', 'tc_nat' ), 't_a' ) ) ) ] )
% 133.06/133.48 , clause( 183536, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ] )
% 133.06/133.48 , clause( 183537, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ] )
% 133.06/133.48 , clause( 183538, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ] )
% 133.06/133.48 , clause( 183539, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_Ring__and__Field_Ono__zero__divisors'( X ) ] )
% 133.06/133.48 , clause( 183540, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ] )
% 133.06/133.48 , clause( 183541, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_OrderedGroup_Oab__semigroup__add'( X ) ] )
% 133.06/133.48 , clause( 183542, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_Ring__and__Field_Odivision__ring'( X ) ] )
% 133.06/133.48 , clause( 183543, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_OrderedGroup_Ocomm__monoid__add'( X ) ] )
% 133.06/133.48 , clause( 183544, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_Ring__and__Field_Ozero__neq__one'( X ) ] )
% 133.06/133.48 , clause( 183545, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_Ring__and__Field_Ocomm__ring__1'( X ) ] )
% 133.06/133.48 , clause( 183546, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_Ring__and__Field_Osemiring__1'( X ) ] )
% 133.06/133.48 , clause( 183547, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_Ring__and__Field_Osemiring__0'( X ) ] )
% 133.06/133.48 , clause( 183548, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 133.06/133.48 , clause( 183549, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_Ring__and__Field_Omult__zero'( X ) ] )
% 133.06/133.48 , clause( 183550, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_OrderedGroup_Omonoid__mult'( X ) ] )
% 133.06/133.48 , clause( 183551, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_OrderedGroup_Omonoid__add'( X ) ] )
% 133.06/133.48 , clause( 183552, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_OrderedGroup_Ogroup__add'( X ) ] )
% 133.06/133.48 , clause( 183553, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_Ring__and__Field_Oring__1'( X ) ] )
% 133.06/133.48 , clause( 183554, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_Ring__and__Field_Oidom'( X ) ] )
% 133.06/133.48 , clause( 183555, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 133.06/133.48 'class_Power_Opower'( X ) ] )
% 133.06/133.48 , clause( 183556, [
% 133.06/133.48 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 133.06/133.48 )
% 133.06/133.48 , clause( 183557, [
% 133.06/133.48 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 133.06/133.48 )
% 133.06/133.48 , clause( 183558, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 133.06/133.48 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183559, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 133.06/133.48 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183560, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 133.06/133.48 'tc_nat' ) ] )
% 133.06/133.48 , clause( 183561, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat'
% 133.06/133.48 ) ] )
% 133.06/133.48 , clause( 183562, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat'
% 133.06/133.48 ) ] )
% 133.06/133.48 , clause( 183563, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' )
% 133.06/133.48 ] )
% 133.06/133.48 , clause( 183564, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 133.06/133.49 ] )
% 133.06/133.49 , clause( 183565, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 133.06/133.49 )
% 133.06/133.49 , clause( 183566, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ]
% 133.06/133.49 )
% 133.06/133.49 , clause( 183567, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ]
% 133.06/133.49 )
% 133.06/133.49 , clause( 183568, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 133.06/133.49 , clause( 183569, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ] )
% 133.06/133.49 , clause( 183570, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 133.06/133.49 , clause( 183571, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 133.06/133.49 , clause( 183572, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 133.06/133.49 , clause( 183573, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 133.06/133.49 , clause( 183574, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 133.06/133.49 , clause( 183575, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 133.06/133.49 , clause( 183576, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 133.06/133.49 , clause( 183577, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 133.06/133.49 , clause( 183578, [ 'class_Power_Opower'( 'tc_nat' ) ] )
% 133.06/133.49 ] ).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 eqswap(
% 133.06/133.49 clause( 183967, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ), ~(
% 133.06/133.49 'class_Ring__and__Field_Ofield'( 't_a' ) ) ] )
% 133.06/133.49 , clause( 183317, [ ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ), ~( =(
% 133.06/133.49 'v_a', 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ) ] )
% 133.06/133.49 , 1, substitution( 0, [] )).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 subsumption(
% 133.06/133.49 clause( 334, [ ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ), ~( =(
% 133.06/133.49 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ) ] )
% 133.06/133.49 , clause( 183967, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ),
% 133.06/133.49 ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ) ] )
% 133.06/133.49 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 133.06/133.49 ).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 eqswap(
% 133.06/133.49 clause( 184522, [ =( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.49 'c_Power_Opower__class_Opower'( X, Y, T ), 'c_Power_Opower__class_Opower'(
% 133.06/133.49 X, Z, T ), T ), 'c_Power_Opower__class_Opower'( X,
% 133.06/133.49 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), T ) ), ~(
% 133.06/133.49 'class_Ring__and__Field_Ofield'( T ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 133.06/133.49 ) ), =( X, 'c_HOL_Ozero__class_Ozero'( T ) ) ] )
% 133.06/133.49 , clause( 183494, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 133.06/133.49 'tc_nat' ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.49 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 133.06/133.49 Y, T, X ), X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 133.06/133.49 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.49 , 1, substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )
% 133.06/133.49 ).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 subsumption(
% 133.06/133.49 clause( 474, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.49 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 133.06/133.49 ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 133.06/133.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 133.06/133.49 'tc_nat' ), X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 133.06/133.49 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.49 , clause( 184522, [ =( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.49 'c_Power_Opower__class_Opower'( X, Y, T ), 'c_Power_Opower__class_Opower'(
% 133.06/133.49 X, Z, T ), T ), 'c_Power_Opower__class_Opower'( X,
% 133.06/133.49 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), T ) ), ~(
% 133.06/133.49 'class_Ring__and__Field_Ofield'( T ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 133.06/133.49 ) ), =( X, 'c_HOL_Ozero__class_Ozero'( T ) ) ] )
% 133.06/133.49 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, X )] ),
% 133.06/133.49 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 133.06/133.49 ).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 subsumption(
% 133.06/133.49 clause( 483, [ 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ] )
% 133.06/133.49 , clause( 183504, [ 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ] )
% 133.06/133.49 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 subsumption(
% 133.06/133.49 clause( 502, [ 'class_Ring__and__Field_Ofield'( 't_a' ) ] )
% 133.06/133.49 , clause( 183532, [ 'class_Ring__and__Field_Ofield'( 't_a' ) ] )
% 133.06/133.49 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 resolution(
% 133.06/133.49 clause( 186276, [ ~( =( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'v_m', 't_a' ),
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ), 't_a' ),
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.49 'v_m', 'v_n', 'tc_nat' ), 't_a' ) ) ) ] )
% 133.06/133.49 , clause( 183534, [ ~( =( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'v_m', 't_a' ),
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ), 't_a' ),
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.49 'v_m', 'v_n', 'tc_nat' ), 't_a' ) ) ), ~( 'c_lessequals'( 'v_n', 'v_m',
% 133.06/133.49 'tc_nat' ) ) ] )
% 133.06/133.49 , 1, clause( 483, [ 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ] )
% 133.06/133.49 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 subsumption(
% 133.06/133.49 clause( 503, [ ~( =( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'v_m', 't_a' ),
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ), 't_a' ),
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.49 'v_m', 'v_n', 'tc_nat' ), 't_a' ) ) ) ] )
% 133.06/133.49 , clause( 186276, [ ~( =( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'v_m', 't_a' ),
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ), 't_a' ),
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.49 'v_m', 'v_n', 'tc_nat' ), 't_a' ) ) ) ] )
% 133.06/133.49 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 resolution(
% 133.06/133.49 clause( 186279, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ) ] )
% 133.06/133.49 , clause( 334, [ ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ), ~( =(
% 133.06/133.49 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ) ] )
% 133.06/133.49 , 0, clause( 502, [ 'class_Ring__and__Field_Ofield'( 't_a' ) ] )
% 133.06/133.49 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 subsumption(
% 133.06/133.49 clause( 915, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ) ] )
% 133.06/133.49 , clause( 186279, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ) ]
% 133.06/133.49 )
% 133.06/133.49 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 eqswap(
% 133.06/133.49 clause( 186281, [ ~( =( 'c_Power_Opower__class_Opower'( 'v_a',
% 133.06/133.49 'c_HOL_Ominus__class_Ominus'( 'v_m', 'v_n', 'tc_nat' ), 't_a' ),
% 133.06/133.49 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'( 'v_a',
% 133.06/133.49 'v_m', 't_a' ), 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ),
% 133.06/133.49 't_a' ) ) ) ] )
% 133.06/133.49 , clause( 503, [ ~( =( 'c_HOL_Oinverse__class_Odivide'(
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'v_m', 't_a' ),
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ), 't_a' ),
% 133.06/133.49 'c_Power_Opower__class_Opower'( 'v_a', 'c_HOL_Ominus__class_Ominus'(
% 133.06/133.49 'v_m', 'v_n', 'tc_nat' ), 't_a' ) ) ) ] )
% 133.06/133.49 , 0, substitution( 0, [] )).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 eqswap(
% 133.06/133.49 clause( 186282, [ =( 'c_Power_Opower__class_Opower'( X,
% 133.06/133.49 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_nat' ), Z ),
% 133.06/133.49 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'( X, Y, Z
% 133.06/133.49 ), 'c_Power_Opower__class_Opower'( X, T, Z ), Z ) ), ~(
% 133.06/133.49 'class_Ring__and__Field_Ofield'( Z ) ), ~( 'c_lessequals'( T, Y, 'tc_nat'
% 133.06/133.49 ) ), =( X, 'c_HOL_Ozero__class_Ozero'( Z ) ) ] )
% 133.06/133.49 , clause( 474, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 133.06/133.49 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 133.06/133.49 ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 133.06/133.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 133.06/133.49 'tc_nat' ), X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 133.06/133.49 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 133.06/133.49 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T )] )
% 133.06/133.49 ).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 resolution(
% 133.06/133.49 clause( 186285, [ ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ), ~(
% 133.06/133.49 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ), =( 'v_a',
% 133.06/133.49 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ] )
% 133.06/133.49 , clause( 186281, [ ~( =( 'c_Power_Opower__class_Opower'( 'v_a',
% 133.06/133.49 'c_HOL_Ominus__class_Ominus'( 'v_m', 'v_n', 'tc_nat' ), 't_a' ),
% 133.06/133.49 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'( 'v_a',
% 133.06/133.49 'v_m', 't_a' ), 'c_Power_Opower__class_Opower'( 'v_a', 'v_n', 't_a' ),
% 133.06/133.49 't_a' ) ) ) ] )
% 133.06/133.49 , 0, clause( 186282, [ =( 'c_Power_Opower__class_Opower'( X,
% 133.06/133.49 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_nat' ), Z ),
% 133.06/133.49 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'( X, Y, Z
% 133.06/133.49 ), 'c_Power_Opower__class_Opower'( X, T, Z ), Z ) ), ~(
% 133.06/133.49 'class_Ring__and__Field_Ofield'( Z ) ), ~( 'c_lessequals'( T, Y, 'tc_nat'
% 133.06/133.49 ) ), =( X, 'c_HOL_Ozero__class_Ozero'( Z ) ) ] )
% 133.06/133.49 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_a' ), :=( Y, 'v_m'
% 133.06/133.49 ), :=( Z, 't_a' ), :=( T, 'v_n' )] )).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 resolution(
% 133.06/133.49 clause( 186286, [ ~( 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ), =( 'v_a',
% 133.06/133.49 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ] )
% 133.06/133.49 , clause( 186285, [ ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ), ~(
% 133.06/133.49 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ), =( 'v_a',
% 133.06/133.49 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ] )
% 133.06/133.49 , 0, clause( 502, [ 'class_Ring__and__Field_Ofield'( 't_a' ) ] )
% 133.06/133.49 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 eqswap(
% 133.06/133.49 clause( 186287, [ =( 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ), ~(
% 133.06/133.49 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ) ] )
% 133.06/133.49 , clause( 186286, [ ~( 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ), =( 'v_a'
% 133.06/133.49 , 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ] )
% 133.06/133.49 , 1, substitution( 0, [] )).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 subsumption(
% 133.06/133.49 clause( 168626, [ ~( 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ), =(
% 133.06/133.49 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ] )
% 133.06/133.49 , clause( 186287, [ =( 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ), ~(
% 133.06/133.49 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ) ] )
% 133.06/133.49 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 133.06/133.49 ).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 resolution(
% 133.06/133.49 clause( 186290, [ =( 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ] )
% 133.06/133.49 , clause( 168626, [ ~( 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ), =(
% 133.06/133.49 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ] )
% 133.06/133.49 , 0, clause( 483, [ 'c_lessequals'( 'v_n', 'v_m', 'tc_nat' ) ] )
% 133.06/133.49 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 resolution(
% 133.06/133.49 clause( 186291, [] )
% 133.06/133.49 , clause( 915, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ) ] )
% 133.06/133.49 , 0, clause( 186290, [ =( 'c_HOL_Ozero__class_Ozero'( 't_a' ), 'v_a' ) ] )
% 133.06/133.49 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 subsumption(
% 133.06/133.49 clause( 182890, [] )
% 133.06/133.49 , clause( 186291, [] )
% 133.06/133.49 , substitution( 0, [] ), permutation( 0, [] ) ).
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 end.
% 133.06/133.49
% 133.06/133.49 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 133.06/133.49
% 133.06/133.49 Memory use:
% 133.06/133.49
% 133.06/133.49 space for terms: 4339843
% 133.06/133.49 space for clauses: 7870425
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 clauses generated: 1636049
% 133.06/133.49 clauses kept: 182891
% 133.06/133.49 clauses selected: 2411
% 133.06/133.49 clauses deleted: 9922
% 133.06/133.49 clauses inuse deleted: 113
% 133.06/133.49
% 133.06/133.49 subsentry: 8514080
% 133.06/133.49 literals s-matched: 5123828
% 133.06/133.49 literals matched: 4918470
% 133.06/133.49 full subsumption: 2089211
% 133.06/133.49
% 133.06/133.49 checksum: -733591335
% 133.06/133.49
% 133.06/133.49
% 133.06/133.49 Bliksem ended
%------------------------------------------------------------------------------